Department of Mathematics at UTSA - User contributions [en]

MAT2313

2023-08-14T22:49:38Z

Eduardo.duenez: /* Topics List */

= Combinatorics and Probability - MAT2313=
''Corequisite'': [[MAT1224]].

''Content'': Basic counting principles. Permutations and combinations. Binomial and multinomial coefficients. Pigeonhole and inclusion-exclusion principles. Graphs, colorings, planarity. Eulerian and Hamiltonian graphs. Recurrence relations. Generating functions. Prerequisites: MAT1224 Calculus II and MAT 1313 Algebra and Number Systems. 3 Credit Hours

''Sample textbooks'': Alan Tucker, Applied Combinatorics (6th ed). Wiley (2012).

==Topics List==
Course outline:

Week 1: Finite sets, strings, enumeration, the addition and product rules.

Week 2: Combinations, permutations.

Week 3: Binomial and multinomial coefficients.

Week 4: The Pigeonhole Principle. The Inclusion-Exclusion Formula, derangements, the Euler ɸ function (totient).

Week 5: Review. First midterm exam.

Week 6: Graphs and multigraphs.

Week 7: Eulerian and Hamiltonian graphs.

Week 8: Trees. Colorings. Planarity.

Week 9: Review. Second midterm exam.

Week 10: Generating functions. The Binomial Theorem. Partitions.

Week 11: Recurrence relations. Linear recurrences.

Week 12: Solving recurrences by generating functions.

Week 13: Exponential generating functions. Nonlinear recurrences.

Week 15: Review.

Main Page

2023-04-01T23:31:19Z

Eduardo.duenez: Renamed MAT2243->2253

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)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT2214]] Calculus III (4 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]] Foundations of Mathematics, Data Science, and Artificial Intelligence in Cultural Context
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2253]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] 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 eventually replaced by [[MAT3003]] Discrete Mathematics (below).
* [[MAT3003]] Discrete Mathematics
* [[MAT3203]] Linear Algebra II
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be eventually 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
* [[MAT4373]] Mathematical Statistics I

===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 M.Sc. Studies ===
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 course in discrete mathematics among the following:
** [[MAT5423]] Discrete Mathematics I (fall even years)
** [[MAT5433]] Discrete Mathematics II (spring even years)
* One course in computation among the following:
** [[MAT5373]] Mathematical Statistics I (fall even years)
** [[MDC5153]] Data Analytics
* [[MAT5283]] Linear Algebra (fall odd years)

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (fall, even years) (Pure, Applied tracks)
* [[MAT5123]] Cryptography (spring even years) (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (spring odd years) (Pure, Applied tracks))
* [[MAT5213]] Analysis II (spring even years) (Pure track)
* [[MAT5113]] Computing for Mathematics (spring even years) (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (spring odd years) (Pure, Applied tracks)
* [[MAT5383]] Mathematical Statistics II (fall even years) (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT5443]] Logic and Computability
* [[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 ===
* [[MDC5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===

MAT2253

2023-04-01T23:31:01Z

Eduardo.duenez: Create MAT2253 to remove 2243 (number unavailable).

==Applied Linear Algebra==

Prerequisite: [[MAT1214]]/[[MAT1213]] Calculus I

This comprehensive course in linear algebra provides an in-depth exploration of core concepts and their applications to optimization, data analysis, and neural networks. Students will gain a strong foundation in the fundamental notions of linear systems of equations, vectors, and matrices, as well as advanced topics such as eigenvalues, eigenvectors, and canonical solutions to linear systems of differential equations. The course also delves into the critical techniques of calculus operations in vectors and matrices, optimization, and Taylor series in one and multiple variables. By the end of the course, students will have a thorough understanding of the mathematical framework underlying principal component analysis, gradient descent, and the implementation of simple neural networks.

==List of Topics==

{| class="wikitable"
! Week !! Section !! Topic !! Prerequisites !! SLOs
|-
| 1 || || Notions of linear systems of equations to introduce the concepts of vector and matrices. || ||
|-
| 2 || || Vector and matrix operations: Dot and cross products, matrix transpose, determinants. || ||
|-
| 3 || || Vector and matrix operations: Matrix addition, multiplication and inverse. || ||
|-
| 4 || || Cramer's rule and solutions of linear systems || ||
|-
| 5 || || Full rank, undetermined, and overdetermined systems. Least square solutions || ||
|-
| 6 || || Eigenvalues and eigenvectors. Canonical solution to linear systems of differential equations. || ||
|-
| 7 || || Calculus operations in vectors and matrices, i.e. how to derive a matrix with respect to a vector? || ||
|-
| 8 || || Optimization: Linear problems, and nonlinear problems (constrained and unconstrained) || ||
|-
| 9 || || Lagrange multiplier || ||
|-
| 10 || || Taylor series in one and multiple variables. Jacobians and Hessians, i.e. nabla and Laplace operators. || ||
|-
| 11 || || Principal component analysis || ||
|-
| 12 || || Gradient descent || ||
|-
| 13 || || Neural networks as nonlinear transformations || ||
|-
| 14 || || Implementation of a simple neural network with gradient descent
|}

MAT2243

2023-04-01T23:30:22Z

Eduardo.duenez: Removed 2243, renaming to 2253.

