Difference between revisions of "Main Page"

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* [[MAT3003]] Discrete Mathematics  
 
* [[MAT3003]] Discrete Mathematics  
 
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
 
* <del>[[MAT3013]] Foundations of Mathematics</del> Course transitioning to be replaced by [[MAT3003]] Discrete Mathematics (below).
−
* [[MAT3203]] Abstract Linear Algebra
 
 
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be replaced by [[MAT3333]] Fundamentals of Analysis and Topology (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
 
* [[MAT3333]] Fundamentals of Analysis and Topology
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* [[MAT3633]] Numerical Analysis  
 
* [[MAT3633]] Numerical Analysis  
 
* [[MAT3223]] Complex Variables  
 
* [[MAT3223]] Complex Variables  
−
* [[MAT4033]] Abstract Linear Algebra II
+
* [[MAT4033]] Linear Algebra II
 
* [[MAT4213]] Real Analysis I  
 
* [[MAT4213]] Real Analysis I  
 
* [[MAT4223]] Real Analysis II  
 
* [[MAT4223]] Real Analysis II  
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== Graduate Studies ==
 
== Graduate Studies ==
−
=== Core M.Sc. 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.  
 
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.  
−
* Two courses in the Analysis & Algebra sequences in the following combinations:
+
 
−
** [[MAT5173]] Algebra  I & [[MAT5183]] Algebra II.
 
−
** [[MAT5173]] Algebra  I & [[MAT5243]] General Topology I.
 
−
** [[MAT5243]] General Topology I & [[MAT5253]] General Topology II.
 
−
** [[MAT5203]] Analysis I  & [[MAT5213]] Analysis II
 
−
** [[MAT5173]] Algebra I &  [[MAT5203]] Analysis I.
 
−
** [[MAT5173]] Algebra  I & [[MAT5123]] Cryptography I.
 
−
** [[MAT5123]] Cryptography I &  [[MAT5323]] Cryptography II.
 
−
* Two courses in Discrete Mathematics among the following:
 
−
** [[MAT5423]] Discrete Mathematics I
 
−
** [[MAT5433]] Discrete Mathematics II
 
−
* One course in computation among the following:
 
−
** [[MAT5373]] Mathematical Statistics I
 
−
** [[MDC5153]] Data Analytics
 
 
* [[MAT5283]] Linear Algebra
 
* [[MAT5283]] Linear Algebra
 +
* [[MAT5253]] Real Analysis I
 +
* [[MAT5603]] Numerical Analysis
 +
* [[MAT5603]] Differential Equations I
 +
 +
During completion of the required coursework, students must choose three distinct specialization tracks. For each of the three chosen tracks, the doctoral candidate must pass a qualifying examination that covers a two-semester course sequence approved for the given track. Courses with a numbered sequence I and II must be taken consecutively, and courses without a number can be taken in any order. Each track can be satisfied with any pair of these courses, unless otherwise noted.  Each track has a list of courses from which the two-semester course sequence for the examination must be chosen. Below is a list of approved qualifying tracks with their respective lists of courses:
 +
 +
=== Qualifying Exam Track: Algebra-Cryptography  ===
 +
 +
* [[MAT 5173]] Abstract Algebra I
 +
* [[MAT 5183]] Abstract Algebra II
 +
* [[MAT 5123]] Introduction to Cryptography
 +
* [[MAT 5243]] Cryptography II
 +
 +
=== 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 Track: Mathematics of Information, Data and Communications  ===
 +
 +
* [[MAT5123]] Introduction to Cryptography
 +
* [[MAT5323]] Cryptography II
 +
* [[MAT5433]] Graph Theory (Discrete Mathematics II)
 +
* [[MAT5153]] Data Analytics
 +
* [[MAT5XXX]] Quantum Information
 +
* [[MAT5ZZZ]] Mathematics of AI
 +
 +
=== Qualifying Exam Track: Differential Equations ===
 +
 +
* [[MAT5653]] Differential Equations I
 +
* [[MAT5673]] Partial Differential Equations I
 +
* [[MAT5683]] Partial Differential Equations II
 +
 +
=== Qualifying Exam Track: Scientific Computing ===
 +
 +
* [[MAT5603]] Numerical Analysis
 +
* [[MAT5293]] Numerical Linear Algebra
 +
* [[MAT5613]] Numerical Solutions of Differential Equations
 +
* [[MAT5163]] Probability and Computing
  
