Mathematics (MS)

The Master of Science (MS) in Mathematics program is designed to provide Additional requirements for international applicants: a graduate level education for students who intend to teach at various  TOEFL or IELTS Language Proficiency Test with minimum scores: 550 on levels, students who will continue or seek employment within the industrial paper-based, 213 on computer based, or 79 on internet-based for the sector, and students who intend to continue their education beyond the TOEFL; 6.5 for the IELTS. TOEFL and IELTS scores are valid for 2 years. master’s level at other institutions. For additional information, click here.  English translation of educational records. The Master of Science in Mathematics has a concentration in Mathematical  Transcript Evaluation by the Foreign Credentials Service of America Sciences. This program will not prepare the students for any license or (FCSA). For additional information, click here. certification.  Financial Documentation showing sufficient funds (minimum of *This program has the option to be completed fully ONLINE. $25,000) to cover all expenses (living and academic) for the first year of study. For additional information, click here. A dm i ss i on Requirements  Immigration documents, including a current copy of your valid Apply to the UTRGV Graduate College: passport. For additional information, click here.

Step #1: Submit a UTRGV Graduate Application at Program Contact http://www.utrgv.edu/graduate/for-future-students/how-to-apply/ Program Director: Dr. Timothy Huber Phone: (956) 665-2173 The university application fee can be paid online by credit card or E-Mail: [email protected] electronic check (in the online application). All application fees are nonrefundable.

Step #2: Request your transcripts, two letters of recommendation, and other supporting documentation to be mailed to:

The University of Texas Rio Grande Valley Deadlines The Graduate College Fall Spring Summer I Summer II Marialice Shary Shivers Bldg. 1.158 Domestic April 15 October 1 March 1 March 1 1201 W. University Drive International April 15 October 1 March 1 March 1 Edinburg, TX 78539-2999  Review and submit all Program Requirements:  Bachelor’s degree in mathematics or related field with a minimum of 12 hours of upper-division mathematics or statistics course work and a grade of ‘B’ or better on all upper-division mathematics and/or statistics course work.  Undergraduate GPA of at least 3.0 in upper-level Mathematics courses.  Official transcripts from each institution attended (must be submitted directly to UTRGV).  Two letters of recommendation from professional or academic sources.  Letter of Intent detailing professional goals and reasons for pursuing the graduate degree.  GRE General Test. GRE test scores are valid for 5 years.

Additional requirements for domestic applicants who attended foreign universities:  TOEFL or IELTS Language Proficiency Test with minimum scores: 550 on paper-based, 213 on computer based, or 79 on internet-based for the TOEFL; 6.5 for the IELTS. TOEFL and IELTS scores are valid for 2 years. For additional information, click here.  English translation of educational records.  Transcript Evaluation by the Foreign Credentials Service of America (FCSA). For additional information, click here.

www.utrgv.edu/grad

Program Requirements Choose one of the following capstone options:

Required Courses 9 Capstone Requirement 6 MATH 6330: Linear Algebra 3 Thesis MATH 6331: Algebra I 3 MATH 7300: Thesis I 3 MATH 6352: Analysis I 3 MATH 7301: Thesis II 3

Choose one of the following concentrations: OR

Mathematics Concentration Project MATH 6391: Master’s Project 3 Required Courses 6 Additional 3 hours of electives 3 MATH 6332: Algebra II 3 MATH 6353: Analysis II 3 OR

Designated Electives 15 Chosen from the following: Non‐Thesis MATH 6323: 3 Additional 6 hours of electives 6 MATH 6329: 3 Written and/or Oral Comprehensive Exam MATH 6339: Complex Analysis 3 MATH 6359: Applied Analysis 3 Total graduate hours for degree: 36

MATH 6360: Ordinary Differential Equations 3 MATH 6361: Partial Differential Mathematics Teaching Equations 3 Concentration MATH 6362: Fourier Analysis 3 MATH 6363: Integrable Systems 3 Required Courses 9 MATH 6364: Statistical Methods 3 Chosen from the following: MATH 6366: Micro‐local Analysis 3 MATH 6325: Contemporary Geometry 3 MATH 6367: Functional Analysis 3 MATH 6327: Mathematical Modeling MATH 6368: Operator Theory 3 with Technology 3 MATH 6370: Topology 3 MATH 6329: Number Theory 3 MATH 6371: Differential Geometry 3 MATH 6365: Probability and Statistics 3 MATH 6372: 3 MATH 6373: Algebraic Geometry 3 Designated Electives 12 MATH 6375: Numerical Analysis 3 Chosen from the following: MATH 6376: Numerical Methods for MATH 6305: History of Mathematics 3 Partial Differential Equations 3 MATH 6307: Collegiate Mathematics MATH 6385: Cryptology and Codes 3 Teaching 3 MATH 6387: Mathematical Modeling 3 MATH 6309: Integrating Technology MATH 6388: Discrete Mathematics 3 into Mathematics 3 MATH 6399: Special Topics in MATH 6310: Mathematics Teaching Mathematics 3 and Learning 3 MATH 6323: Group Theory 3 MATH 6328: Special Topics in Mathematics Teaching 3

