Mathematics (MATH)

MATH 1101. Math Education Intervention.

This course provides supplemental mathematics instruction designed to strengthen students’ readiness for entry‑level college mathematics. Students receive targeted support based on college‑readiness indicators or other diagnostic information, allowing instruction to be tailored to individual learning needs. The course focuses on reviewing and reinforcing key pre‑requisite mathematical concepts, offering structured practice and guided problem solving. Students enrolled in 1000‑level mathematics courses may use this class to enhance their understanding, build confidence, and improve foundational skills necessary for success in their credit‑bearing coursework. Instruction emphasizes clear explanations, practice opportunities, and individualized learning strategies. Prerequisite: Departmental Approval. Corequisite: MATH 1312 or MATH 1315 or MATH 1316 or MATH 1319 with a grade of "D" or better.

MATH 1300. Elementary Algebra.

This course reviews and strengthens foundational mathematical skills necessary for college-level mathematics. Topics include number concepts, operations with fractions and decimals, percents, order of operations, algebraic expressions, solving linear equations, proportional reasoning, and introductory geometry concepts. Emphasis is placed on numerical fluency, algebraic reasoning, and problem-solving strategies that support success in subsequent coursework. Credit earned for this course does not apply toward degree requirements Credit earned for this course does not apply toward degree requirements.

MATH 1311. Intermediate Algebra.

This course strengthens foundational algebraic concepts in preparation for College Algebra. Topics include linear equations and inequalities, rational expressions, exponents and radicals, quadratic equations, graphing techniques, and application problems. Emphasis is placed on symbolic manipulation, equation solving, and interpretation of algebraic models in quantitative contexts. The course is designed for students who have graduated from high school with no more than the minimum mathematics requirements or for students who have been away from mathematics for a number of years. Credit earned for this course does not apply toward degree requirements. Prerequisites: A Texas Success Initiative Assessment (TSIA) 2.0 score of 945 or more.

MATH 1312. College Statistics and Algebra.

This course integrates algebraic techniques and statistical reasoning. Topics include linear and quadratic equations and inequalities, functions and their graphs, logarithmic functions, systems of equations, and mathematical modeling. Statistical concepts include data collection and presentation, probability, normal distributions, linear and quadratic regression, confidence intervals, and hypothesis testing. Emphasis is placed on quantitative reasoning, interpretation of data, and application of algebraic and statistical methods in contextual settings. This course does not substitute for MATH 1315 as a prerequisite. Prerequisite: College Readiness in Mathematics according to the TSI regulations.

MATH 1315. College Algebra.

This course is designed to provide introductory knowledge in algebra and strengthen the skills that students will use in future STEM courses. Topics include solving equations and inequalities, analyzing properties of functions, applying graphing techniques, solving systems of equations both directly and by utilizing matrices, answering application problems by creating and solving related equations, and other algebraic concepts as time permits. The functions covered include linear, quadratic, rational, polynomial, exponential, and logarithmic. Prerequisite: College Readiness in Mathematics according to the TSI regulations.

MATH 1316. Survey of Contemporary Mathematics.

This course introduces contemporary mathematical ideas and quantitative reasoning intended for non-STEM (Science, Technology, Engineering, and Mathematics) majors. Topics include introductory treatments of sets and logic, financial mathematics, probability, statistics, voting theory, and related applications. Number sense, proportional reasoning, estimation, technology, and communication are integrated throughout the course to support interpretation and use of quantitative information in everyday and civic contexts. Prerequisite: College Readiness in Mathematics according to TSI regulations.

MATH 1317. Plane Trigonometry.

This course introduces students to the fundamental concepts and techniques of plane trigonometry. Topics include right‑triangle trigonometry, angle measurement in degrees and radians, trigonometric functions and their graphs, inverse trigonometric functions, and identities such as sum, difference, multiple‑angle, and half‑angle formulas. Students also study trigonometric equations, the Law of Sines and Law of Cosines, and applications involving general triangles and complex numbers in trigonometric form. Emphasis is placed on developing computational skills, interpreting trigonometric relationships, and applying concepts to mathematical and real‑world problem solving. Prerequisite: [MATH 1315 with a grade of "C" or better] or [Accuplacer College Mathematics score of 86 or better] or [Compass College Algebra score of 46 or better] or [Next-Generation Advanced Algebra and Functions Test of 263 or better].

MATH 1319. Mathematics for Business and Economics I.

This course is a basic introduction to the mathematics of business and economics. Topics include the theories of elementary functions and their graphs, including polynomial, exponential, logarithmic, and rational functions with an emphasis on application of these functions to situations in business, economics, and the social sciences. These applications include the mathematics of finance, including simple and compound interest and annuities; systems of linear equations; matrices; linear programming; basic set theory; and probability, including expected value. Prerequisite: College Readiness in Mathematics according to the TSI regulations.

MATH 1329. Mathematics for Business and Economics II.

This course is a basic introduction to the exploration of limits, continuity, differentiation, and integration. Topics include conceptual and theoretical definitions, but with an aim towards understanding economic and social science mathematical applications. This includes studying algebraic, exponential, and logarithmic functions as well as covering the theories of monotonicity, concavity, optimization, graph sketching, method of substitution, and basic multivariable functions. Applications may include marginal analysis, end behavior of financial functions, profit optimization, and diminishing returns. Prerequisite: [MATH 1315 or MATH 1319 or MATH 2321 or MATH 2417 with a grade of "C" or better] or [ACT Mathematics score of 27 or better] or [SAT Math Section score of 600 or better] or [Accuplacer College Mathematics score of 86 or better] or [Compass College Algebra score of 46 or better] or [Next-Generation Advanced Algebra and Functions Test of 263 or better].

MATH 2311. Principles of Mathematics I.

This course develops foundational mathematical concepts and reasoning essential for teaching elementary and middle school mathematics. Topics include the conceptual development of the base-ten numeration system, the structure and properties of whole numbers, integers, rational numbers, and decimals, operations and their algorithms, proportional reasoning, and introductory number theory including factors, multiples, prime numbers, greatest common factor, and least common multiple. Emphasis is placed on mathematical reasoning, justification, and connections among representations. Prerequisite: MATH 1312 or MATH 1315 or MATH 1319 or MATH 2321 or MATH 2417 with a grade of “C” or better.

MATH 2312. Informal Geometry.

This course develops foundational concepts of geometry, measurement, probability, and statistics with emphasis on geometry and measurement for elementary and middle grades. Topics include points, lines, planes, polygons, circles, polyhedra, congruence and similarity, geometric transformations, constructions, measurement systems and units, perimeter, area, surface area, volume, proportional reasoning, and introductory probability and data analysis. The course emphasizes reasoning, justification, and connections among geometric representations. Prerequisite: MATH 2311 with a grade of “C” or better.

MATH 2321. Calculus for Life Sciences I.

This course introduces differential and integral calculus with an emphasis on applications relevant to the life sciences. Topics include graphs, limits, derivatives of algebraic, exponential, logarithmic, and trigonometric functions, basic techniques of integration, and interpretation of calculus concepts in biological contexts. Mathematical models drawn from population dynamics, rates of change, and related life science applications illustrate how calculus is used to analyze quantitative relationships in biological systems. Prerequisite: [MATH 1315 or MATH 1319 or MATH 1329 or MATH 2417 with a grade of "C" or better] or [ACT Mathematics score of 24 or better] or [New ACT Mathematics score of 25 or better] or [SAT Math Section score of 550 or better] or [Accuplacer College Mathematics score of 86 or better] or [Compass College Algebra score of 46 or better] or [Next-Generation Advanced Algebra and Functions Test of 263 or better].

MATH 2328. Elementary Statistics.

This course is an algebra-based introduction to descriptive statistics, interpretation of data, random sampling, design of experiments, probability, and the Central Limit Theorem. Topics include graphical and numerical summaries of data, probability models, discrete and continuous random variables, binomial and normal distributions, sampling distributions, confidence intervals, hypothesis testing, and simple linear regression. Emphasis is placed on statistical reasoning, interpretation of results, and application of inferential methods to data arising in scientific and social contexts. Prerequisite: [MATH 1312 or MATH 1315 or MATH 1319 with a grade of "C" or better] or [MATH 1329 or 2321 or MATH 2417 or MATH 2471 with a grade of "D" or better] or [ACT Mathematics score of 24 or better] or [New ACT Mathematics score of 25 or better] or [SAT Math Section score of 550 or better] or [Next-Generation Advanced Algebra and Functions Test of 263 or better].

MATH 2331. Calculus for Life Science II.

This course is an extension of MATH 2321 and develops additional techniques and applications of integral calculus for students in the life sciences. Topics include methods of integration, applications of definite integrals, volumes, improper integrals, first-order differential equations and population models, probability, and discrete and continuous probability distributions. Emphasis is placed on modeling biological processes, interpreting accumulation and growth phenomena, and applying calculus and probability concepts to life science contexts. Prerequisite: [MATH 2321 with a grade of “C” or better] or MATH 2471 with a grade of “D” or better.

MATH 2358. Discrete Mathematics I.

This course introduces discrete mathematical structures commonly encountered in computing and mathematical reasoning. Topics include propositional and predicate logic, methods of proof, mathematical induction, sets, functions, sequences and summations, elementary number theory including divisibility, integer representation and modular arithmetic, and introductory graph theory including trees, weighted graph algorithms, search algorithms and connectivity. Emphasis is placed on rigorous reasoning, construction of formal proofs, and the analysis of discrete structures fundamental to computer science and related disciplines. Prerequisite: [MATH 1315 or MATH 1329 with a grade of "C" or better] or [MATH 2417 or MATH 2471 with a grade of “D” of better].

MATH 2393. Calculus III.

This course extends calculus to functions of several variables and to vector-valued functions. Topics include vectors and the geometry of space, functions of multiple variables, partial derivatives and extreme values, multiple integrals, and vector fields. Line and surface integrals are introduced, along with Green’s Theorem, Stokes’ Theorem, divergence and curl, and the Divergence Theorem. Applications emphasize the use of multivariable calculus to model and analyze problems arising in scientific and engineering contexts. Prerequisite: MATH 2472 with a grade of "C" or better.

MATH 2417. Pre-Calculus Mathematics.

This course develops the mathematical concepts needed to prepare students for calculus through the study of functions and their representations. Topics include rates of change, exponential and logarithmic functions, trigonometric functions and their applications, polar coordinates, vectors, and parametric equations. Emphasis is placed on understanding functional relationships, graphical and algebraic connections, and mathematical models that arise in applied contexts to strengthen problem solving and better prepare students for further study in mathematics, science, and engineering. Prerequisites: [MATH 1315 or MATH 1319 with a grade of C or better] or [ACT Mathematics score of 24 or better] or [New ACT Mathematics score of 25 or better] or [SAT Math Section score of 550 or better] or [Accuplacer College Mathematics score of 86 or better] or [Compass College Algebra score of 46 or better] or [Next-Generation Advanced Algebra and Functions Test of 263 or better].