Main Page

2023-03-31T19:11:13Z

Eduardo.duenez: Improved formatting of deprecated 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)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT2214]] Calculus III (4 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]] Foundations of Mathematics, Data Science, and Artificial Intelligence in Cultural Context
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2243]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] 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 eventually replaced by [[MAT3003]] Discrete Mathematics (below).
* [[MAT3003]] Discrete Mathematics
* [[MAT3203]] Linear Algebra II
* <del>[[MAT3213]] Foundations of Analysis</del> Course transitioning to be eventually 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
* [[MAT4373]] Mathematical Statistics I

===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 M.Sc. Studies ===
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 course in discrete mathematics among the following:
** [[MAT5283]] Linear Algebra (fall odd years)
** [[MAT5423]] Discrete Mathematics I (fall even years)
** [[MAT5433]] Discrete Mathematics II (spring even years)
* One course in computation among the following:
** [[MAT5373]] Mathematical Statistics I (fall even years)
** [[MDC5153]] Data Analytics

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (fall, even years) (Pure, Applied tracks)
* [[MAT5123]] Cryptography (spring even years) (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (spring odd years) (Pure, Applied tracks))
* [[MAT5213]] Analysis II (spring even years) (Pure track)
* [[MAT5113]] Computing for Mathematics (spring even years) (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (spring odd years) (Pure, Applied tracks)
* [[MAT5383]] Mathematical Statistics II (fall even years) (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT5443]] Logic and Computability
* [[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 ===
* [[MDC5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===

Main Page

2023-03-31T19:09:52Z

Eduardo.duenez: Typo

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)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT2214]] Calculus III (4 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]] Foundations of Mathematics, Data Science, and Artificial Intelligence in Cultural Context
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2243]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] 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> Eventually to be replaced by [[MAT3003]] Discrete Mathematics (below).
* [[MAT3003]] Discrete Mathematics
* [[MAT3203]] Linear Algebra II
* <del>[[MAT3213]] Foundations of Analysis</del> Eventually 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
* [[MAT4373]] Mathematical Statistics I

===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 M.Sc. Studies ===
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 course in discrete mathematics among the following:
** [[MAT5283]] Linear Algebra (fall odd years)
** [[MAT5423]] Discrete Mathematics I (fall even years)
** [[MAT5433]] Discrete Mathematics II (spring even years)
* One course in computation among the following:
** [[MAT5373]] Mathematical Statistics I (fall even years)
** [[MDC5153]] Data Analytics

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (fall, even years) (Pure, Applied tracks)
* [[MAT5123]] Cryptography (spring even years) (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (spring odd years) (Pure, Applied tracks))
* [[MAT5213]] Analysis II (spring even years) (Pure track)
* [[MAT5113]] Computing for Mathematics (spring even years) (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (spring odd years) (Pure, Applied tracks)
* [[MAT5383]] Mathematical Statistics II (fall even years) (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT5443]] Logic and Computability
* [[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 ===
* [[MDC5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===

Main Page

2023-03-31T19:09:24Z

Eduardo.duenez: Improved formatting of deprecated 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)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT2214]] Calculus III (4 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]] Foundations of Mathematics, Data Science, and Artificial Intelligence in Cultural Context
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2243]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] 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> Eventually to be replaced by [[MAT3003]] Discrete Mathematics (below).
* [[MAT3003]] Discrete Mathematics
* [[MAT3203]] Linear Algebra II
* <del>[[MAT3213]] Foundations of Analysis</del>
Eventually 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
* [[MAT4373]] Mathematical Statistics I

===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 M.Sc. Studies ===
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 course in discrete mathematics among the following:
** [[MAT5283]] Linear Algebra (fall odd years)
** [[MAT5423]] Discrete Mathematics I (fall even years)
** [[MAT5433]] Discrete Mathematics II (spring even years)
* One course in computation among the following:
** [[MAT5373]] Mathematical Statistics I (fall even years)
** [[MDC5153]] Data Analytics

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (fall, even years) (Pure, Applied tracks)
* [[MAT5123]] Cryptography (spring even years) (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (spring odd years) (Pure, Applied tracks))
* [[MAT5213]] Analysis II (spring even years) (Pure track)
* [[MAT5113]] Computing for Mathematics (spring even years) (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (spring odd years) (Pure, Applied tracks)
* [[MAT5383]] Mathematical Statistics II (fall even years) (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT5443]] Logic and Computability
* [[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 ===
* [[MDC5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===

Main Page

2023-03-31T19:07:21Z

Eduardo.duenez: Make eventuall-to-be-obsolete courses 3013/3213 still available.