MATH 6399: Special Topics in MATH 6376: Numerical Methods for Mathematics 3 Partial Differential Equations 3 MATH 6377: Mathematical Fluid Choose one of the following capstone options: Mechanics 3 MATH 6378: Inverse Problem and Capstone Requirement 6 Image Reconstruction 3 Thesis MATH 6379: Stochastic Processes 3 MATH 7300: Thesis I 3 MATH 6385: Cryptology and Codes 3 MATH 7301: Thesis II 3 MATH 6387: Mathematical Modeling 3 MATH 6388: Discrete Mathematics 3 OR MATH 6399: Special Topics in Mathematics 3 Project MATH 6455: Applied Mathematics I 4 MATH 6391: Master’s Project 3 MATH 6456: Applied Mathematics II 4 Additional 3 hours of electives 3 Choose one of the following capstone options: OR Capstone Requirement 6 Non‐Thesis Thesis Additional 6 hours of electives 6 MATH 7300: Thesis I 3 Written and/or Oral Comprehensive Exam MATH 7301: Thesis II 3

Total graduate hours for degree: 36 OR

Project Industrial and Applied Mathematics MATH 6391: Master’s Project 3 Additional 3 hours of electives 3 Concentration OR Required Courses 9 MATH 6360: Ordinary Differential Non‐Thesis Equations 3 Additional 6 hours of electives 6 MATH 6361: Partial Differential Written and/or Oral Comprehensive Exam Equations 3 MATH 6375: Numerical Analysis 3 Total graduate hours for degree: 36

Designated Electives 12 Chosen from the following: Statistics Concentration MATH 6332: Algebra II 3 MATH 6339: Complex Analysis 3 Required Courses 9 MATH 6353: Analysis II 3 MATH 6364: Statistical Methods 3 MATH 6362: Fourier Analysis 3 MATH 6365: Probability and Statistics 3 MATH 6363: Integrable Systems 3 MATH 6375: Numerical Analysis 3 MATH 6364: Statistical Methods 3 MATH 6365: Probability and Statistics 3 Designated Electives Chosen 12 MATH 6366: Micro‐local Analysis 3 from the following: MATH 6336: MATH 6367: Functional Analysis 3 Advanced Sampling 3 MATH 6368: Operator Theory 3 MATH 6353: Analysis II 3 MATH 6369: Mathematical Methods 3 MATH 6379: Stochastic Processes 3 MATH 6380: Time Series Analysis 3 MATH 6381: Mathematical Statistics 3 MATH 6307: Collegiate Mathematics MATH 6382: Statistical Computing 3 Teaching [3‐0] MATH 6383: Experimental Design and This course provides opportunities for students Categorical Data 3 to have a practical experience in teaching MATH 6384: Biostatistics 3 college‐level mathematics courses supervised MATH 6386: Applied Research by faculty. Prerequisite: Departmental Design and Analysis 3 approval. MATH 6387: Mathematical Modeling 3 MATH 6388 Discrete Mathematics 3 MATH 6309: Integrating Technology into MATH 6399: Special Topics in Mathematics [3‐0] Mathematics 3 This is an introductory course related to the latest technological computer programs, Choose one of the following capstone options: especially in mathematics. It covers some of the following educational computer softwares: Capstone Requirement 6 graphing calculator, dynamic geometry, Thesis computer algebra systems, publishing softwares MATH 7300: Thesis I 3 and some multimedia and internet related MATH 7301: Thesis II 3 softwares. Prerequisite: Departmental approval. OR MATH 6310: Mathematics Teaching and Project Learning [3‐0] MATH 6391: Master’s Project 3 This course examines issues, trends and Additional 3 hours of electives 3 research related to the teaching/learning of secondary school mathematics. Specific topics OR will vary, but could include: technology in the classroom, mathematical problem solving and Non‐Thesis the use of applications in the teaching of Additional 6 hours of electives 6 mathematics. Prerequisite: Graduate standing Written and/or Oral Comprehensive Exam in mathematics.