MATH 2471. Calculus I.

This course introduces the fundamental concepts of differential and integral calculus for functions of one variable. It explores limits and continuity, differentiation and its applications, basic techniques of integration, and the Fundamental Theorem of Calculus. Through analytical, graphical, and numerical approaches, this course strengthens problem solving and mathematical reasoning skills, preparing students for further study in mathematics, science, engineering, and other quantitative disciplines that support academic success and professional readiness in STEM fields worldwide today. Prerequisites: [MATH 2417 with a grade of C or better] or [ACT Mathematics score of 27 or better] or [SAT Math Section score of 600 or better] or [Accuplacer College Mathematics score of 103 or better] or [Compass Trigonometry score of 46 or better] or [Next-Generation Advanced Algebra and Functions Test score of 276 or better].

MATH 2472. Calculus II.

This course continues the study of differential and integral calculus from MATH 2471. Topics include advanced techniques of integration, improper integrals, parametric equations, polar coordinates, and applications of calculus to physical and mathematical problems. Additional topics include sequences and series, including convergence tests and power series representations, and an introduction to partial derivatives. Emphasis is placed on connecting algebraic, graphical, and analytical perspectives to deepen understanding of calculus concepts that support further study in mathematics, science, and engineering. Prerequisite: MATH 2471 with a grade of “C” or better.

MATH 2473. Integral Calculus with Multivariables and Series.

This course is a continuation of differential and integral calculus. The topics covered include methods of integration, sequences and series, and derivatives and integrals of multivariable functions. The methods of integration include partial fraction decompositions, trigonometric substitutions, integration by parts, as well as the numerical method of Simpson's Rule. The emphasized applications of these topics to physics and engineering include the computations of volume, work, hydrostatic force, and centers of mass, as well as the approximation of functions via power series. Prerequisite: MATH 2471 with a grade of "C" or better.

MATH 3305. Introduction to Probability and Statistics.

This course provides a calculus-based introduction to probability and statistics. Topics include sample spaces, counting techniques, probability rules, conditional probability, the law of total probability and Bayes’ theorem, discrete and continuous random variables, probability distributions, expectation and variance, joint distributions, covariance and correlation, common distributional models, moments, and moment-generating functions. Emphasis is placed on probabilistic reasoning, mathematical modeling, and interpretation of results in applied contexts, including scientific, economic, and engineering applications with data-driven decision making. Prerequisite: MATH 2472 with a grade of “C” or better.

MATH 3306. Introduction to Statistical Methods.

This course provides a calculus-based introduction to probability and statistical methods. Topics include sample spaces, counting techniques, probability rules, conditional probability, discrete and continuous random variables, common probability distributions, expectation and variance, joint distributions, covariance and correlation, sampling distributions, confidence intervals, hypothesis testing, and moment-generating functions. Applications involve probabilistic modeling, statistical inference, and analysis of quantitative and qualitative data. Prerequisite: MATH 2472 with a grade of "C" or better and a 2.75 overall GPA.

MATH 3315. Foundations of Geometry.

This course provides a foundational study of Euclidean geometry and an introduction to selected non‑Euclidean geometries. Students explore geometric vocabulary, parallel line theorems, congruence, similarity, polygons, circles, measurement formulas, and Euclidean constructions, as well as transformations, isometries, and introductory analytic geometry. Additional topics include hyperbolic, taxicab, and spherical geometries. The course emphasizes reasoning, proof, and the analysis of geometric structures using classical tools and dynamic geometry software. Historical perspectives are integrated to support understanding of the development of geometric thought. Designed primarily for students preparing for mathematics teacher certification, the course strengthens conceptual understanding, visualization, and mathematical communication; it does not apply toward a minor in mathematics. Prerequisite: MATH 2321 or MATH 2471 with a grade of “C” or better.

MATH 3323. Differential Equations.

This course provides an introduction to ordinary differential equations with emphasis on first‑ and second‑order equations and their applications. Students study separable, linear, and exact equations; direction fields; second‑order linear equations with constant coefficients; nonhomogeneous equations; numerical approximation methods; power series solutions; and Laplace transform techniques. The course highlights analytical, qualitative, and computational approaches for solving ODEs. Applications include physical and geometric interpretations such as spring–mass systems, oscillations, and mathematical models arising in science and engineering. Prerequisite: MATH 2472 or MATH 2473 with a grade of “C” or better.

MATH 3324. Applied Multivariate Statistics.

This course introduces students to applied multivariate statistical methods, including multiple regression, analysis of variance, logistic regression, and introductory time series techniques. Students learn to use statistical software to organize data, fit appropriate models, assess assumptions, and interpret results. Emphasis is placed on understanding model limitations, selecting appropriate procedures, and applying methods across a variety of empirical contexts. The course develops practical analytic skills while reinforcing fundamental statistical concepts. Students gain experience evaluating multivariate relationships, diagnosing model performance, and communicating statistical findings clearly and accurately. Prerequisite: [MATH 2471 or MATH 2321] and [MATH 2328 or MATH 3305] with a “C” or better.

MATH 3325. Number Systems.

This course develops algebraic constructions of the natural, integer, rational, real, and complex number systems. Students examine axiomatic foundations, semigroups, groups, fields, and ordered fields while analyzing structural properties of integers, rationals, and real numbers. The course introduces the Cauchy construction of the real numbers, extensions to complex and p‑adic numbers, and related ideas from abstract algebra and real analysis. Emphasis is placed on logical reasoning, proof techniques, and the structural relationships that connect various number systems. Additional topics may include countability, infinite set size, and algebraic tools that support further study in analysis and algebra. Corequisite: MATH 2471 with a grade of "D" or better.

MATH 3330. Introduction to Advanced Mathematics.

This course introduces fundamental methods of mathematical proof and the core language of modern mathematics. Students study sets, logic, quantifiers, relations, functions, equivalence relations, and the cardinality of countable and uncountable sets. Additional topics include divisibility properties of integers and the structure of mathematical definitions and theorems. Emphasis is placed on rigorous argumentation, recognizing logical structure, constructing proofs using standard techniques, and evaluating the soundness of mathematical arguments. These skills prepare students for higher‑level mathematics courses that rely on formal reasoning and abstract frameworks. Prerequisite: MATH 2471 with a grade of "C" or better.

MATH 3348. Deterministic Operations Research.

This course provides a broad study of deterministic operations research methods with an emphasis on mathematical modeling and analytical solution techniques. Students learn to formulate optimization models, solve linear programming problems using the simplex method, and analyze duality and sensitivity. Additional topics include integer programming and branch‑and‑bound methods, transportation and assignment models, network flow algorithms, max‑flow/min‑cut theory, and game theory and decision models. Applications draw from science, engineering, and other fields where optimization supports informed decision‑making. Prerequisite: MATH 2472 with a grade of "C" or better.

MATH 3376. Applied Linear Algebra.

This course develops linear algebra and matrix theory with emphasis on computational methods and applications. Topics include solving systems of linear equations, matrix algebra, LU factorization, vector spaces, linear independence, inner product spaces, orthogonality, least-squares methods, Gram–Schmidt and QR factorization, determinants, eigenvalues and eigenvectors, singular value decomposition, and matrix norms and condition numbers. Applications emphasize techniques relevant to engineering, applied mathematics, and numerical modeling. Prerequisite: MATH 2472 or MATH 2473 with a grade of “C” or better.

MATH 3377. Linear Algebra.

This course introduces the theory and applications of linear algebra. Topics include systems of linear equations, matrix operations, determinants, vector spaces and subspaces, linear independence, bases and dimension, linear transformations, eigenvalues and eigenvectors, inner products, orthogonality, diagonalization, and least-squares methods. Emphasis is placed on mathematical reasoning, proof, and connections between algebraic techniques, geometric interpretations, and applications in mathematics, science, and engineering. Prerequisite: MATH 2472 with a grade of “C” or higher.

MATH 3380. Analysis I.

This course introduces the theory of real functions and the foundations of mathematical analysis. Topics include properties of the real number system, supremum and completeness, sequences and their limits, Cauchy sequences, subsequences, compactness, limits and continuity of functions, uniform continuity, Heine-Borel Theorem, Min-Max Theorem, and convergences of sequences. Emphasis is placed on rigorous proof, precise definitions, and logical development of fundamental concepts in real analysis. The course strengthens analytical reasoning skills by exploring metric spaces, compactness, connectedness, and uniform continuity. By engaging with formal definitions and logical structures, students gain a solid theoretical foundation that supports advanced study in mathematics. Prerequisite: MATH 3330 and MATH 2472 with grades of “C” or better.

MATH 3383. Numerical Analysis I.

This course introduces numerical methods for solving mathematical problems arising in scientific and engineering contexts. Topics include root-finding methods for nonlinear equations, fixed-point iteration, Newton’s method for systems, polynomial interpolation, divided differences, spline approximation, numerical differentiation, numerical integration techniques including Gaussian and adaptive quadrature, and initial value problems for ordinary differential equations. Emphasis is placed on algorithm development, error analysis, convergence, and implementation of numerical methods. Prerequisite: MATH 2472 with a grade of “C” or better.

MATH 3398. Discrete Mathematics II.

This course examines discrete mathematics with emphasis on combinatorics, discrete probability, recurrence relations, generating functions, relations, and algorithmic complexity. Topics include counting techniques, Pigeonhole principle, permutations and combinations, the binomial theorem, discrete probability models, Baye’s Theorem, expected value, growth of functions, big-O notation, recursive definitions, divide-and-conquer algorithms, and equivalence relations and partial orders. The course develops mathematical reasoning and discrete structures fundamental to computer science and related disciplines. Prerequisite: MATH 2358 with a grade of “C” or better.

MATH 4302. Principles of Mathematics II.

This course integrates algebraic reasoning, proportional thinking, geometry, statistics, and probability with pedagogical practices for middle school mathematics. Topics include fraction operations, algebraic concepts and linear functions, ratios and proportional reasoning, surface area and volume, similarity and the Pythagorean Theorem, data analysis, and probability models. Emphasis is placed on mathematical modeling, multiple representations, and analysis of student thinking within the context of current state standards. The course emphasizes conceptual understanding and instructional coherence across core mathematical domains. Prerequisite: MATH 2312 with a grade of “C” or better.

MATH 4303. Capstone Mathematics for Middle School Teachers.

