MAA 5104 Advanced Calculus for Engineers and Physical Scientists I 3 Credits
Grading Scheme: Letter Grade
Advanced Calculus for Engineers and Physical Scientists I
Catalog Program Pages Referencing MAA 5104
MAA 5105 Advanced Calculus for Engineers and Physical Scientists II 3 Credits
Grading Scheme: Letter Grade
Advanced Calculus for Engineers and Physical Scientists II
Prerequisite: MAA 5104.
Catalog Program Pages Referencing MAA 5105
MAA 5228 Modern Analysis I 3 Credits
Grading Scheme: Letter Grade
Topology of metric spaces, numerical sequences and series, continuity, differentiation, the Riemann-Stieltjes integral, sequences and series of functions, the Stone-Weierstrass theorem, and the Lebesgue theory.
Prerequisite: advanced calculus.
Catalog Program Pages Referencing MAA 5228
MAA 5229 Modern Analysis II 3 Credits
Grading Scheme: Letter Grade
Modern Analysis II
Prerequisite: MAA 5228.
Catalog Program Pages Referencing MAA 5229
MAA 5404 Introduction to Complex Variables for Engineers and Physical Scientists 3 Credits
Grading Scheme: Letter Grade
Introduction to Complex Variables for Engineers and Physical Scientists
Catalog Program Pages Referencing MAA 5404
MAA 6406 Complex Analysis I 3 Credits
Grading Scheme: Letter Grade
Rapid survey of properties of complex numbers, linear transformations, geometric forms and necessary concepts from topology. Complex integration. Cauchy's theorem and its corollaries. Taylor series and the implicit function theorem in complex form. Conformality and the Riemann-Caratheodory mapping theorem. Theorems of Bloch, Schottky, and the big and little theorems of Picard. Harmonicity and Dirichlet's problems.
Prerequisite: MAA 5229.
Catalog Program Pages Referencing MAA 6406
MAA 6407 Complex Analysis II 3 Credits
Grading Scheme: Letter Grade
Complex Analysis II
Prerequisite: MAA 6406.
Catalog Program Pages Referencing MAA 6407
MAA 6616 Analysis I 3 Credits
Grading Scheme: Letter Grade
Fundamentals of measure and integration theory, including Lp spaces and the Radon-Nikodym theorem. Introduction to functional analysis: Banach spaces, Hilbert spaces, and the theory of linear operators.
Prerequisite: MAA 5229.
Catalog Program Pages Referencing MAA 6616
MAA 6617 Analysis II 3 Credits
Grading Scheme: Letter Grade
Continuation of MAA 6616 Analysis I.
Prerequisite: MAA 6616.
Catalog Program Pages Referencing MAA 6617
MAA 7526 Advanced Topics in Functional Analysis I 3 Credits, Max 6 Credits
Grading Scheme: Letter Grade
Algebraic and topological approach to current material and methods in analysis.
Prerequisite: MAA 6617
Catalog Program Pages Referencing MAA 7526
MAA 7527 Advanced Topics in Functional Analysis II 3 Credits, Max 6 Credits
Grading Scheme: Letter Grade
Advanced Topics in Functional Analysis II
Prerequisite: MAA 7526.
Catalog Program Pages Referencing MAA 7527
MAD 6206 Combinatorial Theory I 3 Credits
Grading Scheme: Letter Grade
Matching theory, Ramsey's theorem, lattice theory, Mobius inversion, generating functions. Polya's theorem, matroids, applications, block designs, graph theory.
Catalog Program Pages Referencing MAD 6206
MAD 6207 Combinatorial Theory II 3 Credits
Grading Scheme: Letter Grade
Combinatorial Theory II
Prerequisite: MAD 6206.
Catalog Program Pages Referencing MAD 6207
MAD 6406 Numerical Linear Algebra 3 Credits
Grading Scheme: Letter Grade
Topics most useful in applications with emphasis on numerical techniques: systems of linear equations, positive definite and toeplitz systems, least squares problems, singular value decomposition, and eigenvalues. Numerical stability and efficiency of algorithms as well as effect of perturbations on the problem. Companion to MAD 6407.
Prerequisite: MAS 3114, 4105, or 4124; and programming language.
Catalog Program Pages Referencing MAD 6406
MAD 6407 Numerical Analysis 3 Credits
Grading Scheme: Letter Grade
Numerical techniques to solve systems of nonlinear equations to approximate functions, to compute derivatives, to evaluate integrals, and to integrate systems of differential equations. Introduction to numerical techniques for partial differential equations. Companion to MAD 6406.
