Department of Mathematics at UTSA - User contributions [en]

MAT5283

2026-03-25T01:48:28Z

Jose.iovino:

Introduction to the theory of finite-dimensional vector spaces.

'''Catalog entry'''

''Prerequisite'': Prerequisite: Math 2233 Linear Algebra, Math 2243 Applied Linear Algebra or instructor approval. , or instructor consent.

''Contents'':
(1) Algebraic Structures: rings, matrices, polynomials, fields and finite fields (2) Vector
spaces: subspaces, linear independence, basis, dimension (3) Linear transformations, isomor-
phisms, Rank-Nullity Theorem, Product and Quotient Spaces (3) Matrices and Linear Transfor-
mations: Matrix representation, change of basis, equivalence of matrices, similarity (4) Eigen-
values and Eigenvectors: The Cayley-Hamilton Theorem, Diagonalization and Jordan Canoni-
cal forms (4) Real and Complex Inner Product Spaces: Norm, distances, Cauchy-Schwartz in-
equality, Gram-Schmidt Orthogonalization process, The Projection Theorem, Riez Representa-
tion Theorem (5) Orthogonality over finite fields (6) Multilinear algebra : Bilinear Forms and
Functionals, Tensor product of vector spaces and Matrices.

MAT5433

2026-03-25T01:30:36Z

Jose.iovino:

== Catalog entry ==

''Prerequisite'':
Discrete Mathematics (MAT 3003) or Real Analysis I (MAT 4213), or instructor consent.

''Contents''
The Zermelo-Fraenkel axioms, ordinals and cardinals, the Axiom of Foundation, the Reflection Principle, ordinal-definable sets, relative consistency of the Axiom of Choice, Fraenkel-Mostowski models, relative consistency of the negation of the Axiom of Choice, consistency of the Generalized Continuum Hypothesis.

MAT5YYY

2026-03-25T00:03:11Z

Jose.iovino: /* Mathematics of AI - MAT4YYY/5YYY */

=Mathematics of AI - MAT4YYY/5YYY=

'''Catalog description'''

''Prerequisites'': Prerequisites:
[[MAT2233]] Linear Algebra, or [[MAT 253]] Applied Linear Algebra;
[[STA3513]] Probability and Statistics
[[MAT2213]] Calculus 3
CS 1063 Introduction to Computer Programming, or CS 1083 Programming I for Computer Scientists.

''Content'':
Vectors, matrices and tensors; discrete and continuous probability; random variables and expectation; elements of information theory; basic methods for probabilistic learning (maximum likelihood, Bayesian statistics); supervised and unsupervised learning algorithms; neural networks: feedforward, convolutional, recurrent/recursive; loss functions and gradient-based learning; optimization and regularization methods; algorithm implementations; testing on real-world datasets.

MAT5YYY

2026-03-25T00:02:54Z

Jose.iovino: /* Sample textbook */

MAT5433

2026-03-24T23:11:28Z

Jose.iovino:

== Catalog entry ==

''Prerequisite'':Discrete Mathematics (MAT 3003) or Real Analysis I (MAT 4213), or instructor consent.

''Contents''
The Zermelo-Fraenkel axioms, ordinals and cardinals, the Axiom of Foundation, the Reflection Principle, ordinal-definable sets, relative consistency of the Axiom of Choice, Fraenkel-Mostowski models, relative consistency of the negation of the Axiom of Choice, consistency of the Generalized Continuum Hypothesis.

MAT5283

2026-03-24T23:06:09Z

Jose.iovino:

Introduction to the theory of finite-dimensional vector spaces.

'''Catalog entry'''

''Prerequisite'': Prerequisite: Math 2233 Linear Algebra, Math 2243 Applied Linear Algebra or instructor approval. , or instructor consent.

''Contents''
(1) Algebraic Structures: rings, matrices, polynomials, fields and finite fields (2) Vector
spaces: subspaces, linear independence, basis, dimension (3) Linear transformations, isomor-
phisms, Rank-Nullity Theorem, Product and Quotient Spaces (3) Matrices and Linear Transfor-
mations: Matrix representation, change of basis, equivalence of matrices, similarity (4) Eigen-
values and Eigenvectors: The Cayley-Hamilton Theorem, Diagonalization and Jordan Canoni-
cal forms (4) Real and Complex Inner Product Spaces: Norm, distances, Cauchy-Schwartz in-
equality, Gram-Schmidt Orthogonalization process, The Projection Theorem, Riez Representa-
tion Theorem (5) Orthogonality over finite fields (6) Multilinear algebra : Bilinear Forms and
Functionals, Tensor product of vector spaces and Matrices.

MAT 5183

2026-03-24T23:01:36Z

Jose.iovino: /* Catalog entry */

Introduction to algebraic codes.

== Sample textbook ==

[1] Tzuong-Tsien Moh, ''Introduction to Algebraic Codes'', 2008. Freely available to UTSA students.

== Catalog entry ==

''Prerequisite'':
Math 2233 Linear Algebra, Algebra I, MAT4233 Modern Abstract Algebra, MAT
5173 Abstract Algebra I or Instructor approval.

''Contents'':
(1) Finite Fields: Fields, Polynomial rings, Structure of Finite Fields, Minimal Poly-
nomials. (2) Linear codes: Linear codes, Hamming weight and distances, Dual codes, Genera-
tor and Parity-Check Matrices (3) Equivalence of Linear codes: Permutation Equivalent Codes,
Monomial Equivalent Codes (4) Encoding of Linear codes: Encoding using generator matri-
ces, Systematic Encoding (5) Syndrome decoding of linear codes: Cosets, Nearest neighbour
decoding, syndrome decoding (6) Bounds for linear codes: Singleton bound and MDS codes,
Sphere covering bound, Gilbert-Varshamov bound (7) Important Linear codes: Hamming codes
-Encoding and decoding, Binary Golay Codes, Reed-Muller Codes. (8) Cyclic codes: Defini-
tion of cyclic codes, Polynomial representation, Generator polynomials and generator matrices,
Reciprocal polynomials and parity-check matrices, practical implementation of cyclic codes, de-
coding of cyclic codes (9) BCH codes: Definition, Parameters, Decoding BCH codes (10) Reed-
Solomon codes: Definition, Parameters, Encoding, Decoding Reed-Solomon codes (10) Low-
Density Parity-Check Codes: Definition, Tanner Graph Representation, Constructions, Gallager
Decoding Algorithm.

