MATH 502 LOGIC AND SET THEORY (3-0-3)(F)(Odd years). This course is structured as three five-week components: formal logic, set theory, and topics to be determined by the instructor. The logic component will include: formalization of language and proof, the completeness theorem, the Lowenheim-Skolem theorem. The set orderings, ordinals, the transfinite recursion theorem, the Axiom of Choice and its equivalents. PREREQ: 314.
MATH 505 ABSTRACT ALGEBRA (3-0-3)(F)(Odd-numbered years). Topics in group theory, ring theory and field theory with emphasis on finite and solvable groups, polynomials and factorization, extensions of fields. PREREQ: MATH 301 and MATH 305.
MATH 506 ADVANCED ALGEBRA (3-0-3)(S)(Even-numbered years). The study of algebraic topics taken from mappings, semi-groups, groups, Sylow Theorems, group actions, rings, ascending and descending chain conditions, polynomial rings, fields, field extensions, Galois theory, Modules, Tensor products. PREREQ: MATH 405 or MATH 505.
MATH 507 ADVANCED NUMBER THEORY (3-0-3)(F) (Even years).Arithmetic functions, Mobius Inversion, Fundamental Algorithms, Prime numbers, Factoring, quantification of number theoretic results. PREREQ: MATH 306.
MATH 509 SYMMETRIC KEY CRYPTOLOGY (3-0-3)(S)(Even years). One-way function, Hash function, pseudo-random number generators, DES, Rijndael and other symmetric key cryptosystems. PREREQ: MATH 305 or MATH 306 and one of the following: MATH 307, MATH 308, CS 367, CS 368, CS 567, CS 568.
MATH 511 INTRODUCTION TO TOPOLOGY (3-0-3)(F) (Even years). Sets, metric and topological spaces, product and quotient topology, continuous mappings, connectedness and compactness, homeomorphisms, fundamental group, covering spaces. PREREQ: MATH 314.
MATH 512 ADVANCED TOPOLOGY (3-0-3)(S)(Odd years). Introduction into concepts of algebraic and geometric topology: homotopy and homology groups, cohomology, manifolds, duality theorems, special topics. PREREQ: MATH 411 or 511 or PERM/INST.
MATH 514 ADVANCED CALCULUS
(4-0-4)(F). Introduction to fundamental elements of Analysis on Euclidean spaces including the basic differential and integral calculus. Topics include: Infinite series, sequences and series of function, uniform convergences, theory of integration, implicit function theorem and applications. PREREQ: MATH 275, MATH 301, and MATH 314.
MATH 515 ADVANCED ANALYSIS
(3-0-3)(S). Introduction to the fundamental elements of real
analysis and a foundation for writing graduate level proofs. Topics may
include: Banach spaces, Lebesgue measure and integration, metric and
topological spaces. The exact content is to be determined by the instructor.
PREREQ: MATH 414 or MATH 514. MATH 526 COMPLEX VARIABLES
(3-0-3)(S)(Odd years). Complex numbers, functions of a complex variable, analytic functions, infinite series, infinite products, integration, proofs and applications of basic results of complex analysis. Topics include the Cauchy integral formulas, the residue theorem, the Riemann mapping theorem and conformal mapping. PREREQ: MATH 275.
MATH 533 ORDINARY DIFFERENTIAL
EQUATIONS (3-0-3)(S) (Odd years). Theory of linear and nonlinear ordinary differential equations and their systems, including Dynamical systems theory. Properties of solutions including existence, uniqueness, asymptotic behavior, stability, singularities and boundedness. PREREQ: MATH 333.. MATH 536 PARTIAL DIFFERENTIAL
EQUATIONS (3-0-3)(S)(Even years). Theory of partial
differential equations and boundary value problems with applications to the
physical sciences and engineering. Detailed analysis of the wave equation, the
heat equation, and Laplace's equation using Fourier series and other tools.
PREREQ: MATH 333 or MATH 433 or MATH 533. MATH 537 APPLIED MATHEMATICS
(3-0-3)(S). Survey of mathematical models for problems in the
applied sciences and engineering, coming from areas such as fluid dynamics,
solid mechanics, and electromagnetism. Ordinary and partial differential
equations modeling physical problems will be studied. Mathematical techniques
may include perturbation analysis, calculus of variations, stability theory and
simple numerical methods. Programming assignments. PREREQ: MATH 275 and MATH 333. MATH 562 PROBABILITY AND
STATISTICS II(3-0-3)(F).
MATH 565 NUMERICAL ANALYSIS I (3-0-3)(F). Approximation of functions, solutions of equations in one variable and of linear systems. Polynomial, cubic spline, and trigonometric interpolation. Optimization. Programming assignments. PREREQ: MATH 301 or MATH 333.
MATH 566 NUMERICAL ANALYSIS II (3-0-3)(S). Techniques for finding approximate solutions of ordinary and partial differential equations using MATLAB or other technical computing environment. PREREQ: MATH 565 or PERM/INST.
MATH 571 DATA ANALYSIS (3-0-3)(S)(Even years). Provides an application of the various disciplines in statistics to data analysis, introduction to statistical software, demonstration of interplay between probability models and statistical inference. Topics include introduction to concepts of random sampling and statistical inference, goodness of fit tests for model adequacy, outlier detection, estimation and testing hypotheses of means and variances, analysis of variance, regression analysis and contingency tables. PREREQ:MATH 361.
MATH 572 COMPUTATIONAL STATISTICS (3-0-3)(F)(Even years). Introduction to the trend in modern statistics of basic methodology supported by state-of-art computational and graphical facilities, with attention to statistical theories and complex real world problems. Includes: data visualization, data partitioning and resampling, data fitting, random number generation, stochastic simulation, Markov chain Monte Carlo, the EM algorithm, simulated annealing, model building and evaluation. A statistical computing environment will be used for students to gain hands-on experience of practical programming techniques. PREREQ: MATH 361.
MATH 573 TIME SERIES ANALYSIS (3-0-3)(F)(Odd years). Introduction to time series analysis with an emphasis on application to interdisciplinary projects using SAS/ETS; autoregressive-moving average models, seasonal models, model identification, parameter estimation, model checking, forecasting, estimation of trends and seasonal effects, transfer function models, and spectral analysis. PREREQ: MATH 361.
MATH 574 LINEAR MODELS (3-0-3)(S)(Odd years). Introduction to the Gauss-Markov model with use of relevant statistical software. Includes linear regression, analysis of variance, parameter estimation, hypothesis testing, model building and variable selection, multicollinearity, regression diagnostics, prediction, general linear models, split plot designs, repeated measures analyses, random effects models. PREREQ: MATH 361.
MATH 579 TEACHING COLLEGE MATHEMATICS (1-0-1) Development of skills in the teaching of college mathematics. Effective use of class time, syllabus and test construction, learning styles, and disability issues. Lecturing, use of group work, and other teaching techniques. Graded Pass/Fail. PREREQ: PERM/INST.
SELECTED TOPICS (Variable credit) In depth study of advanced topics in targeted areas of mathematics.
MATH 580
TOPICS IN SET THEORY
MATH 581
TOPICS IN LOGIC
MATH 582
TOPICS IN TOPOLOGY
MATH 583
TOPICS IN COMPUTATIONAL MATHEMATICS
MATH 584
TOPICS IN COMPUTATIONAL ALGEBRA
MATH 585
TOPICS IN CRYPTOLOGY
MATH 586
TOPICS IN STATISTICS
MATH 587 TOPICS
IN DIFFERENTIAL EQUATIONS
MATH 588
TOPICS IN INVERSE THEORY