Prerequisite: MAA 4212, MAA 5105, or MAA 5229; and programming language.
Catalog Program Pages Referencing MAD 6407
MAD 7396 Topics in Combinatorial Theory I 3 Credits, Max 6 Credits
Grading Scheme: Letter Grade
Topics chosen from among graph theory, coding theory, matroid theory, finite geometries, projective geometry, difference methods, and Latin squares.
Prerequisite: MAS 5312.
Catalog Program Pages Referencing MAD 7396
MAD 7397 Topics in Combinatorial Theory II 3 Credits
Grading Scheme: Letter Grade
Topics in Combinatorial Theory II
Prerequisite: MAD 7396.
Catalog Program Pages Referencing MAD 7397
MAE 6940 Supervised Teaching 1-5 Credits, Max 5 Credits
Grading Scheme: S/U
Supervised Teaching
Prerequisite: consent of graduate adviser.
Catalog Program Pages Referencing MAE 6940
MAE 6943 Internship in College Teaching 3 Credits, Max 6 Credits
Grading Scheme: Letter Grade
Internship in College Teaching
Prerequisite: consent of graduate adviser.
Catalog Program Pages Referencing MAE 6943
MAP 5304 Intermediate Differential Equations for Engineers and Physical Scientists 3 Credits
Grading Scheme: Letter Grade
Intermediate Differential Equations for Engineers and Physical Scientists
Catalog Program Pages Referencing MAP 5304
MAP 5345 Introduction to Partial Differential Equations 3 Credits
Grading Scheme: Letter Grade
Introduction to Partial Differential Equations
Catalog Program Pages Referencing MAP 5345
MAP 5489 Modeling in Mathematical Biology 3 Credits
Grading Scheme: Letter Grade
Mathematical models of biological systems. Models of growth, predator-prey populations, competition, chemostat, epidemics, excitable systems, and analytical tools such as linearization, phase-plane analysis, Poincare-Bendixson theory, Lyapunov functions, and bifurcation analysis.
Prerequisite: undergraduate course in ordinary differential equations.
Catalog Program Pages Referencing MAP 5489
MAP 6208 Numerical Optimization 3 Credits
Grading Scheme: Letter Grade
Unconstrained and constrained optimization, linear and nonlinear programming, gradient, multiplier, and quasi-Newton methods. Penalty, multiplier, and projection methods for constrained problems.
Prerequisite: MAD 6406 and MAD 6407 or consent of instructor.
Catalog Program Pages Referencing MAP 6208
MAP 6327 Applied Differential Equations I 3 Credits
Grading Scheme: Letter Grade
Theory and methods for solving linear and nonlinear systems of differential equations and partial differential equations. Applications and computer techniques included.
Prerequisite: MAA 5229.
Catalog Program Pages Referencing MAP 6327
MAP 6356 Partial Differential Equations I 3 Credits
Grading Scheme: Letter Grade
Cauchy-Kowalewski theorem, first order equations, classification of equations, hyperbolic equations, elliptic equations, parabolic equations, hyperbolic systems, nonlinear hyperbolic systems, existence theory based on functional analysis. Applications to physical sciences.
Prerequisite: MAA 5229, MAP 5345 or MAP 6506.
Catalog Program Pages Referencing MAP 6356
MAP 6357 Partial Differential Equations II 3 Credits
Grading Scheme: Letter Grade
Partial Differential Equations II
Prerequisite: MAP 6356.
Catalog Program Pages Referencing MAP 6357
MAP 6375 Numerical Partial Differential Equations 3 Credits
Grading Scheme: Letter Grade
Introduction to partial differential equations and fundamental concepts. Parabolic equations: finite differences, consistency, convergence and stability, 2- and 3-dimensional problems. Elliptic equations: finite differences, solution to linear equations, boundary integral equation methods. Hyperbolic equations: finite differences and method of characteristics. Introduction to finite elements. Methods of lines.
Prerequisite: MAD 6406 and MAD 6407 or consent of instructor.
Catalog Program Pages Referencing MAP 6375
MAP 6376 Finite Element Method 3 Credits
Grading Scheme: Letter Grade
Variational formulations of partial differential equations, finite element approximations; addresses theoretical framework and numerical issues. Finite element spaces in one, two, and three dimensions. Error analysis. Nonconforming finite element spaces. Isoparametric approximations to boundary conditions.
