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UTSA Department of Mathematics

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Undergraduate Studies

STEM Core

• MAT1073 College Algebra for Scientists and Engineers
• MAT1093 Precalculus
• MAT1193 Calculus for Biosciences
• MAT1214 Calculus I (4 credit hours)
• MAT1213 Calculus I (3 credit hours)
• MAT1224 Calculus II (4 credit hours)
• MAT1223 Calculus II (3 credit hours)
• MAT2214 Calculus III (4 credit hours)
• MAT2213 Calculus III (3 credit hours)
• MAT2233 Linear Algebra

Minor in Mathematics

To receive a minor, students must complete at least 18 semester credit hours, including 6 hours at the upper-division level at UTSA, and must achieve a grade point average of at least 2.0 (on a 4.0 scale) on all work used to satisfy the requirements of a minor. See UTSA's Undergraduate Catalog

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

Data & Applied Science Core

Lower Division

• MDC1213 Sociocultural Foundations of Mathematics, Data Science, and Computing
• MAT2253 Applied Linear Algebra (3 credit hours)

Upper Division

• MAT4133/MAT5133 Mathematical Biology
• MAT4143/MAT5143 Mathematical Physics 1
• MAT4XXX/MAT5XXX Mathematical Physics 2
• MAT4XXX/MAT5XXX Introduction to Quantum Information Science and Engineering
• MAT4373/MAT5373 Mathematical Foundations of Statistics I (discrete & continuous PDFs)
• MAT4383/MAT5383 Mathematical Foundations of Statistics II (statistical inference)
• MDC4153/MDC5153 Mathematical Foundations of Data Analytics

Math Major

Lower Division

• MAT1313 Algebra and Number Systems
• MAT2313 Combinatorics and Probability

Upper Division

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

Business

• MAT1053 Algebra for Business
• MAT1133 Calculus for Business

Math for Liberal Arts

• MAT1043 Introduction to Mathematics

Elementary Education

• MAT1023 College Algebra
• MAT1153 Essential Elements in Mathematics I
• MAT1163 Essential Elements in Mathematics II

General Math Studies

• MAT3233 Modern Algebra

Graduate Studies

Core Courses

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

• MAT5283 Linear Algebra
• MAT5253 Real Analysis I
• MAT5603 Numerical Analysis
• MAT5603 Differential Equations I

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

Qualifying Track: Mathematical Biology

• MAT 5133 Mathematical Biology

One of the following:

• MAT 5323 Mathematical Modeling
• Optimal Control and Calculus of Variations*.

Qualifying Track: Mathematics of Information, Data and Communications

• MAT 5123) Introduction to Cryptography
• MAT 5323 Cryptography II*,
• MAT 5433 Graph Theory*, Data Analytics Mathematic of AI*,
• MAT 5153 Data Analytics
• MAT 5XXX Quantum Information
• MAT 5XXX Mathematics of AI

Qualifying Track: Mathematics of Information, Data and Communications

• MAT5183 Algebra II (Pure, Applied tracks)
• MAT5123 Cryptography (Pure, Applied tracks)
• MAT5323 Cryptography II (Pure, Applied tracks))
• MAT5213 Analysis II (Pure track)
• MAT5113 Computing for Mathematics (Pure, Applied tracks)
• MAT5433 Discrete Mathematics II (Pure, Applied tracks)
• MAT5383 Mathematical Statistics II (Applied tracks)
• MAT58XX Mathematics of Quantum Computation (Pure, applied tracks)

Qualifying Track: Analysis

• MAT5203 Real Analysis I
• [[MAT5213] Real Analysis II
• MAT5223 Complex Analysis I
• MAT5233Complex Analysis II
• MAT5553 Harmonic Analysis
• MAT5553 Functional Analysis.

Qualifying Track: Algebra-Cryptography

• MAT 5173 Abstract Algebra I
• MAT 5183 Abstract Algebra II
• MAT 5123 Introduction to Cryptography
• MAT 5YYY Cryptography II*