This course provides a rigorous, integrated analysis of mathematical concepts central to middle school curricula. Topics include algebraic reasoning, functions and rates of change, proportional reasoning, geometry and measurement, probability and statistics, number theory, complex numbers, and axiomatic structures. The course emphasizes connections among mathematical domains, quantitative reasoning, modeling, and structural understanding of mathematical systems. Students will explore problem-solving, mathematical communication, and instructional applications to prepare for effective teaching in middle grades mathematics classrooms. Prerequisite: MATH 3315 with a grade of "C" or better. Corequisite: [MATH 2331 or MATH 2472] with a grade of "C" or better.

MATH 4304. Capstone Mathematics for Secondary Teachers (of Mathematics).

This course examines foundational concepts in algebra, geometry, trigonometry, and calculus from an advanced analytical perspective relevant to secondary mathematics curricula. Topics include functions and transformations, complex numbers, matrices, sequences and series, conic sections, coordinate and non-Euclidean geometry, measurement, probability and statistics, and connections among mathematical domains. The course emphasizes structural reasoning, modeling, and historical and philosophical perspectives underlying high school mathematics content. Prerequisite: MATH 3315 and [MATH 2331 or MATH 2472] with grades of “C” or better.

MATH 4305. Advanced Probability and Statistics.

This course develops the mathematical foundations of statistical inference. Topics include functions of random variables and their distributions, sampling distributions, the Central Limit Theorem, point and interval estimation of population parameters, properties of estimators, maximum likelihood estimation, sufficiency, and hypothesis testing. Emphasis is placed on derivation of estimators, theoretical justification of statistical procedures, and mathematical analysis of inference methods. Prerequisite: MATH 3305 with a grade of “C” or better.

MATH 4306. Fourier Series and Boundary Value Problems.

This course develops advanced solution methods for ordinary and partial differential equations with emphasis on Fourier series and boundary value problems arising in scientific applications. Topics include derivation and solution of the heat and wave equations, separation of variables, eigenvalue problems, Fourier sine and cosine series, term-by-term differentiation and integration of series, nonhomogeneous problems, Sturm–Liouville theory, self-adjoint operators, and higher-dimensional boundary value problems in rectangular and circular domains. Prerequisite: MATH 3323 with a grade of “C” or better.

MATH 4307. Modern Algebra.

This course covers fundamental algebraic structures and structure-preserving functions central to modern algebra, with primary emphasis on group theory. Topics include groups and subgroups, cyclic and permutation groups, cosets and quotient structures, homomorphisms and isomorphisms, and selected applications of algebraic structures. The course emphasizes abstract reasoning, logical argumentation, and proof techniques, providing a rigorous foundation for further study in algebra, discrete mathematics, and related areas of mathematics. Prerequisite: MATH 3330 and [MATH 3325 or MATH 3377] with grades of “C” or better.

MATH 4311. Introduction to the History of Mathematics.

This course surveys the historical development of major mathematical ideas from ancient to modern times. Topics include early counting systems and numeral representations, the evolution of geometry, algebra, and calculus, the emergence of great theorems, and the contributions of influential mathematicians across cultures. Philosophical, cultural, and societal contexts are examined alongside the structure, proofs, and applications of mathematics. Prerequisite: MATH 3315 with a grade of “C” or better.

MATH 4315. Analysis II.

This course introduces students to advanced topics in real analysis with an emphasis on mathematical reasoning and proof construction. Topics include differentiation, the Mean Value Theorem, L’Hôpital’s Rule, Taylor expansions, the Riemann integral, convergence of infinite series, and sequences of functions. Students analyze the behavior of functions through theoretical frameworks and examine how classical results in calculus are derived from foundational principles. Through problem solving and written proofs, students develop the ability to communicate mathematical arguments clearly and rigorously. This course is designed for students pursuing upper‑division mathematics or preparing for graduate‑level study. Prerequisite: MATH 3380 with a grade of “C” or better.

MATH 4327. Introduction to Complex Analysis and Its Applications.

This course provides an introduction to the theory of functions of a complex variable and its applications in science and engineering. Students study analytic functions, contour integration, Taylor and Laurent series, residues, and conformal mappings. Emphasis is placed on understanding Cauchy’s theorems, calculating residues, evaluating contour integrals, and applying complex-analytic methods to real‑valued integrals. Applications include solving boundary value problems, analyzing two‑dimensional heat and fluid flow models, locating zeros of analytic functions, and computing inverse Laplace transforms. The course develops mathematical reasoning through rigorous proofs alongside applied techniques. Prerequisite: [MATH 2393 or MATH 2473] and MATH 3323 with grades of "C" or better.

MATH 4330. General Topology.

This course introduces the foundational concepts of general topology with emphasis on topological and metric spaces. Topics include definitions and examples of topologies, bases and subspace topology, open and closed sets, Hausdorff spaces, continuous functions, homeomorphisms, compactness, connectedness, convergence, product and quotient topologies, and metric-induced topologies. Emphasis is placed on rigorous proof, construction of examples and counterexamples, and analysis of structural properties of topological spaces. Prerequisite: MATH 3330 and MATH 2472 with grades of “C” or better.

MATH 4336. Studies in Applied Mathematics.

This course provides an in‑depth exploration of selected topics in mathematics. Students investigate specialized areas or emerging topics not addressed in existing courses, allowing focused study tailored to the selected theme. Possible topics include mathematical modeling, optimization techniques, numerical methods, dynamical systems, data‑driven approaches, or other applied areas chosen by the instructor. Emphasis is placed on developing analytical reasoning, interpreting mathematical structures in applied contexts, and communicating mathematical ideas clearly. The course may be repeated once for credit with a different topic. Prerequisite: Instructor approval.

MATH 4337B. Research in Discrete Mathematics.

This course introduces students to modern research methods and foundational research practices in discrete mathematics. Depending on interest and available topics, students may investigate areas such as graph theory, combinatorics, number theory, or discrete structures. The course provides structured opportunities to engage in the creative processes of mathematical discovery and supports the development of skills valuable for advanced undergraduate work or preparation for graduate study. Emphasis is placed on analytical reasoning, mathematical writing, and presentation skills used in contemporary mathematical inquiry. Prerequisite: Texas State GPA of 3.25 and MATH 2358 with a grade of "C" or better. Corequisite: MATH 3398 with a grade of a "D" or better.

MATH 4337C. Numerical Methods for Ordinary Differential Equations.

This course examines analytical and numerical methods relevant to ordinary differential equations and modern applied mathematics. Topics include Fourier analysis, harmonic analysis techniques, and convex optimization, with emphasis on theoretical foundations and computational applications. The course integrates functional analytic perspectives and optimization frameworks that support contemporary developments in scientific computing and machine learning. Students engage with selected advanced readings to develop mathematical maturity and analytical skills in applied contexts. Prerequisite: MATH 2472 with a grade of "C" or better.

MATH 4337D. Topics in Topology and Algebra.

This course introduces students to modern research methods in topology and algebra. Specific topics will vary based on student interest and input, but the course maintains a broad exploration of structures, invariants, and reasoning techniques used across these fields. Students engage with research‑level approaches, practice analyzing mathematical objects, and learn to interpret structural properties using topological and algebraic tools. The course emphasizes conceptual understanding and methods used in current mathematical research. Prerequisite: MATH 3330 with a grade of "C" or better and a minimum Texas State GPA of 2.0.

MATH 4337H. Undergraduate Research in Topology and Artificial Neural Networks.

This course introduces the mathematical foundations of Artificial Neural Networks (ANN) with particular attention to topological methods for their analysis. Topics include core machine learning concepts, feedforward neural networks, gradient descent, the universal approximation theorem, convolutional neural networks, basic topology, and VC dimension. Students engage in guided undergraduate research and hands‑on projects involving the customization and analysis of artificial neural networks implemented in Python. Emphasis is placed on mathematical reasoning, interpretation of scholarly literature, and the formulation of research‑driven questions related to neural network design and performance. Prerequisite: MATH 2471 with a grade of "C" or better.

MATH 4350. Introduction to Combinatorics.

This course presents fundamental combinatorial concepts and methods of proof specific to discrete mathematics. Topics include advanced counting techniques, permutations and combinations, inclusion–exclusion, recurrence relations, ordinary and exponential generating functions, special sequences such as Catalan and Stirling numbers, graph theory, spanning trees and the Matrix Tree Theorem, group actions, Burnside’s Lemma, Pólya’s Theorem, partially ordered sets, Möbius inversion, and combinatorial designs. Emphasis is placed on enumeration methods, structural reasoning, and rigorous proof. Prerequisite: MATH 2472 with a grade of "C" or better.

MATH 4383. Numerical Analysis II.

This course develops advanced numerical methods for modeling, analysis, and simulation of scientific and engineering problems. Topics include direct and iterative methods for linear systems, matrix factorizations, eigenvalue algorithms, numerical methods for initial value problems, multistep and Runge–Kutta methods, least-squares approximation, orthogonal systems and Fourier series, Monte Carlo methods, and optimization techniques in one and several variables. Emphasis is placed on algorithm development, stability, convergence, accuracy, efficiency, and practical computational implementation. Prerequisite: MATH 3383 and MATH 3323 with grades of “C” or better.

MATH 4393. Introduction to Finite Element Methods.

This course introduces the weak formulation of partial differential equations and the finite element approximation of these formulations. Students study the mathematical foundations of finite element spaces, derive discrete models, and implement numerical methods for one‑, two‑, and three‑dimensional problems. Emphasis is placed on balancing theory with computation, including the development of simple finite element codes and the use of software for solving applied problems. Applications arise in civil engineering, applied mathematics, and related disciplines where finite element analysis supports modeling and simulation. Prerequisite: [MATH 3376 or MATH 3377] and MATH 3323 with grades of "C" or better.

MATH 5111. Graduate Assistant Training.

This course is concerned with techniques used in the teaching of mathematics and prepares graduate teaching and instructional assistants for responsibilities in collegiate mathematics instruction. Topics include classroom management, communication with students, grading practices, academic integrity, equitable and professional teaching practices, and strategies for supporting student learning in undergraduate mathematics courses. Emphasis is placed on effective instructional preparation, professional expectations, and reflective development as a teaching assistant. This course is required as a condition of employment for graduate teaching and instructional assistants, does not earn graduate degree credit, and may be repeated with different emphasis.

MATH 5199B. Thesis.

This course provides students with the opportunity to conduct an independent, original research project under the supervision of a faculty advisor. Students formulate a research question, engage with relevant scholarly literature, and apply appropriate methods to investigate a focused topic within mathematics, mathematics education, or a closely related field. Emphasis is placed on rigorous reasoning, clear exposition, and adherence to disciplinary standards for scholarship. The course culminates in the completion of a written thesis that demonstrates the student’s ability to conduct sustained inquiry and communicate results effectively.