==Topics List==
{| class="wikitable sortable"
! Week !! Topic !! Sections from Moh's book !! Prerequisite
|-
| 1-2
|| [[Vector space codes]]
|| 1
|| MAT1313, CS2233/2231, or instructor consent.
|-
| 3-4
|| [[Introduction to ring theory]]
|| 2
||
|-
| 5-6
|| [[Ring codes]]
|| 3
||
|-
| 7-8
|| [[Introduction to algebraic geometry]]
|| 4
|-
| 9-10
|| [[Algebraic curve Goppa codes]]
|| 5
||
|-
| 11-13
|| [[Decoding the geometric Goppa codes]]
|| 6
||
|}

MAT 5183

2026-03-24T23:00:17Z

Jose.iovino: /* Catalog entry */

Introduction to algebraic codes.

== Sample textbook ==

[1] Tzuong-Tsien Moh, ''Introduction to Algebraic Codes'', 2008. Freely available to UTSA students.

== Catalog entry ==

''Prerequisite'': Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.

''Contents'':
(1) Finite Fields: Fields, Polynomial rings, Structure of Finite Fields, Minimal Poly-
nomials. (2) Linear codes: Linear codes, Hamming weight and distances, Dual codes, Genera-
tor and Parity-Check Matrices (3) Equivalence of Linear codes: Permutation Equivalent Codes,
Monomial Equivalent Codes (4) Encoding of Linear codes: Encoding using generator matri-
ces, Systematic Encoding (5) Syndrome decoding of linear codes: Cosets, Nearest neighbour
decoding, syndrome decoding (6) Bounds for linear codes: Singleton bound and MDS codes,
Sphere covering bound, Gilbert-Varshamov bound (7) Important Linear codes: Hamming codes
-Encoding and decoding, Binary Golay Codes, Reed-Muller Codes. (8) Cyclic codes: Defini-
tion of cyclic codes, Polynomial representation, Generator polynomials and generator matrices,
Reciprocal polynomials and parity-check matrices, practical implementation of cyclic codes, de-
coding of cyclic codes (9) BCH codes: Definition, Parameters, Decoding BCH codes (10) Reed-
Solomon codes: Definition, Parameters, Encoding, Decoding Reed-Solomon codes (10) Low-
Density Parity-Check Codes: Definition, Tanner Graph Representation, Constructions, Gallager
Decoding Algorithm.

==Topics List==
{| class="wikitable sortable"
! Week !! Topic !! Sections from Moh's book !! Prerequisite
|-
| 1-2
|| [[Vector space codes]]
|| 1
|| MAT1313, CS2233/2231, or instructor consent.
|-
| 3-4
|| [[Introduction to ring theory]]
|| 2
||
|-
| 5-6
|| [[Ring codes]]
|| 3
||
|-
| 7-8
|| [[Introduction to algebraic geometry]]
|| 4
|-
| 9-10
|| [[Algebraic curve Goppa codes]]
|| 5
||
|-
| 11-13
|| [[Decoding the geometric Goppa codes]]
|| 6
||
|}

Main Page

2026-03-24T22:58:52Z

Jose.iovino: /* Graduate Studies */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4JME]]/[[MAT5JME]] Mathematical Physics 2
* [[MAT4XYX]]/[[MAT5XYX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT 5173]] Algebra I
* [[MAT5603]] Differential Equations I

Choose one of the following two:

* [[MAT5123]] Introduction to Cryptography
* [[MAT5603]] Numerical Analysis

=== Qualifying Exam Tracks ===

Complete two qualifying tracks: A track is considered completed by taking at least two of the courses in the track. At least one of your
qualifying tracks needs to complete a sequence begun in the core courses; that is, one of your tracks you must complete one of the
following pairs of courses: Differential Equations I & II, or Algebra I & II, or Theory of Fun. of a Real Variable I & II, or Discrete Mathematics I & II.

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Algebra I
* [[MAT 5183]] Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5JME]] Mathematical Physics II*
* [[MAT5XYX]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-09-24T20:23:52Z

Jose.iovino: /* Qualifying tracks */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4JME]]/[[MAT5JME]] Mathematical Physics 2
* [[MAT4XYX]]/[[MAT5XYX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT 5173]] Abstract Algebra I
* [[MAT5603]] Differential Equations I

Choose one of the following two:

* [[MAT5123]] Introduction to Cryptography
* [[MAT5603]] Numerical Analysis

=== Qualifying Exam Tracks ===

Complete two qualifying tracks: A track is considered completed by taking at least two of the courses in the track. At least one of your
qualifying tracks needs to complete a sequence begun in the core courses; that is, one of your tracks you must complete one of the
following pairs of courses: Differential Equations I & II, or Algebra I & II, or Theory of Fun. of a Real Variable I & II, or Discrete Mathematics I & II.

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5JME]] Mathematical Physics II*
* [[MAT5XYX]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-09-24T20:20:21Z

Jose.iovino: /* Graduate Studies */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4JME]]/[[MAT5JME]] Mathematical Physics 2
* [[MAT4XYX]]/[[MAT5XYX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT 5173]] Abstract Algebra I
* [[MAT5603]] Differential Equations I

Choose one of the following two:

* [[MAT5123]] Introduction to Cryptography
* [[MAT5603]] Numerical Analysis

=== Qualifying tracks ===

Complete two qualifying tracks: A track is considered completed by taking at least two of the courses in the track. At least one of your
qualifying tracks needs to complete a sequence begun in the core courses; that is, one of your tracks you must complete one of the
following pairs of courses: Differential Equations I & II, or Algebra I & II, or Theory of Fun. of a Real Variable I & II, or Discrete Mathematics I & II.