−
=== Qualifying Examination Tracks  ===
+
=== Qualifying Exam Track: Discrete Mathematics and Logic ===
−
* [[MAT5183]] Algebra II (Pure, Applied tracks)
 
−
* [[MAT5123]] Cryptography (Pure, Applied tracks)
 
−
* [[MAT5323]] Cryptography II (Pure, Applied tracks))
 
−
* [[MAT5213]] Analysis II (Pure track)
 
−
* [[MAT5113]] Computing for Mathematics  (Pure, Applied tracks)
 
−
* [[MAT5433]] Discrete Mathematics II  (Pure, Applied tracks)
 
−
* [[MAT5383]] Mathematical Statistics II  (Applied tracks)
 
−
* [[MAT58XX]] Mathematics of Quantum Computation (Pure, applied tracks)
 
  
−
=== M.Sc. Track in Pure Mathematics ===
+
* [[MAT5423]] Discrete Mathematics
 +
* [[MAT5433]] Discrete Mathematics II (Graph Theory)
 
* [[MAT5443]] Logic and Computability
 
* [[MAT5443]] Logic and Computability
 
* [[MAT5453]] Quantum Logic
 
* [[MAT5453]] Quantum Logic
−
* [[MAT5243]] General Topology
 
−
* [[MAT5253]] General Topology II
 
−
* [[MAT5323]] Cryptography II
 
−
* [[MAT5183]] Algebra II
 
−
* [[MAT5223]] Theory of Functions of a Complex Variable
 
−
* [[MAT5343]] Differential Geometry
 
  
−
=== M.Sc. Track in Applied & Industrial Mathematics ===
+
=== Qualifying Exam Track: Topology and Geometry ===
−
* [[MDC5153]] Data Analytics
+
 
−
* [[AIM 5113]] Introduction to Industrial Mathematics
+
* [[MAT5243]] Topology I
−
* [[MAT 5113]] Computing for Mathematics
+
* [[MAT5253]] Topology II
−
* [[MAT 5653]] Differential Equations I
+
* [[MAT5253]] Differential Geometry
−
* [[MAT 5673]] Partial Differential Equations
+
 
 +
=== Qualifying Exam Track: Mathematical Biology  ===
 +
 
 +
* [[MAT5133]] Mathematical Biology
 +
 
 +
Plus one of the following two courses:
  
−
=== M.Sc. in Mathematics Education ===
+
* [[MAT5323]] Mathematical Modeling
 +
* Optimal Control and Calculus of Variations*.

Revision as of 15:44, 17 August 2025

UTSA Department of Mathematics

To edit tables in each course below, you can use MediaWiki-to-Excel converter and/or the 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 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

Math Major

Lower Division

  • MAT1313 Algebra and Number Systems
  • MAT2313 Combinatorics and Probability

Upper Division

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

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.

During completion of the required coursework, students must choose three distinct specialization tracks. For each of the three chosen tracks, the doctoral candidate must pass a qualifying examination that covers a two-semester course sequence approved for the given track. Courses with a numbered sequence I and II must be taken consecutively, and courses without a number can be taken in any order. Each track can be satisfied with any pair of these courses, unless otherwise noted. Each track has a list of courses from which the two-semester course sequence for the examination must be chosen. Below is a list of approved qualifying tracks with their respective lists of courses:

Qualifying Exam Track: Algebra-Cryptography

Qualifying Exam Track: Analysis

Qualifying Track: Mathematics of Information, Data and Communications

Qualifying Exam Track: Differential Equations

  • MAT5653 Differential Equations I
  • MAT5673 Partial Differential Equations I
  • MAT5683 Partial Differential Equations II

Qualifying Exam Track: Scientific Computing

  • MAT5603 Numerical Analysis
  • MAT5293 Numerical Linear Algebra
  • MAT5613 Numerical Solutions of Differential Equations
  • MAT5163 Probability and Computing

Qualifying Exam Track: Discrete Mathematics and Logic

Qualifying Exam Track: Topology and Geometry

Qualifying Exam Track: Mathematical Biology

Plus one of the following two courses:

  • MAT5323 Mathematical Modeling
  • Optimal Control and Calculus of Variations*.
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