MATH 5290. Teaching Geometry through Problem Solving and Discovery Learning.

This course investigates the problem-solving heuristics embedded in the secondary school geometry curriculum and explores how to implement problem solving in geometry classrooms. This course also examines the unique “Hungarian style” method of discovery learning in mathematics, developed for students aged 12-18. The method referred to as the Pósa Method is similar to inquiry based learning with an emphasis on problem solving.

MATH 5299B. Thesis B.

This course provides students with the opportunity to conduct an independent, original research project under the supervision of a faculty advisor. Students formulate a research question, engage with relevant scholarly literature, and apply appropriate methods to investigate a focused topic within mathematics, mathematics education, or a closely related field. Emphasis is placed on rigorous reasoning, clear exposition, and adherence to disciplinary standards for scholarship. The course culminates in the completion of a written thesis that demonstrates the student’s ability to conduct sustained inquiry and communicate results effectively.

MATH 5301. Partial Differential Equations.

This course covers topics that include the derivation and classification of partial differential equations, vector and tensor methods, and first‑order equations. The course studies wave equations, vibrations, and normal modes, with emphasis on Fourier series and Fourier integrals. Classical solution techniques such as Cauchy’s method, characteristics, Green’s functions, potential theory, and boundary‑value problems are developed in detail. Additional methods, including Riemann–Volterra techniques, are introduced to analyze initial‑ and boundary‑value problems. Analytical reasoning and mathematical rigor are emphasized throughout. Prerequisite: MATH 3323 with a grade of "C" or better.

MATH 5303. History of Mathematics.

This course studies the development of mathematics and the accomplishments of mathematicians who contributed to its progress across cultures and historical periods. Topics include the emergence of major mathematical ideas, the historical development of algebra, geometry, calculus, and other significant areas, original and secondary historical sources, and the cultural and philosophical settings in which mathematics evolved. Emphasis is placed on historical interpretation, mathematical communication, understanding mathematics as an evolving human endeavor, and connections between earlier developments, contemporary mathematical thought, and the teaching and learning of mathematics. Cannot be used on a degree plan for M.S. degree.

MATH 5307. Modern Algebra.

This course provides a graduate level introduction to the fundamental structures of modern algebra. Students study groups, rings, fields, and related algebraic systems as needed with an emphasis on axiomatic development, structural properties, and proof techniques. Topics may include homomorphisms, quotient structures, polynomial rings, field extensions, and classical theorems central to algebraic reasoning. The course highlights methods for analyzing abstract structures, constructing examples, and formulating rigorous arguments. This course supports the development of advanced mathematical maturity and prepares students for further study in algebra and related disciplines. Material will be adapted to the needs of the class. Prerequisite: MATH 5384 with a grade of "B" or better.

MATH 5311. Foundations of Differential Equations.

This course provides a foundational study of differential equations, operator spaces, and related core mathematical topics. Students examine classical and modern approaches to these structures while exploring how recent developments contribute to contemporary mathematical analysis. Emphasis is placed on understanding theoretical frameworks, evaluating methods using clear mathematical reasoning, and investigating the logical relationships among differential operators and function spaces. Students are supported in conducting independent, evidence based inquiry that allows them to form their own interpretations grounded in mathematical argumentation. Prerequisite: MATH 5382 with a grade of "C" or better.

MATH 5312. Functions of a Complex Variable.

This course studies modern developments in the theory of functions of a complex variable. Topics may include analytic functions, contour integration, the Cauchy integral theorem and formula, Laurent series, residues, conformal mappings, and related core results of complex function theory. Additional topics may include Riemann surfaces, differential forms, and the Riemann-Roch theorem, with attention to how local complex-analytic methods connect to global structures in topology, geometry, and algebra. Emphasis is placed on rigorous reasoning, conceptual understanding, and the role of complex analysis in advanced mathematical theory. Prerequisite: MATH 5382 with a grade of "C" or better.

MATH 5313. Field Theory.

This course studies field theory with emphasis on separable extensions and Galois theory. Topics include field extensions, polynomial rings, splitting fields, algebraic and transcendental extensions, automorphism groups, and the structure of Galois correspondences. Related algebraic concepts such as rings, ideals, modules, and quotient structures may be developed as needed to support the theory. Emphasis is placed on rigorous proof, structural analysis, and the use of field-theoretic methods in advanced algebra and related areas. Prerequisite: MATH 5384 with a grade of "B" or better.

MATH 5314. Number Theory.

This course examines selected topics in number theory at the graduate level. Content may include elementary number theory, quadratic forms, and introductory concepts from algebraic or analytic number theory, with emphasis on fundamental structures, methods, and proofs. Topics are chosen to provide flexibility while maintaining mathematical rigor and coherence. The course develops techniques for analyzing integers and related algebraic objects, with attention to problem‑solving strategies and theoretical reasoning. Specific topics may vary depending on instructor expertise and student background, but the course is designed to strengthen students’ understanding of core ideas in number theory and prepare them for further study or research in mathematics. Prerequisite: MATH 5384 with a grade of "B" or better.

MATH 5317. Problems in Advanced Mathematics.

This course is open to graduate students on an individual basis by arrangement with the mathematics department. Students investigate topics appropriate to their level of mathematical preparation, applying advanced reasoning and analytical skills to selected problem sets or focused areas of study. The specific emphasis varies and may include theoretical exploration, problem solving techniques, or preparatory work for future coursework. The course supports mathematical development while maintaining flexibility in content, method, and depth. A substantial degree of mathematical maturity is expected, and the course may be repeated with different emphases. This course does not apply toward graduate degree credit.

MATH 5319. The Theory of Integration.

This course covers the theory of integration with special emphasis on Lebesgue integrals. Topics include the Lebesgue integral for bounded, finitely supported, and measurable functions, convergence theorems, differentiability of monotone functions, absolute continuity, Lp spaces, and Lp completeness. Additional attention may be given to convergence theorems, and the role of integration theory in modern analysis. Emphasis is placed on rigorous proof, abstract reasoning, and the analytical foundations needed for advanced work in real analysis, probability, and related mathematical fields.

MATH 5329. General Topology.

This course studies topological spaces and their properties at the graduate level. Topics include topological spaces and continuous functions, connectedness, compactness, separation axioms, product and quotient constructions, metrization, and CW complexes, together with selected related topics as time permits. Emphasis is placed on rigorous proof, careful use of definitions, construction of examples and counterexamples, and the role of topology in advanced study of analysis, geometry, and algebra.

MATH 5331. Metric Spaces.

This course provides an introduction to point set topology with a central focus on the structure and properties of metric spaces. Students study topics such as open and closed sets, convergence, continuity, compactness, completeness, and connectedness within the context of metric spaces. The course also includes a brief introduction to general topological spaces to illustrate how metric spaces fit into broader topological frameworks. Emphasis is placed on rigorous definitions, logical reasoning, and the development of proof based skills that support advanced mathematical study.

MATH 5336. Studies in Applied Mathematics.

This course examines selected topics in applied mathematics at the graduate level. Possible areas of study include optimization and control theory, numerical analysis, calculus of variations, boundary value problems, special functions, tensor analysis, and other subfields of applied mathematics. Topics are chosen to reflect current mathematical methods and applications, with emphasis on analytical techniques, modeling, and problem‑solving. The specific content may vary depending on instructor expertise and student preparation. This course may be repeated for credit when the topic emphasis differs, allowing students to engage with multiple areas of applied mathematics in depth. Prerequisite: Instructor approval.

MATH 5338. Advanced Independent Study in Mathematics or Statistics.

This course provides graduate students with an opportunity to pursue advanced independent study in mathematics or statistics under the supervision of a faculty member. Students investigate specialized topics aligned with faculty research interests through theoretical analysis, empirical investigation, or critical review and synthesis of existing scholarly literature. Emphasis is placed on independent inquiry, depth of understanding, and adherence to disciplinary standards of rigor and clarity. The specific subject matter and methods of study are determined collaboratively by the student and supervising faculty member. This course may be repeated once for credit when the topic emphasis differs. Prerequisite: Instructor approval.

MATH 5340. Scientific Computation.

This course studies computational methods used in science and mathematics through the analysis and implementation of algorithms in a computer algebra or scientific computing environment. Topics include symbolic, numerical, and graphical techniques for solving mathematical problems, algorithmic approaches to scientific computation, and applications drawn from mathematics, science, and engineering. Emphasis is placed on the mathematical structure of computational methods, the interpretation of computed results, and the effective use of computation as a tool for advanced problem solving.

MATH 5350. Combinatorics.

This course studies graduate-level combinatorics with emphasis on enumeration, structure, and proof. Topics may include permutations, combinations, Stirling numbers, chromatic numbers, Ramsey numbers, generating functions, Pólya theory, Latin squares, random block design, and related combinatorial structures. Additional topics may include recurrence relations, special sequences, discrete probability, extremal set theory, and graph-theoretic methods as they support the development of combinatorial reasoning. Emphasis is placed on rigorous proof, effective mathematical communication, and the use of combinatorial techniques in discrete mathematics and related areas. Prerequisite: Instructor Approval.

MATH 5355. Applied and Algorithmic Graph Theory.

This course studies graph theory with emphasis on the close relationship between theoretical and algorithmic aspects of the subject. Topics may include connectivity, trees, planarity, graph coloring, matchings, and network models, together with algorithms such as max-flow min-cut, maximum matching, shortest-path methods, and optimization algorithms for facility location problems in networks. Emphasis is placed on rigorous reasoning, algorithmic analysis, and the application of graph-theoretic methods to discrete structures, optimization, and network-based problems in mathematics and related fields. Prerequisite: MATH 5388 with a grade of 'C' or better.

MATH 5360. Mathematical Modeling.

This course introduces the principles and techniques of mathematical modeling with applications drawn primarily from the natural sciences. Students examine the process of translating real‑world phenomena into mathematical representations and analyzing those models using appropriate analytical and computational tools. Emphasis is placed on deterministic systems, stochastic models, and diffusion processes. The course explores model formulation, assumptions, solution methods, and interpretation of results, with attention to the strengths and limitations of different modeling approaches. Through selected examples, students develop skills in constructing, analyzing, and evaluating mathematical models as tools for understanding complex systems. Prerequisite: MATH 5301 with a grade of "C" or better.

MATH 5373. Theory of Functions of Real Variables.