Total graduate hours for degree: 36 MATH 6323: Group Theory [3‐0] This course is an introduction to group theory, Course Descriptions one of the central areas in modern algebra. Topics will include the theorems of Jordan‐ MATH 6305: History of Mathematics [3‐0] Holder, Sylow, and Schur‐Zassenhaus, the This course introduces students to the history treatment of the generalized Fitting subgroup, a of the development of mathematical ideas and first approach to solvable as well as simple techniques from early civilization to the groups (including theorems of Ph. Hall and present. The focus will be on both the lives and Burnside). Prerequisite: Departmental approval. the works of some of the most important mathematicians. Prerequisite: Departmental MATH 6325: Contemporary Geometry [3‐0] approval. This course contains selected topics in computational, combinatorial and differential geometry as well as combinatorial topology. Topics include the point location problem, triangulations, Voronoi diagrams and Delaunay triangulations, plane curves and curvature, surfaces and polyhedrons and Euler MATH 6330: Linear Algebra [3‐0] characteristic. Prerequisite: Departmental Topics include the proof‐based theory of approval. matrices, determinants, vector spaces, linear spaces, linear transformations and their matrix MATH 6327: Mathematical Modeling with representations, linear systems, linear Technology [3‐0] operators, eigenvalues and eigenvectors, Mathematical Modeling is the art of taking a invariant subspaces of operators, spectral real‐world problem and stating it in decompositions, functions of operators and mathematical terms. It often involves making applications to science, industry and business. simplifying assumptions. Students will gain Prerequisite: MATH 2318 Linear Algebra with a experience in the use of technology such as MS grade of “C” or higher. Excel and Visual Basic programs, and learn how technology may be applied to construct MATH 6331: Algebra I [3‐0] mathematical models in practical. In this course, This course is an extension of the we get in the habit of doing all the parts of the undergraduate course in abstract algebra. math modeling cycle: modeling, solving, Topics include polynomial rings over a field and checking, and guessing. We will also consider finite field extensions. Prerequisite: MATH 3363 many common mathematical models, and Modern Algebra I with a grade of “C” or higher. explore their properties. Prerequisite: Graduate standing in mathematics. MATH 6332: Algebra II [3‐0] The purpose of this course is to provide MATH 6328: Special Topics in Mathematics essential background in groups, rings and fields, Teaching [3‐0] train the student to recognize algebraic A critical analysis of issues, trends and historical structures in various settings and apply the developments in elementary and/or secondary tools and techniques made available by mathematics teaching with emphasis on the algebraic structures. Topics include groups, areas of curriculum and methodology. This structure of groups, rings, modules, Galois course may be repeated for credit when topic theory, structure of fields, commutative rings changes. Prerequisite: Graduate standing in and modules. Prerequisite: MATH 6331. mathematics. MATH 6336: Advanced Sampling [3‐0] MATH 6329: Number Theory [3‐0] This course will focus on planning, execution This course is an introduction to number theory, and analysis of sampling from finite one of the major branches of modern populations; simple, stratified, multistate and mathematics. Topics include arithmetic systematic sampling; ratio estimates. functions, multiplicativity, Moebius inversion, Prerequisite: Departmental approval. modular arithmetic, Dirichlet characters, Gauss sums, primality testing, distribution of primes, MATH 6339: Complex Analysis [3‐0] primitive roots, quadratic reciprocity, This course is an introduction to the Diophantine equations, and continued fundamentals of complex analysis. Topics fractions. Applications and further topics include: The Riemann sphere and stereographic include cryptography, partitions, projection, elementary functions, analytic representations by quadratic forms, elliptic functions, the theory of complex integration, curves, modular forms, irrationality, and power series, the theory of residues, the transcendence. Prerequisite: Departmental Cauchy‐Riemann equations, conformal and approval. isogonal diffeomorphisms, Weierstrass products, the Mittag‐Leffler theorem. Prerequisite: Departmental approval. MATH 6352: Analysis I [3‐0] with a grade of “C” or higher, or consent of The purpose of this course is to provide the instructor. necessary background for all branches of modern mathematics involving analysis and to MATH 6361: Partial Differential train the student in the use of axiomatic Equations [3‐0] methods. Topics include metric spaces, This course considers the existence, uniqueness sequences, limits, continuity, function spaces, and approximation of solutions to linear and series, differentiation and the non‐linear ordinary, partial and functional Riemann integral. Prerequisite: MATH 3372 differential equations. It also considers the Real Analysis I with a grade of “C” or higher. relationships of differential equations with functional analysis. Computer‐related methods MATH 6353: Analysis II [3‐0] of approximation are also discussed. The purpose of this course is to present Prerequisite: MATH 3341 Differential Equations advanced topics in analysis. Topics may be with a grade of “C” or higher, or consent of chosen from (but not restricted to) normed instructor. linear spaces, Hilbert spaces, elementary spectral theory, complex analysis, measure and MATH 6362: Fourier Analysis [3‐0] integration theory. Prerequisite: MATH 6352. The course includes trigonometric series and Fourier Series, Dirichlet Integral, convergence MATH 6359: Applied Analysis [3‐0] and summability of Fourier Series, uniform This course provides an introduction to convergence and Gibbs phenomena, L2 space, methods and applications of mathematical properties of Fourier coefficients, Fourier analysis. Topics include: function spaces, linear transform and applications, Laplace transform spaces, inner product spaces, Banach and and applications, distributions, Fourier series of Hilbert spaces; linear operators on Hilbert distributions, Fourier transforms of generalized spaces, eigenvalues and eigenvectors of functions and orthogonal systems. Prerequisite: operators and orthogonal systems; Green’s MATH 6353 or consent of instructor. functions as inverse operators; relations between integral and ordinary differential MATH 6363: Integrable Systems [3‐0] equations and methods of solving integral This course includes solitons and integrable equations. Some special functions important for systems. The purpose of the course is to show applications are shown. students how to analyze nonlinear partial Prerequisites: MATH 2318 Linear Algebra, differential equations for physical problems and MATH 3341 Differential Equations, and MATH how to solve the equations using traveling wave 4344 Boundary Value Problems or equivalent. settings. Prerequisite: MATH 3349 with a grade MATH 6352 is recommended. of “C” or higher or consent of instructor