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5JME]] Mathematical Physics II*
* [[MAT5XYX]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-09-24T20:18:25Z

Jose.iovino: /* Graduate Studies */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4JME]]/[[MAT5JME]] Mathematical Physics 2
* [[MAT4XYX]]/[[MAT5XYX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT 5173]] Abstract Algebra I
* [[MAT5603]] Differential Equations I

Choose one of the following two:

* [[MAT5123]] Introduction to Cryptography
* [[MAT5603]] Numerical Analysis

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5JME]] Mathematical Physics II*
* [[MAT5XYX]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-09-16T02:39:48Z

Jose.iovino: /* Core Courses */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4JME]]/[[MAT5JME]] Mathematical Physics 2
* [[MAT4XYX]]/[[MAT5XYX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT 5173]] Abstract Algebra I
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5JME]] Mathematical Physics II*
* [[MAT5XYX]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-09-09T12:43:41Z

Jose.iovino: /* Qualifying Exam Track: Mathematical Physics */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4JME]]/[[MAT5JME]] Mathematical Physics 2
* [[MAT4XYX]]/[[MAT5XYX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5JME]] Mathematical Physics II*
* [[MAT5XYX]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-09-01T17:55:21Z

Jose.iovino: /* Upper Division */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4JME]]/[[MAT5JME]] Mathematical Physics 2
* [[MAT4XYX]]/[[MAT5XYX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XYX]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-09-01T17:54:20Z

Jose.iovino: /* Upper Division */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4JME]]/[[MAT5JME]] Mathematical Physics 2
* [[MAT4JME]]/[[MAT5JME]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XYX]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-09-01T17:53:42Z

Jose.iovino: /* Upper Division */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MAT5ZZZ]] Mathematical Physics 2
* [[MAT4JME]]/[[MAT5JME]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XYX]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T19:44:59Z

Jose.iovino: /* Qualifying Exam Track: Mathematical Physics */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MAT5ZZZ]] Mathematical Physics 2
* [[MAT4XYX]]/[[MAT5XYX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XYX]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T19:44:15Z

Jose.iovino: /* Qualifying Exam Track: Scientific Computing */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MAT5ZZZ]] Mathematical Physics 2
* [[MAT4XYX]]/[[MAT5XYX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XYXY]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T19:43:12Z

Jose.iovino: /* Qualifying Track: Mathematics of Information, Data and Communications */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MAT5ZZZ]] Mathematical Physics 2
* [[MAT4XYX]]/[[MAT5XYX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYX]] Quantum Information Science and Engineering
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYXY]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XYXY]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

MAT4XYX

2025-08-30T19:42:33Z

Jose.iovino: /* Introduction to Quantum Information Science and Engineering - MAT4XXX/5XXX */

=Introduction to Quantum Information Science and Engineering - MAT4XYX/5XYX=

==Course description==
This course will be an introduction accessible and welcoming to all STEM students. No prior quantum mechanics courses are expected since all the principles and techniques of quantum information will be taught during the course. The focus will be on qubits, entanglement, and decoherence, three key building blocks of quantum computing.

==Catalog entry==

''Prerequisite'':
Linear Algebra [[MAT2233]] or Applied Linear Algebra [[MAT2253]], or equivalent (can be waived with approval of instructor), with a letter grade of C- or better, or successful completion of at least three credits of equivalent courses.

''Content'':
Foundations of quantum mechanics such as unitary time evolution, entanglement, and the EPR paradox approached from the information perspective, and quantum entropy. Information and its encoding into physical systems such as photons, atoms, and superconducting circuits.
Quantum control using quantum logic gates, providing a foundation for quantum programming.
Applications: quantum teleportation, quantum cryptography, quantum computing.

'''Textbook:'''

* Nielsen, M. and Chuang, I. Quantum Computation and Quantum Information. UK, Cambridge University Press, 2012.

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
*
||
An overview of quantum computing and information.
||

||
*
|-
|Week 2
||
*
||
Classical Information Theory. Connection between information and thermodynamics
||

||
*
|-
|Week 3
||
*
||
Communications Theory. Physical qubits: spinning particles and photons
||

||
*
|-
|Week 4
||
*
||
Operators in Quantum Mechanics. Classical cryptography
||

||
*
|-
|Week 5
||
*
||
Quantum cryptography. Entanglement.
||

||
*
|-
|Week 6
||
*
||
Mixed states and the density operator. Local measurements & open quantum systems.
||

||
*
|-
|Week 7
||
*
||
Quantum non-locality and the Einstein-Podolsky-Rosen paradox
||

||
*
|-
|Week 8
||
*
||
Bell’s inequality. Quantum dense coding. Quantum teleportation
||

||
*
|-
|Week 9
||
*
||
Quantum non-locality and the Einstein-Podolsky-Rosen paradox
||

||
*
|-
|Week 10
||

||
Quantum computation.
||

||
*
|-
|Week 11
||
*
||
Von Neumann measurements
||

||
*

|-
|Week 12
||

||
Many-worlds interpretation of quantum mechanics.
||
*
||
*
|-
|Week 13
||
*
||
Selected topic 1.
||

||
*
|-
|Week 14
||
*
||
Presentations by students
||
*
||
*
|}

MAT5XYX

2025-08-30T19:41:41Z

Jose.iovino: Created page with "=Introduction to Quantum Information Science and Engineering - MAT4XXX/5XXX= ==Course description== This course will be an introduction accessible and welcoming to all STEM s..."

=Introduction to Quantum Information Science and Engineering - MAT4XXX/5XXX=

==Course description==
This course will be an introduction accessible and welcoming to all STEM students. No prior quantum mechanics courses are expected since all the principles and techniques of quantum information will be taught during the course. The focus will be on qubits, entanglement, and decoherence, three key building blocks of quantum computing.

==Catalog entry==

''Prerequisite'':
Linear Algebra [[MAT2233]] or Applied Linear Algebra [[MAT2253]], or equivalent (can be waived with approval of instructor), with a letter grade of C- or better, or successful completion of at least three credits of equivalent courses.

''Content'':
Foundations of quantum mechanics such as unitary time evolution, entanglement, and the EPR paradox approached from the information perspective, and quantum entropy. Information and its encoding into physical systems such as photons, atoms, and superconducting circuits.
Quantum control using quantum logic gates, providing a foundation for quantum programming.
Applications: quantum teleportation, quantum cryptography, quantum computing.

'''Textbook:'''

* Nielsen, M. and Chuang, I. Quantum Computation and Quantum Information. UK, Cambridge University Press, 2012.