This course covers measure theory with special emphasis on the Lebesgue measure. Topics include the outer measure, sigma-algebra of measurable sets, properties of measurable sets, Borell-Canteli lemma, non-measurable sets, Cantor-Lebesgue function, Lebesgue measurable functions, pointwise limits, simple approximations, and Littlewood’s three principles. Additional attention may be given to convergence theorems, and the role of approximation theory in modern analysis. Emphasis is placed on rigorous proof, abstract reasoning, and the analytical foundations needed for advanced work in real analysis, probability, and related mathematical fields. Prerequisite: Instructor approval.

MATH 5374. Numerical Linear Algebra.

This course introduces tools that mathematical scientists use with vectors and matrices. Topics include direct and iterative methods for solving linear systems, least-squares problems, eigenvalue problems, algorithmic stability under perturbations, and numerical methods for large, sparse systems. Additional topics may include Gaussian elimination, Jacobi and Gauss–Seidel methods, conjugate gradient methods, GMRES, Fast Fourier Transform techniques, and multigrid methods, with attention to both theoretical analysis and computational implementation. Emphasis is placed on balancing rigorous mathematical reasoning with practical numerical computation in applications from science, engineering, and applied mathematics.

MATH 5376F. Introduction to Probability Theory and Models.

This course introduces the definitions, constructions, theorems, and techniques used to build and analyze probability models. Students explore both the abstract foundations of probability theory and its application to a wide range of modeling contexts. Topics include conditional expectation, convergence of random variables, the weak and strong laws of large numbers, the central limit theorem, random walks, martingales, and Brownian motion. The course emphasizes the active construction and evaluation of probability models while developing the rigorous theoretical background needed to understand their behavior. Students engage with proofs, examples, and analytical methods that support deeper understanding of stochastic processes and probabilistic structures.

MATH 5381. Foundations of Set Theory.

This course provides a graduate-level study of set theory as a foundation for modern mathematics. Topics include sets, relations, functions, finite and infinite structures, cardinality, ordinals, transfinite methods, and basic principles of mathematical logic. Emphasis is placed on precise definitions, rigorous proof, and formal reasoning. The course develops the language and techniques used across advanced areas such as analysis, algebra, topology, and logic. It supports further graduate study and research in theoretical mathematics and foundations.

MATH 5382. Foundations of Real Analysis.

This course covers the foundations of mathematical analysis. Topics include the real number system, sequences, series, limits, and continuity of functions, together with methods of proof used in advanced mathematics. Additional attention may be given to completeness, compactness, inequalities, and the logical structure of rigorous analysis as students transition from computational calculus to proof-based reasoning. Emphasis is placed on precise definitions, careful argumentation, and the development of core concepts that support further study in analysis and related areas. Prerequisite: MATH 5381 with a grade of 'C' or better.

MATH 5384. Geometric Approach to Abstract Algebra.

This course studies the definitions and elementary properties of groups, rings, integral domains, fields, and vector spaces, with particular emphasis on the rings of integers, rational numbers, complex numbers, and polynomials. Attention is given to the structural relationships among these algebraic systems and to the interplay between algebra and geometry. Emphasis is placed on rigorous proof, abstraction, and the use of algebraic structures to analyze mathematical patterns, transformations, and foundational ideas that support advanced study in algebra and related areas. Prerequisite: MATH 5381 with a grade of 'C' or better.

MATH 5386. Knots and Surfaces, An Introduction to Low-Dimensional Topology.

This course introduces fundamental topics in low‑dimensional topology with emphasis on knot theory and the topology of surfaces. Students study knot polynomials and other knot invariants, as well as methods for distinguishing and classifying knots. The course also examines the topological classification of surfaces and associated invariants, including orientability, genus, and Euler characteristic. Emphasis is placed on understanding how invariants are defined and used to distinguish topological spaces. Through selected examples and proofs, students develop familiarity with core concepts, techniques, and reasoning in low‑dimensional topology, preparing them for further study in topology or related areas of mathematics.

MATH 5388. Discrete Mathematics.

This course provides a graduate-level study of discrete mathematics, emphasizing counting techniques, recurrence relations, discrete probability, and graph theory. Topics include permutations and combinations, inclusion-exclusion, generating functions, recurrence methods, discrete probabilistic models, and graph-theoretic structures. Emphasis is placed on rigorous reasoning, proof, and discrete modeling. The course highlights connections among combinatorics, probability, and graph theory and supports applications in mathematics, computation, and related quantitative fields. It prepares students for advanced coursework and research involving discrete structures and mathematical modeling.

MATH 5392. Survey of Geometries.

This course examines major geometric systems through an axiomatic and structural perspective. Topics include the axiomatic development of finite geometries, affine and projective geometry, Euclidean geometry, and selected non‑Euclidean geometries, with emphasis on their relationships to neutral geometry and Hilbert’s axioms. The course also may explore geometric transformations and an introduction to fractal geometry as extensions of classical geometric ideas. Students analyze how different axiom systems give rise to distinct geometric structures and investigate connections among algebraic, transformational, and metric approaches to geometry. Emphasis is placed on logical reasoning, proof techniques, and comparative analysis of geometric frameworks.

MATH 5393. Numerical Optimization.

This course introduces optimization methods used across mathematics, engineering, and applied sciences. Students study foundational concepts in optimization theory and examine numerical algorithms designed to locate points satisfying optimality conditions. Emphasis is placed on convergence analysis, algorithmic behavior, and practical implementation considerations. Topics include gradient based methods, unconstrained and constrained optimization techniques, line search and trust region strategies, and computational approaches for analyzing algorithm performance. Through examples, proofs, and computational exercises, students gain experience interpreting optimality conditions and selecting appropriate numerical techniques for a variety of mathematical problems.

MATH 5399A. Thesis.

This course provides students with the opportunity to conduct an independent, original research project under the supervision of a faculty advisor. Students formulate a research question, engage with relevant scholarly literature, and apply appropriate methods to investigate a focused topic within mathematics, mathematics education, or a closely related field. Emphasis is placed on rigorous reasoning, clear exposition, and adherence to disciplinary standards for scholarship. The course culminates in the completion of a written thesis that demonstrates the student’s ability to conduct sustained inquiry and communicate results effectively. This course represents a student’s initial thesis enrollment. No thesis credit is awarded until student has completed the thesis in Mathematics 5399B.

MATH 5399B. Thesis.

This course provides students with the opportunity to conduct an independent, original research project under the supervision of a faculty advisor. Students formulate a research question, engage with relevant scholarly literature, and apply appropriate methods to investigate a focused topic within mathematics, mathematics education, or a closely related field. Emphasis is placed on rigorous reasoning, clear exposition, and adherence to disciplinary standards for scholarship. The course culminates in the completion of a written thesis that demonstrates the student’s ability to conduct sustained inquiry and communicate results effectively. This represents a student’s continuing thesis enrollment. The student continues to enroll in this course until the thesis is submitted for binding.

MATH 5492. Experiencing the Hungarian Approach through Observation and Teaching Practicum.

This course provides a first-hand experience in putting the Hungarian style guided discovery into practice. As part of the course, students will spend one week at a mathematics camp for secondary students that is being run using the Hungarian style of teaching. Students will observe mathematics classes, discuss pedagogy with camp instructors, and design and teach their own lesson to camp participants.

MATH 5599B. Thesis.

This course provides students with the opportunity to conduct an independent, original research project under the supervision of a faculty advisor. Students formulate a research question, engage with relevant scholarly literature, and apply appropriate methods to investigate a focused topic within mathematics, mathematics education, or a closely related field. Emphasis is placed on rigorous reasoning, clear exposition, and adherence to disciplinary standards for scholarship. The course culminates in the completion of a written thesis that demonstrates the student’s ability to conduct sustained inquiry and communicate results effectively. This represents a student’s continuing thesis enrollment. The student continues to enroll in this course until the thesis is submitted for binding.

MATH 5999B. Thesis.

This course provides students with the opportunity to conduct an independent, original research project under the supervision of a faculty advisor. Students formulate a research question, engage with relevant scholarly literature, and apply appropriate methods to investigate a focused topic within mathematics, mathematics education, or a closely related field. Emphasis is placed on rigorous reasoning, clear exposition, and adherence to disciplinary standards for scholarship. The course culminates in the completion of a written thesis that demonstrates the student’s ability to conduct sustained inquiry and communicate results effectively. This represents a student’s continuing thesis enrollment. The student continues to enroll in this course until the thesis is submitted for binding.

MATH 7111. Seminar in Teaching.

Seminar on individual study projects concerned with selected problems in the teaching of mathematics. This course does not earn graduate degree credit.

MATH 7188. Seminar in Mathematics Education.

This course requires students to participate in weekly research seminars in mathematics education that emphasize scholarly discussion, critical engagement with current research, and professional communication. Students attend presentations by faculty, visiting scholars, and peers, and they contribute to seminar dialogue through questioning and discussion. Each student delivers at least one formal research presentation during the semester, drawing on original research, dissertation work, or a critical analysis of existing literature in mathematics education. The course supports the development of research communication skills, familiarity with ongoing research agendas, and participation in the professional community. This course is repeatable for credit when seminar content varies.

MATH 7199A. Dissertation.

This course provides doctoral students with the opportunity to conduct an independent, original research project that contributes new knowledge to mathematics, mathematics education, or a closely related field under the supervision of a faculty advisor. Students identify a significant research problem, engage deeply with the scholarly literature, and employ appropriate theoretical, empirical, or methodological approaches to address the problem. Emphasis is placed on originality, rigor, and sustained scholarly inquiry consistent with professional standards of doctoral research. The course culminates in the completion and defense of a written dissertation that demonstrates the student’s ability to conduct independent research and communicate results at a professional level. While conducting dissertation research and writing, students must be continuously enrolled each long semester.

MATH 7299A. Dissertation.

This course provides doctoral students with the opportunity to conduct an independent, original research project that contributes new knowledge to mathematics, mathematics education, or a closely related field under the supervision of a faculty advisor. Students identify a significant research problem, engage deeply with the scholarly literature, and employ appropriate theoretical, empirical, or methodological approaches to address the problem. Emphasis is placed on originality, rigor, and sustained scholarly inquiry consistent with professional standards of doctoral research. The course culminates in the completion and defense of a written dissertation that demonstrates the student’s ability to conduct independent research and communicate results at a professional level. While conducting dissertation research and writing, students must be continuously enrolled each long semester. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: Instructor Approval.

MATH 7301. Studies in Mathematics.

This course provides foundational preparation in graduate mathematics for students entering doctoral study in mathematics or mathematics education. Topics may include essential concepts and methods from advanced algebra, analysis, topology, discrete mathematics, and proof-based reasoning, depending on student background and program needs. Emphasis is placed on strengthening mathematical maturity, rigorous communication, abstraction, and the transition to graduate-level expectations in reading, writing, and problem solving. This course may be repeated and does not earn graduate degree credit.