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)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT2214]] Calculus III (4 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]] Foundations of Mathematics, Data Science, and Artificial Intelligence in Cultural Context
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2243]] Applied Linear Algebra (3 credit hours)

==== Upper Division ====
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Statistics II (statistical inference)
* [[MDC4153]]/[[MDC5153]] 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> Replaced by [[MAT3003]] Discrete Mathematics
* [[MAT3203]] Linear Algebra II
* <del>[[MAT3213]] Foundations of Analysis</del> Replaced by [[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
* [[MAT4373]] Mathematical Statistics I

===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 M.Sc. Studies ===
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 course in discrete mathematics among the following:
** [[MAT5283]] Linear Algebra (fall odd years)
** [[MAT5423]] Discrete Mathematics I (fall even years)
** [[MAT5433]] Discrete Mathematics II (spring even years)
* One course in computation among the following:
** [[MAT5373]] Mathematical Statistics I (fall even years)
** [[MDC5153]] Data Analytics

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (fall, even years) (Pure, Applied tracks)
* [[MAT5123]] Cryptography (spring even years) (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (spring odd years) (Pure, Applied tracks))
* [[MAT5213]] Analysis II (spring even years) (Pure track)
* [[MAT5113]] Computing for Mathematics (spring even years) (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (spring odd years) (Pure, Applied tracks)
* [[MAT5383]] Mathematical Statistics II (fall even years) (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT5443]] Logic and Computability
* [[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 ===
* [[MDC5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===

MDC4413

2023-03-30T23:17:27Z

Eduardo.duenez: Changed redirect target from MDC5413 to MDC5153

#REDIRECT[[MDC5153]]

MAT 3313

2023-03-25T23:25:41Z

Eduardo.duenez: Blanked the page

MAT3333

2023-03-25T21:57:00Z

Eduardo.duenez: Spelling…

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 3333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topological notions in the real line and in metric spaces. Convergent sequences. Continuous functions. Connected and compact sets. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1-3
||

Chapters 1 & 2. Appendices C, G & H.
||

Operations, order and intervals of the real line.
Completeness of the real line. Suprema and infima.
Basic topological notions in the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

Chapter 3
||

Continuous functions on ℝ.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

4-5
||

Chapter 4
||

Convergence of real sequences.
The Cauchy criterion. Subsequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.
* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

6
||

Chapter 5
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

7
||

Chapter 6
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

8
||

Chapter 7
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

9 & 10
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

11
||

Chapter 12
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

12
||

Chapter 14
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

13
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

14
||

Chapter 16
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|-
|

15
||

Chapter 18 (time permitting)
||

Complete metric spaces.
||

* Cauchy sequences in metric spaces.
* Metric completness.
* Completeness and compactness.
|}

MAT3333

2023-03-25T21:46:39Z

Eduardo.duenez: Typo.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 3333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topological notions in the real line and in metric spaces. Convergent sequences. Continuious functions. Connected and compact sets. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1-3
||

Chapters 1 & 2. Appendices C, G & H.
||

Operations, order and intervals of the real line.
Completeness of the real line. Suprema and infima.
Basic topological notions in the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

Chapter 3
||

Continuous functions on ℝ.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

4-5
||

Chapter 4
||

Convergence of real sequences.
The Cauchy criterion. Subsequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.
* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

6
||

Chapter 5
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

7
||

Chapter 6
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

8
||

Chapter 7
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

9 & 10
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

11
||

Chapter 12
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

12
||

Chapter 14
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

13
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

14
||

Chapter 16
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|-
|

15
||

Chapter 18 (time permitting)
||

Complete metric spaces.
||

* Cauchy sequences in metric spaces.
* Metric completness.
* Completeness and compactness.
|}

MAT3333

2023-03-25T21:45:48Z

Eduardo.duenez: Make week 15 optional.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 3333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topological notions in the real line and in metric spaces. Convergent sequences. Continuious functions. Connected and compact sets. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1-3
||

Chapters 1 & 2. Appendices C, G & H.
||

Operations, order and intervals of the real line.
Completeness of the real line. Suprema and infima.
Basic topological notions in the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

Chapter 3
||

Continuous functions on ℝ.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

4-5
||

Chapter 4
||

Convergence of real sequences.
The Cauchy criterion. Subsequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.
* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

6
||

Chapter 5
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

7
||

Chapter 6
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

8
||

Chapter 7
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

9 & 10
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

11
||

Chapter 12
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

12
||

Chapter 14
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

13
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

14
||

Chapter 16
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|-
|

15
||

Chapter 18 (time permitting)
||

Complete metric spaces
||

* Cauchy sequences in metric spaces.
* Metric completness.
* Completeness and compactness.
|}

MAT3333

2023-03-25T21:45:30Z

Eduardo.duenez: Week 15

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 3333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topological notions in the real line and in metric spaces. Convergent sequences. Continuious functions. Connected and compact sets. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1-3
||

Chapters 1 & 2. Appendices C, G & H.
||

Operations, order and intervals of the real line.
Completeness of the real line. Suprema and infima.
Basic topological notions in the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

Chapter 3
||

Continuous functions on ℝ.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

4-5
||

Chapter 4
||

Convergence of real sequences.
The Cauchy criterion. Subsequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.
* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

6
||

Chapter 5
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

7
||

Chapter 6
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

8
||

Chapter 7
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

9 & 10
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

11
||

Chapter 12
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

12
||

Chapter 14
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

13
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

14
||

Chapter 16
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|-
|

15
||

Chapter 18
||

Complete metric spaces
||

* Cauchy sequences in metric spaces.
* Metric completness.
* Completeness and compactness.
|}

MAT3333

2023-03-25T21:43:11Z

Eduardo.duenez: Improving catalog entry.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 3333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topological notions in the real line and in metric spaces. Convergent sequences. Continuious functions. Connected and compact sets. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1-3
||