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
*
||
An overview of quantum computing and information.
||

||
*
|-
|Week 2
||
*
||
Classical Information Theory. Connection between information and thermodynamics
||

||
*
|-
|Week 3
||
*
||
Communications Theory. Physical qubits: spinning particles and photons
||

||
*
|-
|Week 4
||
*
||
Operators in Quantum Mechanics. Classical cryptography
||

||
*
|-
|Week 5
||
*
||
Quantum cryptography. Entanglement.
||

||
*
|-
|Week 6
||
*
||
Mixed states and the density operator. Local measurements & open quantum systems.
||

||
*
|-
|Week 7
||
*
||
Quantum non-locality and the Einstein-Podolsky-Rosen paradox
||

||
*
|-
|Week 8
||
*
||
Bell’s inequality. Quantum dense coding. Quantum teleportation
||

||
*
|-
|Week 9
||
*
||
Quantum non-locality and the Einstein-Podolsky-Rosen paradox
||

||
*
|-
|Week 10
||

||
Quantum computation.
||

||
*
|-
|Week 11
||
*
||
Von Neumann measurements
||

||
*

|-
|Week 12
||

||
Many-worlds interpretation of quantum mechanics.
||
*
||
*
|-
|Week 13
||
*
||
Selected topic 1.
||

||
*
|-
|Week 14
||
*
||
Presentations by students
||
*
||
*
|}

MAT4XYX

2025-08-30T19:41:20Z

Main Page

2025-08-30T19:40:39Z

Jose.iovino: /* Data & Applied Science Core */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MAT5ZZZ]] Mathematical Physics 2
* [[MAT4XYX]]/[[MAT5XYX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYXY]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYXY]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XYXY]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

MAT5XYXY

2025-08-30T19:39:34Z

Jose.iovino: Created page with "=Introduction to Quantum Information Science and Engineering - MAT4XYX/5XYX= ==Course description== This course will be an introduction accessible and welcoming to all STEM s..."

Main Page

2025-08-30T19:38:38Z

Jose.iovino: /* Upper Division */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MAT5ZZZ]] Mathematical Physics 2
* [[MAT4XXX]]/[[MAT5XYXY]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYXY]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYXY]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XYXY]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T19:38:08Z

Jose.iovino: /* Upper Division */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MAT5ZZZ]] Mathematical Physics 2
* [[MAT4XXXX]]/[[MAT5XYXY]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYXY]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYXY]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XYXY]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T19:36:26Z

Jose.iovino: /* Qualifying Exam Track: Mathematical Physics */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MAT5ZZZ]] Mathematical Physics 2
* [[MAT4XYXY]]/[[MAT5XYXY]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYXY]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYXY]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XYXY]] Quantum Information Science and Engineering*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T19:35:44Z

Jose.iovino: /* Upper Division */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MAT5ZZZ]] Mathematical Physics 2
* [[MAT4XYXY]]/[[MAT5XYXY]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYXY]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYXY]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XXX]] Quantum Information*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T19:35:11Z

Jose.iovino: /* Qualifying Track: Mathematics of Information, Data and Communications */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MAT5ZZZ]] Mathematical Physics 2
* [[MAT4XXX]]/[[MAT5XXX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XYXY]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYXY]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XXX]] Quantum Information*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T19:34:36Z

Jose.iovino: /* Qualifying Exam Track: Scientific Computing */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MAT5ZZZ]] Mathematical Physics 2
* [[MAT4XXX]]/[[MAT5XXX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XXX]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XYXY]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XXX]] Quantum Information*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T19:33:38Z

Jose.iovino: /* Qualifying Exam Track: Scientific Computing */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MAT5ZZZ]] Mathematical Physics 2
* [[MAT4XXX]]/[[MAT5XXX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XXX]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XXX]] Quantum Information Science and Engineering
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XXX]] Quantum Information*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

MAT5323

2025-08-30T17:41:09Z

Jose.iovino: Replaced content with "Note by JI: This will be modified as Systems Biology""

Note by JI:

This will be modified as Systems Biology"

MAT 5143

2025-08-30T17:38:22Z

Jose.iovino:

'''Catalog entry'''

''Prerequisite'': Prerequisite: MAT 1313, or CS 2233 and CS 2231, , or instructor consent.

''Contents''
Topics may include: (1) Introduction to post-quantum cryptography, (2) Quantum computing, (3) Hash-based Digital Signature Schemes, (4) Code-based cryptography, (5) Lattice-based Cryptography, (6) Multivariate Public Key Cryptography, and (7) Homomorphic encryption.
MAT 5143 Cryptography II (post-quantum cryptography).

'''Sample textbook''':

[1] Daniel Bernstein, Johannes Buchmann, Erik Dahmen, ''Post-Quantum Cryptography'', Springer, 2010.

'''Catalog entry'''

''Prerequisite'': Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.

''Contents'':
(1) Introduction to post-quantum cryptography.
(2) Quantum computing.
(3) Hash-based Digital Signature Schemes.
(4) Code-based cryptography.
(5) Lattice-based Cryptography
(6) Multivariate Public Key Cryptography.
(7) Homomorphic encryption.

==Topics List==
{| class="wikitable sortable"
! Week !! Topic !! Chapter 1 from the Bernstein-Johannes Buchmann-Dahmen book !! MAT1313, or CS2233/2231, or instructor consent.
|-
| 1-3
|| [[Introduction to post-quantum cryptography]]
|| 1
|| MAT1313 or CS2233/2231, or equivalent.
|-
| 2-4
|| [[Quantum computing]]
|| 2
||
|-
| 5-6
|| [[Hash-based Digital Signature Schemes]]
|| 3
||
|-
| 7-8
|| [[Code-based cryptography]]
|| 4
||
|-
| 9-10
|| [[Lattice-based Cryptography]]
|| 5
||
|-
| 11-12
|| [[Multivariate Public Key Cryptography]]
|| 6
||
|-
| 13-end
|| [[Homomorphic encryption]]
||
||
|}

MAT4ZZZ

2025-08-30T17:28:49Z

Jose.iovino: Created page with "=Mathematical Physics - MATZZZ/5ZZZ= ==Course description== Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their unders..."

=Mathematical Physics - MATZZZ/5ZZZ=

==Course description==
Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their understanding of mathematical methods used in physics. This course is also suitable for Mathematics majors, who can deepen their understanding of applications and proofs of major theorems in Functional Analysis.

==Catalog entry==

''Prerequisite'': Calculus III [[MAT2214]] and Differential Equations II [[MAT3623]] with a letter grade of C- or better, or successful completion of at least three credits of equivalent courses.

MAT5ZZZ

2025-08-30T17:28:10Z

Jose.iovino: Created page with "=Mathematical Physics - MAT4ZZZ/5ZZZ= ==Course description== Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their under..."