MATH 7302. History of Mathematics.

This course emphasizes the development of mathematics and the accomplishments of mathematicians who contributed to its progress across cultures and historical periods. Topics include the emergence of major mathematical ideas, the historical development of algebra, geometry, calculus, and other significant areas, original and secondary historical sources, and the cultural and philosophical settings in which mathematics evolved. Students will be able to explain the historical significance of various mathematical achievements and discuss connections between earlier developments, contemporary mathematical thought, and the teaching and learning of mathematics.

MATH 7303. Analysis I.

This course covers measure theory with special emphasis on the Lebesgue measure. Topics include the outer measure, sigma-algebra of measurable sets, properties of measurable sets, Borell-Canteli lemma, non-measurable sets, Cantor-Lebesgue function, Lebesgue measurable functions, pointwise limits, simple approximations, and Littlewood’s three principles. Additional attention may be given to convergence theorems, and the role of approximation theory in modern analysis. Emphasis is placed on rigorous proof, abstract reasoning, and the analytical foundations needed for advanced work in real analysis, probability, and related mathematical fields.

MATH 7306. Current Research in Math Education.

This course examines foundational and contemporary research in mathematics education with attention to the social, political, and economic trends that shape research agendas in local, state, national, and international settings. Topics include major themes in mathematics education research, research traditions and methods, contemporary debates in the field, and the interpretation of scholarly literature within broader educational contexts. Students will be able to discuss contemporary and historical trends and issues in mathematics education, develop skills for written synthesis of academic arguments, and identify research areas of interest and develop expertise in those areas.

MATH 7307. Algebra I.

This course examines the structure and methods of modern algebra with emphasis on group‑theoretic foundations and select topics from ring theory. Topics include permutation groups, symmetry groups, Sylow theorems, and selected topics from ring theory. Additional attention is given to homomorphisms, quotient structures, and related algebraic constructions that support advanced study in abstract algebra. Emphasis is placed on rigorous proof, structural reasoning, and the analysis of algebraic systems that arise throughout advanced mathematics. The course prepares students for further doctoral‑level work in algebra and related fields by strengthening abstract reasoning and proof‑writing skills.

MATH 7309. Topology I.

This course studies point-set topology at the doctoral level. Topics include topological spaces, continuous functions, connectedness, compactness, countability, separability, metrizability, CW complexes, simplicial complexes, nerves, and dimension theory. Additional attention may be given to product and quotient constructions, subspace topology, and examples that connect foundational topology to later study in geometry, algebra, and analysis. Emphasis is placed on rigorous proof, precise use of definitions, and structural reasoning in abstract topological settings.

MATH 7313. Analysis II.

This course covers the theory of integration with special emphasis on Lebesgue integrals. Topics include the Lebesgue integral for bounded, finitely supported, and measurable functions, convergence theorems, differentiability of monotone functions, absolute continuity, Lp spaces, and Lp completeness. Additional attention may be given to convergence theorems, and the role of integration theory in modern analysis. Emphasis is placed on rigorous proof, abstract reasoning, and the analytical foundations needed for advanced work in real analysis, probability, and related mathematical fields. Prerequisite: Math 7303 with a grade of "B" or better.

MATH 7315. Calculus of Variations.

This course examines the theoretical foundations of the calculus of variations with emphasis on variational principles and their applications. Topics include properties of functionals, first and second variations, extremal problems, Euler–Lagrange equations, and stability theory. The course considers variational formulations in multiple settings. Emphasis is placed on rigorous analysis, derivation of variational conditions, and interpretation of solutions. The course prepares doctoral students for advanced research involving variational methods and related analytical techniques. Prerequisite: MATH 7303 with a grade of "B" or higher.

MATH 7317. Algebra II.

This course examines advanced algebraic structures of rings and fields at the doctoral level. Topics include rings, ideals, modules, polynomial rings, the Euclidean algorithm, finite fields, and field extensions, along with an introduction to Galois theory and selected geometric applications. Emphasis is placed on rigorous proof, structural reasoning, and the analysis of algebraic systems that support advanced study in algebra, geometry, number theory, and related areas of mathematics. The course prepares students for further doctoral‑level work by strengthening abstract reasoning, proof construction, and the ability to connect algebraic structures across mathematical disciplines. Prerequisite: MATH 7307 with a grade of 'B' or better.

MATH 7319. Topology II: Algebraic Topology.

This course covers the fundamental concepts and tools of algebraic topology. Topics include the fundamental group, covering spaces, homotopy type, the higher homotopy groups, singular homology theory, and the computation of homology groups via exact sequences and applications. Additional attention may be given to representative examples, computational methods, and the role of algebraic invariants in distinguishing and analyzing topological spaces. Emphasis is placed on rigorous proof, structural reasoning, and the use of algebraic methods to study topological phenomena. Prerequisite: MATH 7307 and MATH 7309 with grades of 'B' or better.

MATH 7321. Graph Theory.

This course studies graph theory at an advanced level with emphasis on both structural and applied aspects of graphs. Topics include trees, connectivity of graphs, Eulerian graphs, Hamiltonian graphs, planar graphs, graph coloring, matchings, factorizations, digraphs, networks, and network flow problems. Attention may also be given to algorithms, optimization questions, and representative applications in discrete mathematics and related fields. Emphasis is placed on rigorous proof, structural analysis, and graph-theoretic reasoning.

MATH 7323. Theories of Knowing and Learning in Mathematics Education.

This course surveys the major theories of knowing and learning that have influenced mathematics education. Topics include behaviorism, constructivism, sociocultural theories, situated cognition, and other theoretical perspectives used to explain how learners develop mathematical understanding. Attention is given to how these theories define knowledge, learning, teaching, and participation, and to the ways they shape curriculum, research, and classroom practice in mathematics education. Students will be able to compare theoretical frameworks and interpret their implications for the teaching and learning of mathematics.

MATH 7324. Curriculum Design & Analysis.

This course examines, analyzes, and evaluates the various concepts, topics, methods, and techniques related to curriculum design in mathematics education for grade levels P-16. Topics may include curriculum theory, the historical development of mathematics curricula, standards and policy, curricular coherence across grade bands, implementation issues, and the evaluation of instructional materials and curricular models. Students will be able to analyze curricular materials, evaluate design principles, and analyze relationships among curriculum, instruction, assessment, and equity in mathematics education.

MATH 7328. Instructional Techniques & Assessments.

This course examines, analyzes, and evaluates the various concepts, topics, methods, and techniques of instruction in mathematics education and the related assessment procedures for grade levels P–20. Topics may include instructional design, teaching practices, classroom discourse, formative and summative assessment, task design, feedback, evaluation of student thinking, and the interpretation of assessment data in mathematics education. Students will be able to apply research-based perspectives on teaching and learning to classroom practices and to evaluate alignment among mathematical learning goals, instructional decisions, and assessment practices.

MATH 7331. Combinatorics.

This course is a study of fundamental principles of combinatorics. Topics include permutations and combinations, the Pigeonhole principle, the principle of inclusion–exclusion, binomial and multinomial theorems, special counting sequences, partitions, posets, extremal set theory, generating functions, recurrence relations, and the Pólya theory of counting. Emphasis is placed on rigorous proof, enumeration methods, structural reasoning, and the analysis of finite discrete structures that support further study in combinatorics, graph theory, and related areas of mathematics.

MATH 7342. Research in Undergraduate Mathematics Education I.

This course examines the theoretical foundations of Research in Undergraduate Mathematics Education (RUME). Students study historical and contemporary theoretical perspectives that inform research on the teaching and learning of mathematics at the undergraduate level. Emphasis is placed on critically reading, analyzing, and interpreting research literature in the field. Students will be able to discuss how theoretical frameworks shape research questions, methodologies, and interpretations within RUME. Prerequisite: Math 7306 with a grade of a "B" or better.

MATH 7344. Research in Undergraduate Mathematics Education II.

This course examines advanced research design and development in Research in Undergraduate Mathematics Education (RUME). Through a topic-driven analysis of current RUME literature, students will examine how research is designed and conducted in relation to the teaching and learning of advanced undergraduate mathematics topics such as proof, calculus and analysis, abstract algebra, linear algebra, and differential equations. At the end of the course, students will be able to connect theoretical perspectives to research questions, methodologies, and data interpretations. Students will be able to design and execute research studies in RUME that are appropriate for dissertation-level work. Prerequisite: MATH 7306 and MATH 7342 with grades of a "B" or better.

MATH 7346. Quantitative Research Analysis in Mathematics Education.

This course surveys research techniques used in quantitative analysis for mathematics education. Topics include experimental design, statistical analysis, and the use of appropriate design methodologies to achieve the strongest possible evidence to support or refute a knowledge claim. Additional attention may be given to measurement, validity, inferential reasoning, interpretation of quantitative findings, and the alignment of research questions, methods, and evidence. Students will be able to evaluate the quality of quantitative studies and design rigorous quantitative research in mathematics education. Prerequisite: MATH 7306 and MATH 7325 with grades of 'B' or better.

MATH 7352. Introduction to Qualitative Research in Mathematics Education.

This course introduces doctoral students to principles and techniques of qualitative research as applied to mathematics education. Topics include qualitative research design, sampling strategies, data sources, methods of constant comparison, and conceptualizations of validity and rigor within qualitative research paradigms. Students examine how qualitative methodologies are used to investigate teaching and learning in mathematics education and how such studies are evaluated within the scholarly literature. At the end of the course, students will be able to implement basic qualitative methodologies, interpret qualitative data, and critique published research. Prerequisite: Math 7306 with a grade of "B" or better.

MATH 7354. Advanced Qualitative Research.

This course examines advanced qualitative research methods used in mathematics education. Emphasis is placed on techniques for qualitative data collection and analysis, including interpreting data and representing findings. Topics include qualitative research design, data collection strategies, analytic frameworks, trustworthiness, ethics, and methodological coherence. Through engaging in sustained analyses of qualitative evidence, students will be able to apply established qualitative methods to research problems in mathematics education. Students will be able to critique qualitative methods, evaluate published studies, and discuss strengths and weaknesses of various approaches relative to the aims of the research problem. Prerequisite: MATH 7352 or ED 7352 with a grade of "B" or better.

MATH 7356C. Action Research in Mathematics Education.

This course examines the theoretical foundations, methodological approaches, and practical considerations of action research in mathematics education. Emphasis is placed on the systematic study of instructional practices, curriculum design, assessment strategies, and classroom‑based problem solving. Students analyze published action research studies, evaluate issues of validity, ethics, and rigor, and design an original action research proposal grounded in relevant literature. The course supports the development of research questions, data collection strategies, and analytic techniques appropriate for educational settings. Attention is given to the role of reflective practice and evidence‑based decision making in mathematics education contexts. Prerequisite: MATH 7346 or MATH 7352 or ED 7352 with a grade of "B" or better.