Chapters 1 & 2. Appendices C, G & H.
||

Operations, order and intervals of the real line.
Completeness of the real line. Suprema and infima.
Basic topological notions in the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

Chapter 3
||

Continuous functions on ℝ.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

4-5
||

Chapter 4
||

Convergence of real sequences.
The Cauchy criterion. Subsequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.
* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

6
||

Chapter 5
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

7
||

Chapter 6
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

8
||

Chapter 7
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

9 & 10
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

11
||

Chapter 12
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

12
||

Chapter 14
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

13
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

14
||

Chapter 16
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:41:32Z

Eduardo.duenez: Shuffling…

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 3333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topological notions in the real line and in metric spaces. Convergence of sequences and functions. Continuity. Connectedness and compactness. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1-3
||

Chapters 1 & 2. Appendices C, G & H.
||

Operations, order and intervals of the real line.
Completeness of the real line. Suprema and infima.
Basic topological notions in the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

Chapter 3
||

Continuous functions on ℝ.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

4-5
||

Chapter 4
||

Convergence of real sequences.
The Cauchy criterion. Subsequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.
* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

6
||

Chapter 5
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

7
||

Chapter 6
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

8
||

Chapter 7
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

9 & 10
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

11
||

Chapter 12
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

12
||

Chapter 14
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

13
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

14
||

Chapter 16
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:39:07Z

Eduardo.duenez: Shuffling…

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 3333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topological notions in the real line and in metric spaces. Convergence of sequences and functions. Continuity. Connectedness and compactness. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1-2
||

Chapters 1 & 2. Appendices C, G & H.
||

Operations, order and intervals of the real line.
Completeness of the real line. Suprema and infima.
Basic topological notions in the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
3
||

Chapter 3
||

Continuous functions on ℝ.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

4-5
||

Chapter 4
||

Convergence of real sequences.
The Cauchy criterion. Subsequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.
* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

6
||

Chapter 5
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

7
||

Chapter 6
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

8
||

Chapter 7
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

9
||


||


||


|-
|

10 & 11
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

12
||

Chapter 12
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

13
||

Chapter 14
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

14
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

15
||

Chapter 16
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:38:05Z

Eduardo.duenez: Shuffling…

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 3333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topological notions in the real line and in metric spaces. Convergence of sequences and functions. Continuity. Connectedness and compactness. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1-2
||

Chapters 1 & 2. Appendices C, G & H.
||

Operations, order and intervals of the real line.
Completeness of the real line. Suprema and infima.
Basic topological notions in the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
3
||

Chapter 3
||

Continuous functions on ℝ.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

4-5
||

Chapter 4
||

Convergence of real sequences.
The Cauchy criterion. Subsequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.
* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

6
||

---
||

Review. First midterm exam.
||


|-
|

7
||

Chapter 5
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

8
||

Chapter 6
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

9
||

Chapter 7
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

10
||


||


||


|-
|

11 & 12
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

13
||

Chapter 12
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

14
||

Chapter 14
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

15
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

16
||

Chapter 16
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:35:01Z

Eduardo.duenez: Shuffled/merged.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 3333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topological notions in the real line and in metric spaces. Convergence of sequences and functions. Continuity. Connectedness and compactness. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1-2
||

Chapters 1 & 2. Appendices C, G & H.
||

Operations, order and intervals of the real line.
Completeness of the real line. Suprema and infima.
Basic topological notions in the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
3
||

3.1–3.3
||

Continuous functions on ℝ.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

4-5
||

Chapter 4
||

Convergence of real sequences.
The Cauchy criterion. Subsequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.
* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

7
||

Chapter 5
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

8
||

Chapter 6
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

9
||

Chapter 7
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

10 & 11
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

12
||

Chapter 12
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

13
||

Chapter 14
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

14
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

15
||

16.2-16.4
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:30:26Z

Eduardo.duenez: Merging…

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 3333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topological notions in the real line and in metric spaces. Convergence of sequences and functions. Continuity. Connectedness and compactness. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1-2
||

Chapters 1 & 2. Appendices C, G & H.
||

Operations, order and intervals of the real line.
Completeness of the real line. Suprema and infima.
Basic topological notions in the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
3
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

4-5
||

Chapter 4
||

Convergence of real sequences.
The Cauchy criterion. Subsequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.
* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

7
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

8
||

6.1, 6.2, 6.3
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

9
||

7.1, 7.2
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

10 & 11
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

12
||

12.1-12.3
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

13
||

14.1-14.3
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

14
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

15
||

16.2-16.4
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:29:23Z

Eduardo.duenez: Merging weeksl

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 3333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topological notions in the real line and in metric spaces. Convergence of sequences and functions. Continuity. Connectedness and compactness. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1-2
||

Chapters 1 & 2. Appendices C, G & H.
||

Operations, order and intervals of the real line.
Completeness of the real line. Suprema and infima.
Basic topological notions in the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
3
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

5
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-
|

6
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

7
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

8
||

6.1, 6.2, 6.3
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

9
||

7.1, 7.2
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

10 & 11
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

12
||

12.1-12.3
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

13
||

14.1-14.3
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

14
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

15
||

16.2-16.4
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:26:16Z

Eduardo.duenez: Fixed course number!

