Department of Mathematics

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.