=Mathematical Physics - MAT4ZZZ/5ZZZ=

==Course description==
Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their understanding of mathematical methods used in physics. This course is also suitable for Mathematics majors, who can deepen their understanding of applications and proofs of major theorems in Functional Analysis.

==Catalog entry==

''Prerequisite'': Calculus III [[MAT2214]] and Differential Equations II [[MAT3623]] with a letter grade of C- or better, or successful completion of at least three credits of equivalent courses.

MAT 5183

2025-08-30T17:24:09Z

Jose.iovino: Created page with "Introduction to algebraic codes. == Sample textbook == [1] Tzuong-Tsien Moh, ''Introduction to Algebraic Codes'', 2008. Freely available to UTSA students. == Catalog en..."

Introduction to algebraic codes.

== Sample textbook ==

[1] Tzuong-Tsien Moh, ''Introduction to Algebraic Codes'', 2008. Freely available to UTSA students.

== Catalog entry ==

''Prerequisite'': Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.

''Contents'':
Vector space codes, introduction to rings, ring codes, introduction to algebraic geometry, algebraic geometry codes.

==Topics List==
{| class="wikitable sortable"
! Week !! Topic !! Sections from Moh's book !! Prerequisite
|-
| 1-2
|| [[Vector space codes]]
|| 1
|| MAT1313, CS2233/2231, or instructor consent.
|-
| 3-4
|| [[Introduction to ring theory]]
|| 2
||
|-
| 5-6
|| [[Ring codes]]
|| 3
||
|-
| 7-8
|| [[Introduction to algebraic geometry]]
|| 4
|-
| 9-10
|| [[Algebraic curve Goppa codes]]
|| 5
||
|-
| 11-13
|| [[Decoding the geometric Goppa codes]]
|| 6
||
|}

Main Page

2025-08-30T17:18:12Z

Jose.iovino: /* Data & Applied Science Core */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MAT5ZZZ]] Mathematical Physics 2
* [[MAT4XXX]]/[[MAT5XXX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XXX]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XXX]] Quantum Information
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XXX]] Quantum Information*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T17:17:21Z

Jose.iovino: /* Qualifying Exam Track: Mathematical Physics */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MATZZZ]] Mathematical Physics 2
* [[MAT4XXX]]/[[MAT5XXX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XXX]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XXX]] Quantum Information
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MAT5ZZZ]] Mathematical Physics II*
* [[MAT5XXX]] Quantum Information*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

MAT4813

2025-08-30T17:16:11Z

Jose.iovino: Created page with "=Mathematical Physics - MAT4813/5863= ==Course description== Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their under..."

=Mathematical Physics - MAT4813/5863=

==Course description==
Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their understanding of mathematical methods used in physics. This course is also suitable for Mathematics majors, who can deepen their understanding of applications and proofs of major theorems in Functional Analysis.

==Catalog entry==

''Prerequisite'': Calculus III [[MAT2214]] and Differential Equations II [[MAT3623]] with a letter grade of C- or better, or successful completion of at least three credits of equivalent courses.

''Content'':
1. Topics in Complex Analysis.
2. Differential Equations: Dynamical systems, nonlinearity & chaos.
3. Nonlinear Waves in PDEs: Continuous Systems, Hamiltonian formulation of plasmas
and fluids, KdV eq., Nonlinear Schroedinger Eq., Sine/Klein-Gordon Equation(s).
4. Asymptotic Analysis methods, time-dependent/independent perturbation theory.
5. Functional Analysis in Mathematical Physics
6. Mathematical Formalism of PDEs for Physicists
7. Group Theory in Physics, Lie Algebras.
8. Tensor calculus: theory and applications. 3 Credit Hours

'''Textbooks:'''

* Needham, T. (1997). Visual Complex Analysis. United Kingdom: Clarendon Press.
* Grimshaw, R. (1993). Nonlinear Ordinary Differential Equations (1st ed.). Routledge.
* R. Courant and D. Hilbert, Methods of Mathematical Physics. Vol. II: Partial Differential Equations, Wiley Classics Library, John Wiley & Sons Inc., New York, 1989.
* Bender, C. and Orszag, S. Advanced Mathematical Methods for Scientists and Engineers. Mc-Graw Hill.
* Kreyszig, E. (1989). Introductory Functional Analysis with Applications. Wiley.
* Methods of Applied Mathematics. Todd Arbogast and Jerry L. Bona. Department of Mathematics, and Institute for Computational Engineering and Sciences, University of Texas at Austin, 2008.
* P. J. Olver, Applications of Lie Groups to Differential Equations, Second Edition, Graduate Texts in Mathematics, vol. 107, Springer-Verlag, New York, 1993.
* Rutherford Aris, Vectors, Tensors and the Basic Equations of Fluid Mechanics. Dover Publications

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
*
||
Complex Analysis Part I
||

||
* Definition and algebraic properties of complex numbers, Riemann Sphere, Holomorphic functions and conformal mappings
|-
|Week 2
||
*
||
Complex Analysis Part II
||

||
*Integrals in the Complex Plane, Cauchy's theorem, Calculus of Residues
|-
|Week 3
||
*
||
Complex Analysis Part III
||

||
* Harmonic functions and Poisson's formula
|-
|Week 4
||
*
||
Tensor Calculus Basics I
||

||
* Using indices in three-dimensional cartesian vector analysis, deriving vector identities using index calculus, divergence, grad and curl in index notation, divergence and Stokes' theorem.
|-
|Week 5
||
*
||
Tensor Caluclus Basics II
||

||
* Manifolds and coordinate transformations, vector fields, Riemannian geometry, covariant derivatives and Christoffel symbols
|-
|Week 6
||
*
||
Applied Functional Analysis Part I
||

||
* Hilbert spaces and inner products, orthogonality and completeness.
|-
|Week 7
||
*
||
Applied Functional Analysis Part II
||

||
* Operators in Hilbert spaces, eigenvalue problem, self-adjointness and spectral properties
|-
|Week 8
||
*
||
Applied Functional Analysis Part III
||

||
* Examples of Hilbert spaces in quantum mechanics, standard examples such as potential wells and harmonic oscillator
|-
|Week 9
||
*
||
Overview about ordinary differential equations I
||

||
* Systems of nonlinear/linear equations, basic existence and uniqueness theorems
|-
|Week 10
||

||
Overview about ordinary differential equations II
||

||
* Phase-plane, linearization, stability, chaos
|-
|Week 11
||
*
||
PDE's of Mathematical Physics
||

||
* Standard examples, qualitative properties, conservation laws

|-
|Week 12
||

||
Introduction to Lie Groups and Symmetries I
||
*
||
* Definition of a Lie group and examples, commutators and Lie brackets, Lie algebras
|-
|Week 13
||
*
||
Introduction to Lie Groups and Symmetries II
||

||
* Exponential maps, applications of Lie groups to differential equations, Noether's theorem
|-
|Week 14
||
*
||
KdV equation, completely integrable systems
||
*
||
* Soliton solutions, infinite hierarchy of conservation laws
|}

