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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
• MAT4813/MAT5863 Mathematical Physics 1
• MAT4JME/MAT5JME Mathematical Physics 2
• MAT4XYX/MAT5XYX Introduction to Quantum Information Science and Engineering
• MAT4373/MAT5373 Mathematical Foundations of Statistics I (discrete & continuous PDFs)
• MAT4383/MAT5383 Mathematical Foundations of Statistics II (statistical inference)
• MDC4153/MDC5153 Mathematical Foundations of Data Analytics

Math Major

Lower Division

• MAT1313 Algebra and Number Systems
• MAT2313 Combinatorics and Probability

Upper Division

• MAT3003 Discrete Mathematics
• 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
• MAT4YYY/MAT5YYY Mathematics of AI

Business

• MAT1053 Algebra for Business
• MAT1133 Calculus for Business

Math for Liberal Arts

• MAT1043 Introduction to Mathematics

Elementary Education

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

General Math Studies

• MAT3233 Modern Algebra

Graduate Studies

Core Courses

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

• MAT5283 Linear Algebra
• MAT5203 Real Analysis I
• MAT 5173 Abstract Algebra I
• MAT5603 Differential Equations I

Choose one of the following two:

• MAT5123 Introduction to Cryptography
• MAT5603 Numerical Analysis

Qualifying Exam Tracks

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

Qualifying Exam Track: Algebra-Cryptography

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

Qualifying Track: Mathematics of Information, Data and Communications

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

Qualifying Exam Track: Scientific Computing

• MAT5603 Numerical Analysis
• MAT5293 Numerical Linear Algebra
• MAT5XYX Quantum Information Science and Engineering
• MAT5163 Probability and Computing

Qualifying Exam Track: Analysis

• MAT5203 Real Analysis I
• MAT5213 Real Analysis II
• MAT5223 Complex Analysis I
• MAT5233 Complex Analysis II
• MAT5553 Harmonic Analysis
• MAT5553 Functional Analysis

Qualifying Exam Track: Differential Equations

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

Qualifying Exam Track: Discrete Mathematics and Logic

• MAT5423 Discrete Mathematics
• MAT5433 Discrete Mathematics II (Graph Theory)
• MAT5443 Logic and Computability
• MAT5453 Quantum Logic

Qualifying Exam Track: Topology and Geometry

• MAT5243 Topology I
• MAT5253 Topology II
• Differential Geometry

Qualifying Exam Track: Mathematical Physics

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

Qualifying Exam Track: Mathematics of Life Sciences

• MAT5133 Mathematical Biology
• MAT5323 Mathematical Modeling (Systems Biology)