MATH 7358. Advanced Quantitative Research in Mathematics Education.

This course examines advanced quantitative research methods used in mathematics education. Topics include experimental design, statistical modeling, multivariate and multilevel analysis, and methodological considerations for producing and interpreting quantitative evidence. Emphasis is placed on aligning research questions with appropriate quantitative designs and analytic strategies, as well as critically evaluating the strength and limitations of quantitative findings. Students will be able to investigate questions in mathematics education using advanced quantitative techniques and to interpret and evaluate published research literature in mathematics education. Prerequisite: MATH 7346 with a grade of "B" or better.

MATH 7361. Seminar in Advanced Mathematics.

This course is a doctoral‑level seminar in advanced mathematics, where course content varies by offering and is determined by faculty expertise and student research interests. Topics are drawn from areas such as analysis, algebra, topology and geometry, applied mathematics, or probability and statistics. Instructional modality will be appropriate for the topic and determined by the instructor, and may include student‑led presentations, guided discussion, collaborative problem analysis, or directed study of advanced literature. This course may be repeated for credit when the seminar topic differs.

MATH 7363A. COMPLEX ANALYSIS.

This course is a brief introduction to the complex number system and the basic point-set topology of the complex plane, followed by a proof-based and rigorous study of the principal results in the analysis of functions of a single complex variable. Topics may include analytic functions, contour integration, the Cauchy integral theorem and formula, Laurent series, residues, conformal mappings, and selected extensions to more advanced geometric viewpoints such as Riemann surfaces. Emphasis is placed on rigorous proof, conceptual understanding, and the role of complex analysis in advanced mathematics.

MATH 7363B. NUMERICAL ANALYSIS.

This course examines advanced numerical analysis techniques for the analysis and implementation of mathematical algorithms. Emphasis is placed on the theoretical foundations of numerical methods, including stability, convergence, consistency, and error analysis, as well as practical implementation using computational and computer algebra systems. Symbolic, numerical, and graphical techniques are used to analyze algorithm performance. Applications are drawn from mathematics, science, and engineering. Instructional modality will be appropriate for the topic and determined by the instructor.

MATH 7363C. Functional Analysis.

This course examines foundational results and methods in functional analysis at the doctoral level. Core topics include the Hahn-Banach theorem, the uniform boundedness principle, and the open mapping theorem, along with their consequences for normed linear spaces and Banach spaces. Additional topics may include bounded linear operators, dual spaces, weak topologies, and selected applications to analysis and partial differential equations. Emphasis is placed on rigorous proof, abstract reasoning, and the role of functional analytic techniques in modern mathematics. Prerequisite: MATH 7303 with a "C" or better.

MATH 7363E. Numerical Analysis II.

This course examines advanced numerical methods for the solution of partial differential equations. Emphasis is placed on the analysis and numerical implementation of algorithms for linear and selected nonlinear partial differential equations. Topics may include finite difference, finite element, and spectral methods; stability, consistency, and convergence analysis; and the solution of large linear systems arising from discretized PDEs. Applications are drawn from mathematics, science, and engineering to illustrate methodological principles rather than prescribe applied outcomes. Prerequisite: MATH 7363B with a grade of a "C" or better.

MATH 7363F. Functional Analysis II.

This course examines advanced topics in functional analysis with a focus on infinite‑dimensional vector spaces and their applications. The course studies spaces of functions, measures, and distributions, emphasizing the structural and analytical differences between finite‑ and infinite‑dimensional settings. Topics may include Banach and Hilbert space theory, Fourier transform methods, bounded and unbounded linear operators, and selected aspects of operator theory. Attention is given to the role of functional analysis in modern analysis, partial differential equations, and numerical analysis. Emphasis is placed on rigorous proof, abstract reasoning, and the development of techniques used to analyze complex mathematical problems. Prerequisite: MATH 7363C with a grade of "C" or better.

MATH 7366C. Teaching Teachers (In-Service; Pre-Service).

This course examines research‑based approaches to the preparation and professional development of mathematics teachers. Topics include the education of pre‑service and in‑service teachers, theoretical frameworks in teacher learning, and models of mathematics teacher education. The course analyzes research literature, policy documents, and professional standards relevant to mathematics teacher preparation, treating these sources as objects of scholarly study rather than prescriptive mandates. Students will be able to evaluate research-based models of professional development, compare perspectives, and discuss the implications of differing approaches to the teaching and learning of mathematics. Prerequisite: MATH 7306 with a grade of 'B' or better.

MATH 7366D. Teaching Specialized Content.

This course provides an in-depth study of a specialized content area in mathematics with emphasis on teaching and learning. The specific content area will vary by instructor and their specialization. Some examples include geometry, quantitative reasoning, probability and statistics. Attention is given to implications for curriculum, classroom practice, teacher professional development, theories of teaching and learning, and methods for research. Students will be able to interpret, discuss, and synthesize scholarly work on the focal topic.

MATH 7366E. Developmental Mathematics Curriculum.

This course examines research, development, and evaluation related to developmental mathematics curricula. Emphasis is placed on the study of curriculum scope and sequence, instructional goals, and design principles underlying developmental mathematics programs. The course analyzes research literature, research‑based models, and selected policy and professional documents relevant to developmental mathematics, treating these materials as objects of scholarly inquiry rather than prescriptive mandates. Students examine how curricular frameworks are designed, evaluated, and revised in response to research findings.

MATH 7367B. Advanced Group Theory.

This course examines advanced topics in group theory at the doctoral level. Topics may include solvable, p‑solvable, and nilpotent groups; group actions; transfer theorems; simple groups and composition series; the generalized Fitting subgroup; automorphism groups; classical groups; and linear representations of groups. Emphasis is placed on structural results, proof techniques, and the role of group theory in modern algebra. The course develops rigorous reasoning and abstraction skills necessary for advanced study and research in algebra. Prerequisite: MATH 7307 with a grade of "C" or better.

MATH 7369C. Low-Dimensional Topology.

This course introduces advanced topics in low‑dimensional topology at the doctoral level. Topics include the study of surfaces, knots and links, 3‑manifolds, and selected aspects of 4‑manifold theory. Emphasis is placed on foundational results, key techniques, and current research directions in low‑dimensional topology. Students examine how geometric, algebraic, and topological methods are used to analyze low‑dimensional spaces. The course develops rigorous reasoning and familiarity with ideas central to contemporary research in topology, preparing students for further study and research in geometric and topological fields. Prerequisite: MATH 7307 and MATH 7309 with grades of "C" or better.

MATH 7369D. Characteristic Classes.

This course examines vector bundles and characteristic classes at the doctoral level. Topics include Stiefel-Whitney classes, Chern classes, the Euler class, and Pontrjagin classes, with emphasis on their definitions, properties, and methods of computation. Additional topics may include applications to manifold immersion and embedding problems. The course explores how characteristic classes serve as fundamental tools in topology and geometry, connecting algebraic, geometric, and topological techniques. Emphasis is placed on rigorous proof, abstract reasoning, and the role of characteristic classes in contemporary mathematical research. Prerequisite: MATH 7317 and MATH 7319 with grades of a "C" or better.

MATH 7369E. Differential Geometry.

This course examines modern tools and methods of differential geometry at the doctoral level. Topics include smooth manifolds, Riemannian metrics, connections, covariant derivatives, geodesics, curvature, and intrinsic and extrinsic geometric computations. Additional topics may include hyperbolic geometry, Lie groups, Chern-Weil theory, surfaces of prescribed mean curvature, the Gauss-Bonnet theorem, and the Cartan-Hadamard theorem. Emphasis is placed on rigorous proof, geometric intuition, and the role of differential geometry in contemporary mathematical research. Prerequisite: MATH 7307 and MATH 7309 with grades of "C" or better.

MATH 7371A. Advanced Graph Theory.

This course is an advanced study of graph theory, emphasizing both classical results and modern research directions selected by the instructor. Topics may include Turán‑type problems, Ramsey theory, extremal graph theory, random graph theory, algebraic graph theory, domination and distance parameters, and selected applications. The course focuses on theoretical frameworks, proof techniques, and the analysis of graph structures that arise in contemporary combinatorics. Students engage with foundational and current research results to develop advanced problem‑solving skills and mathematical maturity, preparing them for independent research in graph theory and related areas. Prerequisite: MATH 7321 with a grade of "B" or better.

MATH 7371B. Advanced Combinatorics.

This course provides an advanced study of combinatorics with emphasis on both classical structures and modern theoretical developments. Topics may include block designs, Latin squares, combinatorial optimization, coding theory, matroids, difference sets, and finite geometry. The course focuses on rigorous definitions, proof techniques, and the analysis of combinatorial structures that arise across mathematics. Students examine foundational results and selected contemporary work to develop advanced problem‑solving skills and mathematical maturity. The course prepares students for further research in combinatorics and related areas of mathematics. Prerequisite: MATH 7331 with a grade of 'B' or better.

MATH 7371C. Combinatorial Number Theory.

This course provides an advanced study of fundamental techniques in combinatorial number theory. Topics may include additive number theory, Waring’s problem, and probabilistic methods in number theory. Emphasis is placed on rigorous definitions, proof techniques, and structural analysis of number‑theoretic problems using combinatorial methods. Students engage with classical results and selected modern developments to build mathematical maturity and research readiness. The course is designed to support doctoral‑level study by strengthening abstract reasoning skills and preparing students for advanced research in number theory and related areas. Prerequisite: MATH 7331 with a grade of 'B' or better.

MATH 7371D. Discrete Optimization.

This course provides an advanced study of fundamental techniques in discrete optimization. Topics may include linear programming, integer and nonlinear integer programming, dynamic programming, matroids, and computational complexity, as well as classical optimization problems such as scheduling, location, transportation, postman, and traveling salesman problems. The course emphasizes rigorous problem formulation, mathematical modeling, and algorithmic analysis. Students examine theoretical foundations and complexity considerations, including NP‑completeness, to assess problem feasibility and solution approaches. The course prepares students for advanced research and applications in optimization, operations research, theoretical computer science, and applied mathematics. Prerequisite: MATH 7321 and 7331 with grades of "B" or better.

MATH 7371F. Probabilistic Methods in Discrete Mathematics.

This course provides an advanced study of probabilistic techniques used in discrete mathematics. Topics may include linearity of expectation, alterations, second‑moment methods, the Lovász local lemma, correlation inequalities, martingales, the Poisson paradigm, and pseudo‑randomness. These methods are applied to problems arising in graph theory, combinatorics, combinatorial number theory, combinatorial geometry, and the analysis of algorithms. Emphasis is placed on rigorous proofs, careful probabilistic reasoning, and the interpretation of random structures. The course prepares students for advanced research by developing mathematical maturity and familiarity with probabilistic tools central to modern discrete mathematics. Prerequisite: MATH 7321 and 7331 with grades of "B" or better.