MATH 6360: Ordinary Differential MATH 6364: Statistical Methods [3‐0] Equations [3‐0] This is a course in the concepts, methods and This course examines existence and uniqueness usage of statistical data analysis. Topics include theorems, methods for calculating solutions to test of hypotheses and confidence intervals; systems of ordinary differential equations, the linear and multiple regression analysis; study of algebraic and qualitative properties of concepts of experimental design, randomized solutions, iterative methods for numerical blocks and factorial analysis; a brief solutions of ordinary differential equations and introduction to non‐parametric methods; and an introduction to the finite element methods. the use of statistical software. Prerequisite: Prerequisite: MATH 3341 Differential Equations Departmental approval. MATH 6365: Probability and Statistics [3‐0] Theorem, Riesz Theorem, compact operators); Topics in this course include set theory and Hilbert spaces; linear operators on Hilbert concept of probability, conditional probability, spaces; eigenvalues and eigenvectors of random variables, discrete and continuous operators. Prerequisite: MATH 3372 Real probability distributions, distribution and Analysis I with a grade of “C” or higher or expectations of random variables, moment consent of instructor. generating functions, transformation of random variables, order statistics, central limit theorem MATH 6368: Operator Theory [3‐0] and limiting distributions. Prerequisite: MATH This course primarily covers bounded linear 2415 Calculus III with a grade of “C” or higher, operators on a Hilbert spaces. The topics are: or consent of instructor. linear and bilinear functionals, inner product and norm; Hilbert space; subspace; operators; MATH 6366: Micro‐local Analysis [3‐0] spectrum of operators; spectral theorem for Topics include: basic concepts and normal operators; Polar decomposition; computational technique of distributions contractions; isometries; quasinormal (generalized functions, the singular support of operators; subnormal operators; hyponormal distributions, the convolutions of distributions, operators; invariant subspaces. Prerequisite: the structure of distributions, approximations MATH 3372 Real Analysis I with a grade of “C” by test functions, Schwartz space; Fourier or higher or consent of instructor. transforms of test functions and distributions, Paley‐Wiener theorem. Schwartz kernel MATH 6369: Mathematical Methods [3‐0] theorem. Sobolev spaces, symbols, pseudo‐ Special functions, perturbation methods, differential operators (PDOs), the kernel of asymptotic expansion, partial differential pseudo‐local operators, PDOs and Sobolev equation models, existence and uniqueness, spaces, amplitude functions and PDOs, integral transforms, Green functions for ODEs transposed and adjoint to PDO operators. and PDEs, calculus of variations, methods of Proper PDOs, Product of PDOs, asymptotic least squares, Ritz‐Rayleigh and other series and expansions, product formula for approximate methods, integral equations, PDOs, symbols of transposed and adjoint generalized functions. Prerequisite: Graduate operators, symbol of composition and standing, and MATH 2415 Calculus III with a commutator of PDOs, elliptic operators, wave grade of "C" or higher. front set of distributions; Fourier integral operators. Prerequisite: Departmental MATH 6370: Topology [3‐0] approval. This course is a foundation for the study of analysis, geometry and algebraic topology. MATH 6367: Functional Analysis [3‐0] Topics include set theory and logic, topological This course provides an introduction to spaces and continuous functions, methods and applications of functional analysis. connectedness, compactness, countability and Topics include: topological vector spaces; locally separation axioms. Prerequisite: MATH 4355 convex spaces (Hahn‐Banach Theorem, weak Topology with a grade of "C" or higher, or topology, dual pairs); normed spaces; theory of consent of instructor. distributions (space of test functions, convolution, Fourier transform; Sobolev MATH 6371: Differential Geometry [3‐0] spaces); Banach spaces (Uniform Boundedness The course will introduce students to the study Principle, Open