MAT5863

2025-08-30T17:15:15Z

Jose.iovino: /* Mathematical Physics - MAT4143/5153 */

Main Page

2025-08-30T17:14:01Z

Jose.iovino: /* Upper Division */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5863]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MATZZZ]] Mathematical Physics 2
* [[MAT4XXX]]/[[MAT5XXX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XXX]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XXX]] Quantum Information
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MATZZZ]] Mathematical Physics II*
* [[MAT5XXX]] Quantum Information*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T17:13:21Z

Jose.iovino: /* Upper Division */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5883]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MATZZZ]] Mathematical Physics 2
* [[MAT4XXX]]/[[MAT5XXX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XXX]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XXX]] Quantum Information
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MATZZZ]] Mathematical Physics II*
* [[MAT5XXX]] Quantum Information*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T17:11:26Z

Jose.iovino: /* Qualifying Exam Track: Mathematical Physics */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5163]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MATZZZ]] Mathematical Physics 2
* [[MAT4XXX]]/[[MAT5XXX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XXX]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XXX]] Quantum Information
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MATZZZ]] Mathematical Physics II*
* [[MAT5XXX]] Quantum Information*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T17:10:38Z

Jose.iovino: /* Qualifying Exam Track: Mathematical Physics */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5163]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MATZZZ]] Mathematical Physics 2
* [[MAT4XXX]]/[[MAT5XXX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XXX]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XXX]] Quantum Information
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MATZZZ]] Mathematical Physics II*
* [[MATXXX]] Quantum Information*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

MAT5863

2025-08-30T17:07:24Z

Jose.iovino: Created page with "=Mathematical Physics - MAT4143/5153= ==Course description== Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their under..."

=Mathematical Physics - MAT4143/5153=

==Course description==
Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their understanding of mathematical methods used in physics. This course is also suitable for Mathematics majors, who can deepen their understanding of applications and proofs of major theorems in Functional Analysis.

==Catalog entry==

''Prerequisite'': Calculus III [[MAT2214]] and Differential Equations II [[MAT3623]] with a letter grade of C- or better, or successful completion of at least three credits of equivalent courses.

''Content'':
1. Topics in Complex Analysis.
2. Differential Equations: Dynamical systems, nonlinearity & chaos.
3. Nonlinear Waves in PDEs: Continuous Systems, Hamiltonian formulation of plasmas
and fluids, KdV eq., Nonlinear Schroedinger Eq., Sine/Klein-Gordon Equation(s).
4. Asymptotic Analysis methods, time-dependent/independent perturbation theory.
5. Functional Analysis in Mathematical Physics
6. Mathematical Formalism of PDEs for Physicists
7. Group Theory in Physics, Lie Algebras.
8. Tensor calculus: theory and applications. 3 Credit Hours

'''Textbooks:'''

* Needham, T. (1997). Visual Complex Analysis. United Kingdom: Clarendon Press.
* Grimshaw, R. (1993). Nonlinear Ordinary Differential Equations (1st ed.). Routledge.
* R. Courant and D. Hilbert, Methods of Mathematical Physics. Vol. II: Partial Differential Equations, Wiley Classics Library, John Wiley & Sons Inc., New York, 1989.
* Bender, C. and Orszag, S. Advanced Mathematical Methods for Scientists and Engineers. Mc-Graw Hill.
* Kreyszig, E. (1989). Introductory Functional Analysis with Applications. Wiley.
* Methods of Applied Mathematics. Todd Arbogast and Jerry L. Bona. Department of Mathematics, and Institute for Computational Engineering and Sciences, University of Texas at Austin, 2008.
* P. J. Olver, Applications of Lie Groups to Differential Equations, Second Edition, Graduate Texts in Mathematics, vol. 107, Springer-Verlag, New York, 1993.
* Rutherford Aris, Vectors, Tensors and the Basic Equations of Fluid Mechanics. Dover Publications

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
*
||
Complex Analysis Part I
||

||
* Definition and algebraic properties of complex numbers, Riemann Sphere, Holomorphic functions and conformal mappings
|-
|Week 2
||
*
||
Complex Analysis Part II
||

||
*Integrals in the Complex Plane, Cauchy's theorem, Calculus of Residues
|-
|Week 3
||
*
||
Complex Analysis Part III
||

||
* Harmonic functions and Poisson's formula
|-
|Week 4
||
*
||
Tensor Calculus Basics I
||

||
* Using indices in three-dimensional cartesian vector analysis, deriving vector identities using index calculus, divergence, grad and curl in index notation, divergence and Stokes' theorem.
|-
|Week 5
||
*
||
Tensor Caluclus Basics II
||

||
* Manifolds and coordinate transformations, vector fields, Riemannian geometry, covariant derivatives and Christoffel symbols
|-
|Week 6
||
*
||
Applied Functional Analysis Part I
||

||
* Hilbert spaces and inner products, orthogonality and completeness.
|-
|Week 7
||
*
||
Applied Functional Analysis Part II
||

||
* Operators in Hilbert spaces, eigenvalue problem, self-adjointness and spectral properties
|-
|Week 8
||
*
||
Applied Functional Analysis Part III
||

||
* Examples of Hilbert spaces in quantum mechanics, standard examples such as potential wells and harmonic oscillator
|-
|Week 9
||
*
||
Overview about ordinary differential equations I
||

||
* Systems of nonlinear/linear equations, basic existence and uniqueness theorems
|-
|Week 10
||

||
Overview about ordinary differential equations II
||

||
* Phase-plane, linearization, stability, chaos
|-
|Week 11
||
*
||
PDE's of Mathematical Physics
||

||
* Standard examples, qualitative properties, conservation laws

|-
|Week 12
||

||
Introduction to Lie Groups and Symmetries I
||
*
||
* Definition of a Lie group and examples, commutators and Lie brackets, Lie algebras
|-
|Week 13
||
*
||
Introduction to Lie Groups and Symmetries II
||

||
* Exponential maps, applications of Lie groups to differential equations, Noether's theorem
|-
|Week 14
||
*
||
KdV equation, completely integrable systems
||
*
||
* Soliton solutions, infinite hierarchy of conservation laws
|}