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 3333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topological notions in the real line and in metric spaces. Convergence of sequences and functions. Continuity. Connectedness and compactness. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.

|-
|

2
||

1.2. Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

5
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-
|

6
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

7
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

8
||

6.1, 6.2, 6.3
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

9
||

7.1, 7.2
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

10 & 11
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

12
||

12.1-12.3
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

13
||

14.1-14.3
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

14
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

15
||

16.2-16.4
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:23:51Z

Eduardo.duenez: Catalog entry edited.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topological notions in the real line and in metric spaces. Convergence of sequences and functions. Continuity. Connectedness and compactness. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.

|-
|

2
||

1.2. Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

5
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-
|

6
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

7
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

8
||

6.1, 6.2, 6.3
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

9
||

7.1, 7.2
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

10 & 11
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

12
||

12.1-12.3
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

13
||

14.1-14.3
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

14
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

15
||

16.2-16.4
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:17:31Z

Eduardo.duenez: ToC complete.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.

|-
|

2
||

1.2. Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

5
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-
|

6
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

7
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

8
||

6.1, 6.2, 6.3
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

9
||

7.1, 7.2
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|

10 & 11
||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|

12
||

12.1-12.3
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|

13
||

14.1-14.3
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|

14
||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|

15
||

16.2-16.4
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:15:42Z

Eduardo.duenez: Merged topics.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.

|-
|

2
||

1.2. Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

6
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-
|

7
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

8
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

9
||

6.1, 6.2, 6.3
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

11
||

7.1, 7.2
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|


||

Chapters 9, 10, 11
||

The topology of metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.
* Interior, closure, and boundary.
* Accumulation point.
* Boundary point.
* Closure.
* Open and closed sets.
* The relative topology.

|-
|


||

12.1-12.3
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|


||

14.1-14.3
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|


||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|


||

16.2-16.4
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:13:50Z

Eduardo.duenez: Editing contents.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.

|-
|

2
||

1.2. Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

6
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-
|

7
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

8
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

9
||

6.1, 6.2, 6.3
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

11
||

7.1, 7.2
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|


||

9.1-9.3
||

Metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.

|-
|


||

10.1-10.3
||

Interior, closure, and boundary.
||

* Accumulation point.
* Boundary point.
* Closure.
* Examples.

|-
|


||

11.1-11.2
||

The topology of metric spaces
||

* Open and closed sets.
* The relative topology.

|-
|


||

12.1-12.3
||

Sequences in metric spaces.
||

* Convergent sequences.
* Sequential characterizations of topological properties.

|-
|


||

14.1-14.3
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|


||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|


||

16.2-16.4
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:09:56Z

Eduardo.duenez: Remove exam weeks.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.

|-
|

2
||

1.2. Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

6
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-
|

7
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

8
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

9
||

6.1, 6.2, 6.3
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

11
||

7.1, 7.2
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|


||

9.1-9.3
||

Metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.

|-
|


||

10.1-10.3
||

Interior, closure, and boundary.
||

* Accumulation point.
* Boundary point.
* Closure.
* Examples.

|-
|


||

12.1-12.3
||

Sequences in metric spaces.
||


|-
|


||

14.1-14.3
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|


||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|


||

16.2-16.4
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:08:30Z

Eduardo.duenez: Progress on topics.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.

|-
|

2
||

1.2. Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

5
||

---
||

Review. First midterm exam.
||


|-
|

6
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-
|

7
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

8
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

9
||

6.1, 6.2, 6.3
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

10
||

---
||

Review. Second midterm exam.
||


|-
|

11
||

7.1, 7.2
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|


||

9.1-9.3
||

Metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.

|-
|


||

10.1-10.3
||

Interior, closure, and boundary.
||

* Accumulation point.
* Boundary point.
* Closure.
* Examples.

|-
|


||

12.1-12.3
||

Sequences in metric spaces.
||


|-
|


||

14.1-14.3
||

Continuity and limits.
||

* Continuous functions between metric spaces.
* Topological products.
* Limits.

|-
|


||

15.1–15.2
||

Compact metric spaces.
||

* Compactness: definition and elementary properties.
* The Extreme Value Theorem.

|-
|


||

16.2-16.4
||

Sequential compactness and the Heine-Borel Theorem.
||

* Sequential compactness.
* Conditions equivalent to compactness of a metric space.
* The Heine-Borel Theorem.

|}

MAT3333

2023-03-25T21:02:05Z

Eduardo.duenez: General metric topology.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.

|-
|

2
||

1.2. Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

5
||

---
||

Review. First midterm exam.
||


|-
|

6
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-
|

7
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

8
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

9
||

6.1, 6.2, 6.3
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

10
||

---
||

Review. Second midterm exam.
||


|-
|

11
||

7.1, 7.2
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|-
|


||

9.1-9.3
||

Metric spaces.
||

* Metric spaces. Examples.
* Equivalent metrics.

|-
|


||

10.1-10.3
||

Interior, closure, and boundary.
||

* Accumulation point.
* Boundary point.
* Closure.
* Examples.

|}

MAT3333

2023-03-25T20:56:57Z

Eduardo.duenez: Up to week 10

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.