Mapping Theorem, Closed of smooth manifolds, fiber bundles, differential Graph Theorem and applications, Banach‐ forms, and Lie groups. Thereafter, Euclidean Alaoglus Theorem, Krein‐Milman Theorem); geometries and their common generalizations C(X) as a Banach space (Stone‐Weierstrass Klein and Riemannian geometries will be discussed with a focus on examples. If time allows the unifying notion of a Cartan geometry MATH 6376: Numerical Methods for Partial will also be introduced. Prerequisites: MATH Differential Equations [3‐0] 6352 or consent of instructor. This course provides a fundamental introduction to numerical techniques used in MATH 6372: Analytic Number Theory [3‐0] mathematics, computer science, physical This course serves as an introduction to sciences and engineering. The course covers fundamental results from analytic number basic theory and applications in the numerical theory. Its primary aim is to introduce real and solutions of elliptic, parabolic and hyperbolic complex analytic techniques in the theory of partial differential equations. Prerequisites: numbers. Topics include the distribution of MATH 2318 Linear Algebra, 2415 Calculus III primes, the theorem, primes in and MATH 3349 Numerical Methods with “C” or an arithmetic progression, averages of better or graduate‐level Numerical Analysis arithmetic functions, Dirichlet Series, Euler with a “B” or better, some familiarity with products, and representations by quadratic ordinary and partial differential equations and forms. Prerequisites: MATH 3372 Real Analysis I computer programming or consent of and MATH 3365 Number Theory with grades of instructor. "C" or higher, or consent of instructor. MATH 6377: Mathematical Fluid Mechanics [3‐0] This course provides an introduction to MATH 6373: Algebraic Geometry [3‐0] fundamental aspects of mathematical fluid The course will begin with an introduction to mechanics. Topics include classification of polynomials and ideals, Grobner bases, and fluids, flow characteristics, dimensional analysis, affine varieties. This includes the Hilbert Basis derivations of Euler, Bernoulli and Navier‐ Theorem, the Nullstellensatz, and the ideal‐ Stokes equations, complex analysis for two‐ variety correspondence. Thereafter, the course dimensional potential flows, exact solutions for will focus on examples and computations. Topics simple cases of flow such as plane Poiseuille include solving systems by elimination, flow, and Couette flow. Prerequisite: resultants, computations in local rings, modules Departmental approval. and syzygies, and polytopes and toric varieties. Prerequisite: MATH 6331 or consent of instructor. MATH 6378: Inverse Problem and Image Reconstructions [3‐0] MATH 6375: Numerical Analysis [3‐0] Topics include: inverse problem of linear PDEs, This course provides a fundamental Maxwell equation and Fourier integral operator, introduction to numerical techniques used in Back‐projection operator and applications in radar mathematics, computer science, physical image reconstruction, including synthetic sciences and engineering. The course covers aperture radar image and inverse synthetic basic theory on classical fundamental topics in aperture radar images arranged by antenna. numerical analysis such as: computer Prerequisite: Departmental approval. arithmetic, approximation theory, numerical differentiation and integrations, solution of linear and nonlinear algebraic systems, numerical solution of ordinary differential equations and error analysis of the abovementioned topics. Connections are made to contemporary research in mathematics and its applications to the real world. Prerequisites: MATH 2318 Linear Algebra and 2415 Calculus III with grades of “C” or better; and computer programming; or consent of instructor. fixed, random, and mixed models; split plot MATH 6379: Stochastic Processes [3‐0] designs, inference for categorical data, Discrete and Continuous Time Markov contingency tables, generalized linear models, Processes, Poisson Processes, Renewal logistic regression, logit and loglinear models. Processes, Diffusion Processes, Brownian Prerequisite: MATH 6364. Motion. Prerequisite. MATH 6365. MATH 6384: Biostatistics [3‐0] MATH 6380: Time Series Analysis [3‐0] This