Main Page

2025-08-30T17:03:02Z

Jose.iovino: /* Qualifying Exam Track: Mathematical Physics */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5163]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MATZZZ]] Mathematical Physics 2
* [[MAT4XXX]]/[[MAT5XXX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XXX]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XXX]] Quantum Information
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* [[MATZZZ]] Mathematical Physics II*
* Quantum Information*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

Main Page

2025-08-30T17:01:59Z

Jose.iovino: /* Upper Division */

UTSA Department of Mathematics

To edit tables in each course below, you can use [https://tableconvert.com/mediawiki-to-excel MediaWiki-to-Excel converter] and/or the [https://tableconvert.com/excel-to-mediawiki Excel-to-MediaWiki converter]

== Undergraduate Studies ==
===STEM Core===
* [[MAT1073]] College Algebra for Scientists and Engineers
* [[MAT1093]] Precalculus
* [[MAT1193]] Calculus for Biosciences
* [[MAT1214]] Calculus I (4 credit hours)
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2233]] Linear Algebra

===Minor in Mathematics===
To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See [https://catalog.utsa.edu/undergraduate/bachelorsdegreeregulations/minors/ UTSA's Undergraduate Catalog]

The Minor in Mathematics requires the Calculus series plus linear algebra, and upper division courses in either the Math Major or the Data & Applied Science Core

===Data & Applied Science Core===
==== Lower Division ====
* [[MDC1213]] Sociocultural Foundations of Mathematics, Data Science, and Computing
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4813]]/[[MAT5163]] Mathematical Physics 1
* [[MAT4ZZZ]]/[[MATZZZ]] Mathematical Physics 2
* [[MAT4XXX]]/[[MAT5XXX]] Introduction to Quantum Information Science and Engineering
* [[MAT4373]]/[[MAT5373]] Mathematical Foundations of Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Foundations of Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] Mathematical Foundations of Data Analytics

===Math Major===
==== Lower Division ====
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability

==== Upper Division ====
* [[MAT3003]] Discrete Mathematics
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (below).
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3313]] Logic and Computability
* [[MAT3613]] Differential Equations I
* [[MAT3623]] Differential Equations II
* [[MAT3633]] Numerical Analysis
* [[MAT3223]] Complex Variables
* [[MAT4033]] Linear Algebra II
* [[MAT4213]] Real Analysis I
* [[MAT4223]] Real Analysis II
* [[MAT4233]] Modern Abstract Algebra
* [[MAT4273]] Topology
* [[MAT4283]] Computing for Mathematics
* [[MAT4323]] Applied Graph Theory
* [[MAT4373]] Mathematical Statistics I
* [[MAT43XX]]/[[MAT53XX]] Mathematics of Quantum Computing
* [[MAT4YYY]]/[[MAT5YYY]] Mathematics of AI

===Business===
* [[MAT1053]] Algebra for Business
* [[MAT1133]] Calculus for Business

===Math for Liberal Arts===
* [[MAT1043]] Introduction to Mathematics

=== Elementary Education ===
* [[MAT1023]] College Algebra
* [[MAT1153]] Essential Elements in Mathematics I
* [[MAT1163]] Essential Elements in Mathematics II

=== General Math Studies===
* [[MAT3233]] Modern Algebra

== Graduate Studies ==
=== Core Courses ===
Core courses, common across all M.Sc. tracks, must be at least 50% of the credit 30 hours needed to obtain a M.Sc. degree. The following courses add up to 15 credit hours.

* [[MAT5283]] Linear Algebra
* [[MAT5203]] Real Analysis I
* [[MAT5603]] Numerical Analysis
* [[MAT5603]] Differential Equations I

=== Qualifying Exam Track: Algebra-Cryptography ===

* [[MAT 5173]] Abstract Algebra I
* [[MAT 5183]] Abstract Algebra II
* [[MAT 5123]] Introduction to Cryptography
* [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

=== Qualifying Track: Mathematics of Information, Data and Communications ===

* [[MAT5123]] Introduction to Cryptography
* [[MAT5143]] Cryptography II
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5153]] Data Analytics
* [[MAT5XXX]] Quantum Information
* [[MAT5YYY]] Mathematics of AI

=== Qualifying Exam Track: Scientific Computing ===

* [[MAT5603]] Numerical Analysis
* [[MAT5293]] Numerical Linear Algebra
* [[MAT5XXX]] Quantum Information
* [[MAT5163]] Probability and Computing

=== Qualifying Exam Track: Analysis ===

* [[MAT5203]] Real Analysis I
* [[MAT5213]] Real Analysis II
* [[MAT5223]] Complex Analysis I
* [[MAT5233]] Complex Analysis II
* [[MAT5553]] Harmonic Analysis
* [[MAT5553]] Functional Analysis

=== Qualifying Exam Track: Differential Equations ===

* [[MAT5653]] Differential Equations I
* [[MAT5673]] Partial Differential Equations I
* [[MAT5683]] Partial Differential Equations II

=== Qualifying Exam Track: Discrete Mathematics and Logic ===

* [[MAT5423]] Discrete Mathematics
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
* [[MAT5443]] Logic and Computability
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Topology and Geometry ===

* [[MAT5243]] Topology I
* [[MAT5253]] Topology II
* Differential Geometry

=== Qualifying Exam Track: Mathematical Physics ===

* [[MAT5863]] Mathematical Physics I
* Mathematical Physics II*
* Quantum Information*
* Differential Geometry*
* [[MAT5453]] Quantum Logic

=== Qualifying Exam Track: Mathematics of Life Sciences ===

* [[MAT5133]] Mathematical Biology
* [[MAT5323]] Mathematical Modeling (Systems Biology)

MAT 5123

2025-08-30T16:59:40Z

Jose.iovino:

== Catalog entry ==
MAT 5123. Introduction to Cryptography. (3-0) 3 Credit Hours.