|-
|

2
||

1.2. Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

5
||

---
||

Review. First midterm exam.
||


|-
|

6
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-
|

7
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

8
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

9
||

6.1, 6.2, 6.3
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

10
||

---
||

Review. Second midterm exam.
||


|-
|

11
||

7.1, 7.2
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|}

MAT3333

2023-03-25T20:16:17Z

Eduardo.duenez: Up to week 10

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.

|-
|

2
||

1.2. Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

5
||

---
||

Review. First midterm exam.
||


|-
|

6
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-
|

7
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

8
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

9
||

6.1, 6.2, 6.3
||

Compactness and the Extreme Value Theorem.
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|-
|

10
||

7.1, 7.2
||

Limits of real functions.
||

* Limit of a real function at a point.
* Continuity and limits.
* Arithmetic properties of limits.

|}

MAT3333

2023-03-25T20:14:13Z

Eduardo.duenez: Up to week 9

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.

|-
|

2
||

1.2. Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

5
||

---
||

Review. First midterm exam.
||


|-
|

6
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-
|

7
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

8
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|-
|

9
||

6.1, 6.2, 6.3
||

Compactness and the Extreme Value Theorem
||

* Compact subsets of the real line.
* Examples of compact subsets.
* The Extreme Value Theorem.

|}

MAT3333

2023-03-25T20:11:41Z

Eduardo.duenez: Up to week 8

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.

|-
|

2
||

1.2. Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-
|

5
||

---
||

Review. First midterm exam.
||


|-
|

6
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-
|

7
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|-
|

8
||

5.1, 5.2
||

Connectedness and the Intermediate Value Theorem
||

* Connected subsets of ℝ.
* Continuous images of connected sets.
* The Intermediate Value Theorem.

|}

MAT3333

2023-03-25T20:08:47Z

Eduardo.duenez: Up to week 7

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.

|-
|

2
||

1.2. Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Intervals: open, closed, bounded and unbounded.
* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|-

5
||

---
||

Review. First midterm exam.
||


|-

6
||

4.1, 4.2
||

Convergence of real sequences.
||

* Sequences in ℝ.
* Convergent sequences.
* Algebraic operations on convergent sequences.

|-

7
||

4.3, 4.4
||

The Cauchy criterion. Subsequences.
||

* Sufficient conditions for convergence. Cauchy criterion.
* Subsequences.

|}

MAT3333

2023-03-25T19:58:37Z

Eduardo.duenez: Fixed up to week 4.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

Section 1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.

|-
|

2
||

Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
1.2, 2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point (local continuity).
* Continuous functions on ℝ (global continuity).
* Continuous functions on subsets of ℝ.

|}

MAT3333

2023-03-25T19:57:43Z

Eduardo.duenez: Fix row formatting.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
|

1
||

Section 1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.

|-
|

2
||

Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
|
3
||
1.2, 2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

|
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point.
* Continuous functions on ℝ.
* Continuous functions on subsets of ℝ.

|-
|


||


||


||


|-


||


||


||


|-


||


||


||


|}

MAT3333

2023-03-25T19:56:15Z

Eduardo.duenez: Fix row formatting.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
||

1
||

Section 1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.

|-
||

2
||

Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
||
3
||
1.2, 2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

||
4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point.
* Continuous functions on ℝ.
* Continuous functions on subsets of ℝ.

|-
||


||


||


||


|-


||


||


||


|}

MAT3333

2023-03-25T19:54:32Z

Eduardo.duenez: Week 4

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-

1
||

Section 1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.

|-

2
||

Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
3
||
1.2, 2.1, 2.2
||
Basic topological notions in the real line.
||
* Distance.
* Neighborhoods and interior of a set.
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

4
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point.
* Continuous functions on ℝ.
* Continuous functions on subsets of ℝ.
|}

MAT3333

2023-03-25T19:43:01Z

Eduardo.duenez: Week 2

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-

1
||

Section 1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.

|-

2
||

Appendix J.
||

Completeness of the real line. Suprema and infima.
||

* Upper and lower bounds of subsets of ℝ.
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ.
* The Least Upper Bound Axiom (completeness of ℝ).
* The Archimedean property of ℝ.

|-
2
||
1.2
||
Basic topological notions in the real line.
||
* Intervals of the real line.
* Distance.
* Neighborhoods and interior of a set.

|-
2
||
2.1–2.2
||
Elementary topology of the real line.
||
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

3
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point.
* Continuous functions on ℝ.
* Continuous functions on subsets of ℝ.
|}

MAT3333

2023-03-25T19:34:05Z

Eduardo.duenez: Rewriting first couple weeks.

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus.]'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I.]'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-

1
||

Section 1.1. Appendices C, G & H.
||

Operations, order and intervals of the real line.
||

* Arithmetic operations of ℝ.
* Field axioms.
* Order of ℝ.
* Intervals: open, closed, bounded and unbounded.
|-
1
||
1.1-1.2
||
Basic topological notions in the real line.
||
* Intervals of the real line.
* Distance.
* Neighborhoods and interior of a set.

|-
2
||
2.1–2.2
||
Elementary topology of the real line.
||
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

3
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point.
* Continuous functions on ℝ.
* Continuous functions on subsets of ℝ.
|}

MAT3333

2023-03-25T19:24:04Z

Eduardo.duenez: Added textbook information

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry:'''
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites:'''
MAT 1224 and MAT 3003.