course is a survey of crucial topics in This course is an introduction to statistical time biostatistics; application of regression in series analysis. Topics include: ARIMA and other biostatistics; analysis of correlated data; logistic time series models, forecasting, spectral and Poisson regression for binary or count data; analysis, and time domain regression. Model survival analysis for censored outcomes; design identification, estimation of parameters, and and analysis of clinical trials; sample size diagnostic checking are included. Prerequisite: calculation by simulation; bootstrap techniques MATH 6379. for assessing statistical significance; data analysis using R. Prerequisite: Consent of instructor. MATH 6381: Mathematical Statistics [3‐0] This course in mathematical Statistics includes MATH 6385: Cryptology and Codes [3‐0] theory of estimation and hypothesis testing; Topics include: elementary ciphers, error‐ point estimation, interval estimation, sufficient control codes, public key ciphers, random statistics, decision theory, most powerful tests, number generator‐ error codes, and Data likelihood ration tests, chi‐square tests, Encryption Standard. Supporting topics from minimum variance estimation, Neyman‐Pearson number theory, linear algebra, group theory, theory of testing hypotheses, elements of and ring theory will also be decision theory. Prerequisite: MATH 6365. studied. Prerequisite: MATH 3363 Modern Algebra I with a grade of “C” or better. MATH 6382: Statistical Computing [3‐0] A course in modern computationally‐intensive MATH 6386: Applied Research Design and statistical methods including simulation, Analysis [3‐0] optimization methods, Monte Carlo integration, The content of this course will include different maximum likelihood /EM parameter estimation, types of research designs (experimental design, Markov chain Monte Carlo methods, resampling quasi‐experimental design, nonexperimental methods, non‐parametric density estimation. research design , and survey design); proper Prerequisite: Consent of instructor. procedures for research design; different types MATH 6383: Experimental Design and of research methods (introduce both Categorical Data [3‐0] quantitative and qualitative methods, but Design and analysis of experiments, including mainly focus on quantitative methods); how to one‐way and two‐way layouts; factorial use statistical software to perform statistical experiments; balanced incomplete block analysis procedures including logistic designs; crossed and nested classifications; regression, factor analysis, multivariate data analysis, etc., and applications in respective student‐oriented research projects. Prerequisite: Consent of instructor. MATH 6387: Mathematical Modeling [3‐0] This course presents the theory and application of mathematical modeling. Topics will be selected from dynamic models, stable and unstable motion, stability of linear and nonlinear systems, Liapunov functions, feedback, growth and decay, the logistic model, population models, cycles, bifurcation, catastrophe, biological and biomedical models, chaos, strange attractors, deterministic and random behavior. Prerequisite: Consent of instructor.

MATH 6388: Discrete Mathematics [3‐0] This course is an introduction to modern finite mathematics. Topics include methods of enumeration, analytic methods, generating functions, the theory of partitions, graphs, partially ordered sets, and an introduction to Polya’s theory of enumeration. Prerequisite: MATH 3363 Modern Algebra I or consent of instructor.

MATH 6391: Master’s Project [3‐0] Individual work or research on advanced mathematical problems conducted under the direct supervision of a faculty member. Prerequisites: Consent of instructor.

MATH 6399: Special Topics in Mathematics [3‐0] This course covers special topics in graduate level mathematics that are not taught elsewhere in the department. May be repeated for credit when topic is different. Prerequisite: Consent of instructor.

MATH 7300: Thesis I [3‐0] First part of two course sequence. Prerequisites: Graduate standing and consent of thesis advisor.

MATH 7301: Thesis II [3‐0] Second part of two course sequence. Prerequisites: Graduate standing and consent of thesis advisor.