Prerequisite: MAT 4213. Congruences and residue class rings, Fermat’s Little Theorem, the Euler phi-function, the Chinese Remainder Theorem, complexity, symmetric-key cryptosystems, cyclic groups, primitive roots, discrete logarithms, one-way functions, public-key cryptosystems, digital signatures, finite fields, and elliptic curves. Differential Tuition: $150. Course Fees: GS01 $90.

== Textbook ==
J. Hoffstein, J. Pipher, J. H. Silverman, ''An Introduction to Mathematical Cryptography'' (2nd Ed.) Springer Undergraduate Mathematics Series, Springer-Verlag (2014). ISBN: 978-1-4939-1711-2.

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|1
||
1.2, 1.3
||
Substitution ciphers and basic theory of divisibility.
||
* Caesar’s and more general substitution ciphers.
* Greatest common divisor. The extended Euclidean algorithm.
|- 
| 
2
|| 
1.4, 1.5.
|| 
Modular arithmetic and finite fields.
|| 
* Primes and integer factorizations.
* The Fundamental Theorem of Arithmetic.
* Modular arithmetic and shift ciphers.
* Modular rings and finite fields 𝔽ₚ.
* Powers and primitive roots in finite fields. Fermat's Little Theorem.
* Fast exponentiation.
|- 
| 
3
|| 
1.7, 2.1–2.3.
|| 
Public and private-key cryptosystems.

Cyclic groups.

Discrete Logarithms.

Diffie-Hellman key exchange.
|| 
* Symmetric and asymmetric ciphers.
* Encoding schemes.
* Perfect secrecy. Vernon’s cipher.
* Examples of symmetric ciphers.
* Discrete Logarithms.
* The Diffie-Hellman key exchange.
|- 
| 
4
|| 
2.4, 2.5. 2.6, 2.7.
|| 
Elgamal public-key cryptosystem (EGPKC).

Cyclic groups.

Collision algorithms.
|| 
* Theory of finite cyclic groups.
* The Discrete Logarithm Problem (DLP).
* Shanks’ Babystep-Giantstep DLP algorithm.
|- 
| 
5
|| 
2.8, 2.9, 2.10
|| 
Rudiments of ring theory.

The Chinese Remainder Theorem.

The Pohlig-Hellman Algorithm.
|| 
* Rings. Polynomial rings. Quotient rings.
* Systems of congruences. The Chinese Remainder Theorem.
* The Pohlig-Hellman Algorithm.
|- 
| 
6
|| 
None
|| 
Review. First midterm exam.
|| 
|- 
| 
7
|| 
3.1, 3.2, 3.3.
|| 
Modular groups of units.

The RSA cryptosystem.

Practical considerations of security in implementation.
|| 
* Modular groups 𝑈ₙ.
* Euler's “totient” function 𝜑. Euler's Theorem.
* Powers and roots modulo 𝒑𝒒.
* The Rivest-Shamir-Adleman (RSA) cryptosystem.
* Implementation and security issues of cryptosystems: Kerchoff's Principle, Known- and Chosen-Plaintext attacks, Man-in-the-Middle attacks, obfuscation (Random-Oracle) attacks, parameter reuse.
|- 
| 
8
|| 
3.4, 3.5.
|| 
Primality testing and factorization attacks on RSA.
|| 
* Distribution of primes. The Prime Number Theorem.
* Fermat's Little Theorem and Carmichael numbers.
* The Miller-Rabin probabilistic primality test.
* Pollard's “𝒑−𝟣” factorization algorithm.
|- 
| 
9
|| 
4.1, 4.2, 4.3
|| 
Digital Signatures.
|| 
* Definition and uses of digital signatures.
* RSA digital signatures.
* Elgamal digital signatures and DSA.
|- 
| 
10
|| 
5.1, 5.3, 5.6, 5.7.
|| 
Probability, entropy, information theory and complexity.
|| 
* Rudiments of combinatorics and probability.
* Bayes's Formula.
* Random variables and expected values.
* Entropy of a probability distribution.
* Perfect secrecy.
* Complexity theory and 𝒫 versus 𝒩𝒫.
|- 
| 
11
|| 
None
|| 
Review. Second midterm exam.
|- 
| 
12
|| 
6.1, 6.2., 6.3
|| 
Elliptic curves and discrete logarithms.
|| 
* Introduction to elliptic curves (ECs).
* Elliptic curves over finite fields.
* Fast multiples (“powers”) in ECs. The Double-and-Add algorithm.
* The Elliptic Curve Discrete Logarithm Problem (ECDLP).
|- 
| 
13
|| 
6.4, 6.7
|| 
Elliptic-Curve Cryptography (ECC).

Elliptic curves in characteristic 2.
|| 
* EC Diffie-Hellman key exchange.
* EC Elgamal PKC.
* EC digital signature.
* Definition and construction of finite (Galois) fields 𝐺𝐹(2ⁿ).
* Elliptic curves over 𝐺𝐹(2ⁿ).
|- 
| 
14
|| 
6.6

Atkin-Morain's “ECs and Primality Proving” (Math. Comp. 61 (1993) 29–68.
[https://www.ams.org/journals/mcom/1993-61-203/S0025-5718-1993-1199989-X/])
|| 
EC-based primality testing and factorization techniques.
|| 
* Lenstra's EC factorization algorithm.
* EC primality certification.
|- 
| 
15
|| 
None.
|| 
Student Presentations. Wrap-up and review.
|| 
|-
|}

MAT 5123

2025-08-30T16:55:36Z

Jose.iovino: Created page with "Introduction to the theory of finite-dimensional vector spaces. '''Catalog entry''' ''Prerequisite'': Prerequisite: MAT 3233 or MAT 4233, or CS 2233 and CS 2231, , or inst..."

Introduction to the theory of finite-dimensional vector spaces.

'''Catalog entry'''

''Prerequisite'': Prerequisite: MAT 3233 or MAT 4233, or CS 2233 and CS 2231, , or instructor consent.

''Contents''
Congruences and residue class rings, Fermat’s Little Theorem, the Euler phi-function, the Chinese Remainder Theorem; complexity; symmetric-key cryptosystems; cyclic groups, primitive roots, discrete logarithms, one-way functions; public-key cryptosystems (Diffie-Hellman key exchange, RSA, Rabin, El Gamal); digital signatures; and other groups (finite fields, elliptic curves). Generally offered: Spring.