'''Sample textbooks:'''
* John M. Erdman, ''[https://bookstore.ams.org/view?ProductCode=AMSTEXT/32 A Problems Based Course in Advanced Calculus].'' Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
* Jyh-Haur Teh, ''[https://leanpub.com/advancedcalculusi-1 Advanced Calculus I].'' ISBN-13: 979-8704582137.

==Topics List==
(Section numbers refer to Erdman's book.)

{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
1
||
1.1-1.2
||
Basic topological notions in the real line.
||
* Intervals of the real line.
* Distance.
* Neighborhoods and interior of a set.

|-
2
||
2.1–2.2
||
Elementary topology of the real line.
||
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

3
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point.
* Continuous functions on ℝ.
* Continuous functions on subsets of ℝ.
|}

MAT3333

2023-03-25T19:12:17Z

Eduardo.duenez: Week 3

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry''':
MAT 333 Fundamentals of Analysis and Topology.
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites''': MAT 1224 and MAT 3003.

'''Sample textbook''': Introduction to Real Analysis by Bartle and Sherbert

==Topics List==
{| class="wikitable sortable"
! Week !! Sections !! Topics !! Student Learning Outcomes
|-
1
||
1.1-1.2
||
Basic topological notions in the real line.
||
* Intervals of the real line.
* Distance.
* Neighborhoods and interior of a set.

|-
2
||
2.1–2.2
||
Elementary topology of the real line.
||
* Open subsets of ℝ.
* Closed subsets of ℝ.

|-

3
||

3.1–3.3
||

Continuous functions on subsets of the real line.
||

* Continuity at a point.
* Continuous functions on ℝ.
* Continuous functions on subsets of ℝ.
|}

MAT3333

2023-03-25T19:05:39Z

Eduardo.duenez: Weeks 1 & 2.

MAT3333

2023-03-25T18:53:58Z

Eduardo.duenez: Week i

MAT3333

2023-03-25T18:50:17Z

Eduardo.duenez: Formatting preamble

==Course name==
MAT 3333 Fundamentals of Analysis and Topology.

'''Catalog entry''':
MAT 333 Fundamentals of Analysis and Topology
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

'''Prerequisites''': MAT 1224 and MAT 3003.

'''Sample textbook''': Introduction to Real Analysis by Bartle and Sherbert

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Student Learning Outcomes

|-

|}

MAT3333

2023-03-25T18:49:07Z

Eduardo.duenez: MAT3333 page created.

'''Catalog entry''':MAT 333 Fundamentals of Analysis and Topology
Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
Topology of the real line. Introduction to point-set topology.

''Prerequisites'': MAT 1224 and MAT 3003.

''Sample textbook'': Introduction to Real Analysis by Bartle and Sherbert

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Student Learning Outcomes

|-

|}

Main Page

2023-03-25T18:44:47Z

Eduardo.duenez: Removed space from MAT3313 Logic Comput.

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)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2233]] Linear Algebra

===Data & Applied Science Core===
* [[MDC1213]] Mathematics, Data, AI and the Modern World
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2243]] Applied Linear Algebra (3 credit hours)
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Statistics II (statistical inference)
* [[MDC4413]] Data Analytics

===Math Major===
* [[MAT3003]] Discrete Mathematics
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability
* <del>MAT3013 Foundations of Mathematics </del> Replaced by [[MAT3003]] Discrete Mathematics
* [[MAT3203]] Linear Algebra II
* <del>MAT3213 Foundations of Analysis</del> Replaced by [[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
* [[MAT4373]] Mathematical Statistics I

===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 M.Sc. Studies ===
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 and Algebra sequences in the following combinations:
** [[MAT5173]] Algebra I & [[MAT5183]] Algebra II.
** [[MAT5203]] Analysis I & [[MAT5213]] Analysis II
** [[MAT5173]] Algebra & [[MAT5203]] Analysis I.
* [[MAT5283]] Linear Algebra (fall odd years)
* [[MAT5423]] Discrete Mathematics I (fall even years)
* [[MAT4373]]/[[MAT5373]] Mathematical Statistics I (fall even years)

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (fall, even years) (Pure, Applied tracks)
* [[MAT5123]] Cryptography (spring even years) (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (spring odd years) (Pure, Applied tracks))
* [[MAT5213]] Analysis II (spring even years) (Pure track)
* [[MAT5113]] Computing for Mathematics (spring even years) (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (spring odd years) (Pure, Applied tracks)
* [[MAT4383]]/[[MAT5383]] Mathematical Statistics II (fall even years) (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT4423/MAT5443]] Logic and Computability
* [[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 ===
* [[MAT4153]]/[[MAT5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===

MAT3313

2023-03-25T18:44:26Z

Eduardo.duenez: Renamed page to remove space.

'''Catalog description'''

''Prerequisites'': MAT 1214 and MAT 3013.

''Content'': Axiomatizations of propositional logic, axiomatizations of first-order logic, completeness and compactness, structures, compactness and the Henkin method of constructing models by constants, ultraproducts and real-valued logic.

