UTSA MS in Mathematics -- Degree Flowchart (2026 graduate catalog)

Last update: July 20, 2026

UTSA MS in Mathematics -- Degree Flowchart (2026 graduate catalog) START Start MS in Math RAMP Optional ramp courses if needed (consult GAR): • MAT 5033 Foundations and Fundamental Concepts  of Mathematics • MAT 5103 Introduction to Mathematical Analysis START->RAMP CORE Core Courses (15) • MAT 5653 Differential Equations I • MAT 5283 Linear Algebra • MAT 5203 Theory of Functions of a Real Variable I • MAT 5173 Algebra I Choose one course from: • MAT 5423 Discrete Mathematics I • MAT 5603 Numerical Analysis • MAT 5053 Perspectives on Teaching START->CORE RAMP->CORE CHOOSE_CONC Choose one of four concentrations (9 credits in each) CORE->CHOOSE_CONC AIM Applied-Industrial Mathematics (9) • AIM 5113 Introduction to Industrial Mathematics • AIM 6943 Internship and Research Project • MAT 5323 Mathematical Modeling CHOOSE_CONC->AIM MATHED Mathematics Education (9) • MAT 5963 Introduction to Mathematics Education  Research • MAT 5023 Problem-Solving Seminar • MAT 5043 Euclidean and Non-Euclidean Geometry CHOOSE_CONC->MATHED GENSTUDIES General Mathematical Studies (9) Complete 9 hours of graduate-level coursework in the Department of Mathematics. Must be approved by the Graduate Advisor of Record. CHOOSE_CONC->GENSTUDIES PUREMATH Pure Mathematics (9) Complete one Qualifying Exam Track plus one grad-level math course. If a student took a sequenced course in Section A (MAT 5123, MAT 5173, MAT 5203, or MAT 5423), they should select a track that includes the second part of that sequence or MAT 5663. If a student is interested in continuing on to a PhD program, it is strongly recommended to complete two Qualifying Exam Tracks. CHOOSE_CONC->PUREMATH CHOOSE_OPTION Choose one of the following options (6 credits total) AIM->CHOOSE_OPTION MATHED->CHOOSE_OPTION GENSTUDIES->CHOOSE_OPTION QUALTRACKS Qualifying Exam Tracks Note: A track is called complete once a student passes two courses in the track and the qualifying exam for that coursework. Courses marked with * were not found under that course number in UTSA's current graduate catalog listing as of this flowchart's last verification and should be reconfirmed with the Department of Mathematics. ▸ Mathematics of Life Sciences: • MAT 5133 Mathematical Biology • MAT 5323 Mathematical Modeling • MAT 5643 Optimal Control and Calculus of Variations ▸ Scientific Computing: • MAT 5163 Probability Theory and Computing • MAT 5293 Numerical Linear Algebra • MAT 5603 Numerical Analysis • MAT 5613 Numerical Solutions of Differential Equations ▸ Mathematics of Information, Data and Communications: • MAT 5143 Cryptography II • MAT 5123 is a prerequisite • MAT 5153 Data Analytics ▸ Differential Equations: • MAT 5663 Differential Equations II • MAT 5653 is a prerequisite • MAT 5673 Partial Differential Equations I • MAT 5683 Partial Differential Equations II ▸ Foundations of Mathematics: • MAT 5243 General Topology I • MAT 5253 General Topology II • MAT 5433 Discrete Mathematics II • MAT 5423 is a prerequisite • MAT 5453 Quantum Logic ▸ Analysis: • MAT 5213 Theory of Functions of a Real Variable II • MAT 5203 is a prerequisite • MAT 5223 Theory of Functions of a Complex Variable I • MAT 5233 Theory of Functions of a Complex Variable II • MAT 5553 Harmonic Analysis • MAT 5403 Functional Analysis I • MAT 5413 Functional Analysis II ▸ Algebra-Cryptography: • MAT 5143 Cryptography II • MAT 5123 is a prerequisite • MAT 5183 Algebra II • MAT 5173 is a prerequisite ▸ Geometry-Topology: • MAT 5243 General Topology I • MAT 5253 General Topology II • MAT 5343* Differential Geometry ▸ Discrete Math & Logic: • MAT 5433 Discrete Mathematics II • MAT 5423 is a prerequisite • MAT 5453 Quantum Logic ▸ Mathematical Physics: • MAT 5343* Differential Geometry • MAT 5453 Quantum Logic • MAT 5863 Mathematical Physics • MAT 5873* Mathematical Physics II • MAT 6003 • QST 6003 Introduction to Quantum Information ▸ Mathematics Education: • MAT 5053 Perspectives on Teaching • MAT 5963 Introduction to Mathematics Education Research PUREMATH->QUALTRACKS PUREMATH->CHOOSE_OPTION NONTHESIS Non-thesis With GAR advice and approval, choose the requisite number of graduate-level courses from Mathematics or related disciplines to complete their degree. Additionally, candidates must complete one of the following options: • (i) One qualifying examination that has not already been completed (Pure Math conc, or General Math Studies conc) • (ii) One qualifying examination plus an Industry Internship (Applied Mathematics Concentration) • (iii) Qualifying examination in Mathematics Education track; optional: one additional qualifying examination (Mathematics Education Concentration) CHOOSE_OPTION->NONTHESIS THESIS Preparing and defending a Master's thesis Candidates who choose this option must be enrolled for at least six hours of Master's thesis (MAT 6983). The thesis must be on a research project and must be finalized by a public defense. CHOOSE_OPTION->THESIS GRADUATION Graduation NONTHESIS->GRADUATION THESIS->GRADUATION NOTE_DEPTH Note: Qualifying Exam Tracks can exhibit depth (when a 2-course sequence is completed), or breadth (when 2 non- sequenced courses are completed). If a student's desire is to continue to a doctoral program in one of the concentration areas, then depth is preferred, when possible. For the pure math concentration, completing at least one track showing depth is required. NOTE_COMPEXAM Note on what defines a Comprehensive Exam in the Department of Mathematics Non-thesis option: 2 qualifying exams for Pure or General Math; 1 qualifying exam plus an Industry Internship for Applied Math; Math Ed qualifying exam for Math Ed. Thesis option: the successful completion and defense of the thesis.

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