MATH 7371G. Applied Discrete Mathematics.

This course introduces fundamental concepts in applied discrete mathematics, including logic, Boolean algebra, binomial coefficients, graph theory, and combinatorics. Emphasis is placed on the application of discrete mathematical methods to problems arising in areas such as algorithmic complexity and network theory. Topics may vary by instructor, allowing flexibility in the selection of applications and discrete structures. The course focuses on rigorous reasoning, problem formulation, and the use of discrete techniques to analyze applied problems.

MATH 7371H. Combinatorial Networks.

This course provides an advanced study of combinatorial networks, focusing on the use of combinatorial methods to model and analyze interconnected structures. The course introduces fundamental concepts as well as selected recent developments in the field. Emphasis is placed on structural reasoning, abstraction, and rigorous mathematical analysis of networks arising in discrete settings. Students examine theoretical frameworks used to represent complex relationships and dependencies within networked systems. The course is designed for graduate students preparing for research in mathematics and related disciplines and develops mathematical maturity, proof‑based reasoning, and familiarity with modern research directions. Prerequisite: MATH 7307 with a grade of "B" or better.

MATH 7371I. Advanced Set Theory.

This course introduces foundational methods and structures used in contemporary set theory research. Topics include the axioms of Zermelo-Fraenkel set theory with Choice (ZFC), ordinals and cardinals, transfinite recursion, and the von Neumann universe. The course also examines selected advanced topics such as large cardinals, Gödel’s constructible universe, and forcing techniques. Emphasis is placed on formal proof methods, internal model construction, and independence results.

MATH 7373B. Partial Differential Equations I.

This course examines foundational theory and methods for partial differential equations at the graduate level. Topics include typical equations arising in mathematical physics, first‑order equations and the Cauchy problem, classification of second‑order equations, and the Cauchy problem for hyperbolic equations. Additional topics include Duhamel’s principle, potential theory and elliptic equations, the maximum principle, and parabolic equations. Emphasis is placed on rigorous analysis, solution techniques, and interpretation of results within a mathematical framework. The course develops analytical tools essential for advanced study in applied mathematics, analysis, and related fields.

MATH 7373C. Partial Differential Equations II.

This course examines advanced theory of partial differential equations with emphasis on existence and uniqueness results for boundary value problems. Topics include linear evolution equations, variational and non‑variational techniques, Hamilton–Jacobi equations, and conservation laws. Emphasis is placed on rigorous reasoning, theoretical foundations, and connections between partial differential equations, analysis, optimization, and numerical methods. The course builds on prior graduate‑level study of partial differential equations and prepares students for advanced research and coursework in applied and theoretical mathematics. Prerequisite: MATH 7373B with a grade of "B" or better.

MATH 7373G. Spectral Methods.

This course examines spectral methods for the numerical solution of differential equations. Emphasis is placed on spectral collocation techniques and the efficient numerical implementation of algorithms. Topics include Fourier and Chebyshev methods applied to ordinary and partial differential equations arising in areas such as fluid mechanics, wave phenomena, and quantum mechanics. The course addresses accuracy, stability, and computational efficiency of spectral algorithms. By integrating theoretical analysis with computational practice, the course prepares students for advanced study and research involving high‑accuracy numerical methods for differential equations. Prerequisite: MATH 7363E with a grade of "B" or better.

MATH 7378A. Problem Solving, Reasoning, and Proof.

This course examines fundamental concepts of mathematical problem solving, logical reasoning, set theory, and proof within mathematics education. Students study how these concepts are developed, represented, and analyzed across mathematics curricula spanning pre‑college through undergraduate levels P-20. Emphasis is placed on theoretical perspectives, research findings, and instructional frameworks related to reasoning and proof. Through examination of curricular materials and educational practices spanning pre-school through college, students will be able to discuss how these concepts are introduced and developed. Prerequisite: MATH 7306 with a grade of "B" or better.

MATH 7378B. Connecting and Communicating Math.

This course examines one of the basic principles involved in mathematics education: Connecting and Communicating Mathematics. This fundamental theme will be reviewed, researched, and discussed. Prerequisite: MATH 7306.

MATH 7378C. Students’ Mathematical Ideas.

This course examines research‑based perspectives on students’ mathematical ideas and ways of thinking. Emphasis is placed on understanding how students conceptualize mathematical concepts, reason about mathematical problems, and develop mathematical understanding across educational contexts. The course surveys theoretical frameworks and research methodologies used to study students’ mathematical thinking, treating instructional practices and learning theories as objects of scholarly inquiry. Students analyze and interpret students’ mathematical reasoning, evaluate and critique research on student thinking, and synthesize findings across empirical studies. Prerequisite: MATH 7306 with a grade of a "B" or better.

MATH 7378G. Discourse Processes, Traditions, and Analysis in Mathematics Education.

This course examines theories, traditions, and methods of discourse analysis as applied to mathematics education. Drawing on interdisciplinary perspectives from the humanities and social sciences, the course focuses on how discourse is conceptualized, studied, and analyzed in mathematical settings. Students examine theoretical frameworks and methodological approaches used to investigate classroom discourse, mathematical communication, and meaning‑making in mathematics learning. Students explain how different discourse traditions are used to address research questions in mathematics education. Prerequisite: MATH 7306 with a grade of "B" or better.

MATH 7385. Independent Study in Mathematics.

This course provides an individualized graduate‑level study opportunity in mathematics under the supervision of a faculty member. Students investigate a focused topic selected in consultation with the supervising faculty member, engaging with advanced mathematical concepts, methods, and literature appropriate to the chosen area. Emphasis is placed on developing depth of understanding, rigorous reasoning, and scholarly independence. The specific content is determined by the instructor and may include directed readings, problem analysis, or research‑oriented activities. This course may be repeated for credit when the topic emphasis differs.

MATH 7386. Independent Study in Mathematics Education.

This course provides an individualized doctoral‑level study opportunity in mathematics education under the supervision of a faculty member. Students investigate a focused topic selected in consultation with the supervising faculty member, examining relevant research, theories, and methodological approaches. Emphasis is placed on developing scholarly depth, engaging critically with the literature, and applying appropriate analytical or research‑based approaches within the chosen topic area. Instructional modality and expectations are determined by the instructor and may include directed readings, research activities, or analytical projects. This course may be repeated for credit when the topic of emphasis differs.

MATH 7387. Consulting.

This course focuses on developing skills in the collaborative practice of mathematics and statistics. The course will consist of class discussion, readings, and different projects. Topics include the application of mathematics or statistics to solve real-world problems through case studies and collaborative projects, as well as the application of ethical considerations to their professional practice. Taking this course will allow students to gain skills in problem solving and providing mathematical and statistical consulting services.

MATH 7389. Internship.

This course provides a supervised internship experience designed to develop practical and professional skills in mathematics or mathematics education. Students work under the guidance of a faculty supervisor while engaging in applied activities in industry, government agencies, educational institutions, or other approved settings. Internship experiences must directly contribute to the student’s understanding of mathematical applications or mathematics education practice. Emphasis is placed on the integration of academic knowledge with professional experience, reflective analysis of applied work, and communication of outcomes through written documentation or presentations.

MATH 7396. Mathematics Education Research Seminar.

This course engages students in collaborative mathematics education research through supervised faculty mentorship and structured seminar activities. Students identify a researchable problem in mathematics education, review and synthesize relevant literature, formulate a research question, and design an appropriate methodology. Students analyze data using methods aligned with the study design, interpret results, and articulate conclusions and limitations consistent with scholarly standards. Emphasis is placed on research ethics, methodological rigor, and clear academic writing. Students create a draft research manuscript suitable for scholarly review or further development. Prerequisite: MATH 7356 and [ED 7352 or MATH 7352 or MATH 7346] with grades of "B" or better.

MATH 7399A. Dissertation.

This course provides doctoral students with the opportunity to conduct an independent, original research project that contributes new knowledge to mathematics, mathematics education, or a closely related field under the supervision of a faculty advisor. Students identify a significant research problem, engage deeply with the scholarly literature, and employ appropriate theoretical, empirical, or methodological approaches to address the problem. Emphasis is placed on originality, rigor, and sustained scholarly inquiry consistent with professional standards of doctoral research. The course culminates in the completion and defense of a written dissertation that demonstrates the student’s ability to conduct independent research and communicate results at a professional level. While conducting dissertation research and writing, students must be continuously enrolled each long semester. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: Instructor Approval.

MATH 7599A. Dissertation.

This course provides doctoral students with the opportunity to conduct an independent, original research project that contributes new knowledge to mathematics, mathematics education, or a closely related field under the supervision of a faculty advisor. Students identify a significant research problem, engage deeply with the scholarly literature, and employ appropriate theoretical, empirical, or methodological approaches to address the problem. Emphasis is placed on originality, rigor, and sustained scholarly inquiry consistent with professional standards of doctoral research. The course culminates in the completion and defense of a written dissertation that demonstrates the student’s ability to conduct independent research and communicate results at a professional level. While conducting dissertation research and writing, students must be continuously enrolled each long semester. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: Instructor Approval.

MATH 7699A. Dissertation.

This course provides doctoral students with the opportunity to conduct an independent, original research project that contributes new knowledge to mathematics, mathematics education, or a closely related field under the supervision of a faculty advisor. Students identify a significant research problem, engage deeply with the scholarly literature, and employ appropriate theoretical, empirical, or methodological approaches to address the problem. Emphasis is placed on originality, rigor, and sustained scholarly inquiry consistent with professional standards of doctoral research. The course culminates in the completion and defense of a written dissertation that demonstrates the student’s ability to conduct independent research and communicate results at a professional level. While conducting dissertation research and writing, students must be continuously enrolled each long semester. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: Instructor Approval.

MATH 7999A. Dissertation.

This course provides doctoral students with the opportunity to conduct an independent, original research project that contributes new knowledge to mathematics, mathematics education, or a closely related field under the supervision of a faculty advisor. Students identify a significant research problem, engage deeply with the scholarly literature, and employ appropriate theoretical, empirical, or methodological approaches to address the problem. Emphasis is placed on originality, rigor, and sustained scholarly inquiry consistent with professional standards of doctoral research. The course culminates in the completion and defense of a written dissertation that demonstrates the student’s ability to conduct independent research and communicate results at a professional level. While conducting dissertation research and writing, students must be continuously enrolled each long semester. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: Instructor Approval.