Main Page

2023-03-25T18:43:24Z

Eduardo.duenez: Link to 3333 Found Anal Topo

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)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2233]] Linear Algebra

===Data & Applied Science Core===
* [[MDC1213]] Mathematics, Data, AI and the Modern World
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2243]] Applied Linear Algebra (3 credit hours)
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Statistics II (statistical inference)
* [[MDC4413]] Data Analytics

===Math Major===
* [[MAT3003]] Discrete Mathematics
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability
* <del>MAT3013 Foundations of Mathematics </del> Replaced by [[MAT3003]] Discrete Mathematics
* [[MAT3203]] Linear Algebra II
* <del>MAT3213 Foundations of Analysis</del> Replaced by [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT3333]] Fundamentals of Analysis and Topology
* [[MAT 3313]] 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
* [[MAT4373]] Mathematical Statistics I

===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 M.Sc. Studies ===
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 and Algebra sequences in the following combinations:
** [[MAT5173]] Algebra I & [[MAT5183]] Algebra II.
** [[MAT5203]] Analysis I & [[MAT5213]] Analysis II
** [[MAT5173]] Algebra & [[MAT5203]] Analysis I.
* [[MAT5283]] Linear Algebra (fall odd years)
* [[MAT5423]] Discrete Mathematics I (fall even years)
* [[MAT4373]]/[[MAT5373]] Mathematical Statistics I (fall even years)

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (fall, even years) (Pure, Applied tracks)
* [[MAT5123]] Cryptography (spring even years) (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (spring odd years) (Pure, Applied tracks))
* [[MAT5213]] Analysis II (spring even years) (Pure track)
* [[MAT5113]] Computing for Mathematics (spring even years) (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (spring odd years) (Pure, Applied tracks)
* [[MAT4383]]/[[MAT5383]] Mathematical Statistics II (fall even years) (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT4423/MAT5443]] Logic and Computability
* [[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 ===
* [[MAT4153]]/[[MAT5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===

Main Page

2023-03-25T18:42:36Z

Eduardo.duenez: Removed hyperlinks to removed courses 3013 & 3213.

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)
* [[MAT1224]] Calculus II (4 credit hours)
* [[MAT2214]] Calculus III (4 credit hours)
* [[MAT2233]] Linear Algebra

===Data & Applied Science Core===
* [[MDC1213]] Mathematics, Data, AI and the Modern World
* [[MAT1213]] Calculus I (3 credit hours)
* [[MAT1223]] Calculus II (3 credit hours)
* [[MAT2213]] Calculus III (3 credit hours)
* [[MAT2243]] Applied Linear Algebra (3 credit hours)
* [[MAT4133]]/[[MAT5133]] Mathematical Biology
* [[MAT4143]]/[[MAT5143]] Mathematical Physics
* [[MAT4373]]/[[MAT5373]] Mathematical Statistics I (discrete & continuous PDFs)
* [[MAT4383]]/[[MAT5383]] Mathematical Statistics II (statistical inference)
* [[MDC4413]] Data Analytics

===Math Major===
* [[MAT3003]] Discrete Mathematics
* [[MAT1313]] Algebra and Number Systems
* [[MAT2313]] Combinatorics and Probability
* <del>MAT3013 Foundations of Mathematics </del> Replaced by [[MAT3003]] Discrete Mathematics
* [[MAT3203]] Linear Algebra II
* <del>MAT3213 Foundations of Analysis</del> Replaced by [[MAT3333]] Foundamentals of Analysis and Topology
* [[MAT3233]] Modern Algebra
* [[MAT 3313]] 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
* [[MAT4373]] Mathematical Statistics I

===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 M.Sc. Studies ===
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 and Algebra sequences in the following combinations:
** [[MAT5173]] Algebra I & [[MAT5183]] Algebra II.
** [[MAT5203]] Analysis I & [[MAT5213]] Analysis II
** [[MAT5173]] Algebra & [[MAT5203]] Analysis I.
* [[MAT5283]] Linear Algebra (fall odd years)
* [[MAT5423]] Discrete Mathematics I (fall even years)
* [[MAT4373]]/[[MAT5373]] Mathematical Statistics I (fall even years)

=== Qualifying Examination Tracks ===
* [[MAT5183]] Algebra II (fall, even years) (Pure, Applied tracks)
* [[MAT5123]] Cryptography (spring even years) (Pure, Applied tracks)
* [[MAT5323]] Cryptography II (spring odd years) (Pure, Applied tracks))
* [[MAT5213]] Analysis II (spring even years) (Pure track)
* [[MAT5113]] Computing for Mathematics (spring even years) (Pure, Applied tracks)
* [[MAT5433]] Discrete Mathematics II (spring odd years) (Pure, Applied tracks)
* [[MAT4383]]/[[MAT5383]] Mathematical Statistics II (fall even years) (Applied tracks)

=== M.Sc. Track in Pure Mathematics ===
* [[MAT4423/MAT5443]] Logic and Computability
* [[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 ===
* [[MAT4153]]/[[MAT5153]] Data Analytics
* [[AIM 5113]] Introduction to Industrial Mathematics
* [[MAT 5113]] Computing for Mathematics
* [[MAT 5653]] Differential Equations I
* [[MAT 5673]] Partial Differential Equations

=== M.Sc. in Mathematics Education ===