Prerequisite: MAD 6406 and MAD 6407 or consent of instructor.
Catalog Program Pages Referencing MAP 6376
MAP 6467 Stochastic Differential Equations and Filtering Theory I 3 Credits
Grading Scheme: Letter Grade
Introduction to random functions; Brownian motion process. Ito's stochastic integral; Ito's stochastic calculus; stochastic differential equations. Linear filtering; Kalman filtering; nonlinear filtering theory.
Catalog Program Pages Referencing MAP 6467
MAP 6468 Stochastic Differential Equations and Filtering Theory II 3 Credits
Grading Scheme: Letter Grade
Stochastic Differential Equations and Filtering Theory II
Prerequisite: MAP 6467.
Catalog Program Pages Referencing MAP 6468
MAP 6472 Probability and Potential Theory I 3 Credits
Grading Scheme: Letter Grade
Random variables, independence and conditioning. Laws of large numbers and the Central Limit Theorem. Stochastic processes, martingales, Gaussian processes, Markov processes, potentials and excessive functions.
Prerequisite: MAA 5229 or STA 6326.
Catalog Program Pages Referencing MAP 6472
MAP 6473 Probability and Potential Theory II 3 Credits
Grading Scheme: Letter Grade
Probability and Potential Theory II
Prerequisite: MAP 6472
Catalog Program Pages Referencing MAP 6473
MAP 6487 Biomathematics Seminar I 3 Credits
Grading Scheme: Letter Grade
Stochastic processes, differential equations, and reaction-diffusion equations used to model various biological processes. Among the applications covered are the following: population dynamics, epidemiology, genetics, enzyme kinetics, cell differentiation and morphogenesis, nerve impulse generation, and aggregation of slime mold. The course is designed to benefit graduate students in biological sciences, as well as mathematics.
Prerequisite: MAC 2312, MAP 2302, STA 6326 or MAP 4102.
Catalog Program Pages Referencing MAP 6487
MAP 6488 Biomathematics Seminar II 3 Credits
Grading Scheme: Letter Grade
Continuation of MAP 6487.
Prerequisite: MAP 6487.
Catalog Program Pages Referencing MAP 6488
MAP 6505 Mathematical Methods of Physics and Engineering 3 Credits
Grading Scheme: Letter Grade
Orthogonal functions; theory of distributions; integral equations; eigenfunctions and Green's functions; special functions; boundary and initial value problems, with emphasis on potential theory (Laplace and Poisson equations); the wave equation; and the diffusion equation.
Prerequisite: MAA 5404, MAP 5304, MAP 5345, MAS 5157 or equivalent.
Catalog Program Pages Referencing MAP 6505
MAP 6506 Mathematical Methods of Physics and Engineering II 3 Credits
Grading Scheme: Letter Grade
Mathematical Methods of Physics and Engineering II
Prerequisite: MAP 6505.
Catalog Program Pages Referencing MAP 6506
MAP 6941 Internship in Applied Mathematics 1-5 Credits, Max 9 Credits
Grading Scheme: Letter Grade
Mathematical research on projects sponsored by a university laboratory or an off-campus industrial internship program.
Prerequisite: consent of supervisory committee chair.
Catalog Program Pages Referencing MAP 6941
MAP 7436 Seminar in Applied Mathematics I 3 Credits, Max 6 Credits
Grading Scheme: Letter Grade
Various topics in applications of mathematics both classical and in areas of current research.
Catalog Program Pages Referencing MAP 7436
MAP 7437 Seminar in Applied Mathematics II 3 Credits, Max 6 Credits
Grading Scheme: Letter Grade
Seminar in Applied Mathematics II
Catalog Program Pages Referencing MAP 7437
MAS 5311 Introductory Algebra I 3 Credits
Grading Scheme: Letter Grade
The basic algebraic systems: groups, rings, vector spaces, and modules. Linear transformations, matrices, and determinants.
Prerequisite: MAS 4105 and 4302.
Catalog Program Pages Referencing MAS 5311
MAS 5312 Introductory Algebra II 3 Credits
Grading Scheme: Letter Grade
Introductory Algebra II
Prerequisite: MAS 5311.
Catalog Program Pages Referencing MAS 5312
MAS 6331 Algebra I 3 Credits
Grading Scheme: Letter Grade
Solvable and nilpotent groups, Jordan-Holder theorem, abelian groups, Galois theory, Noetherian rings, Dedekind domains, Jacobson radical, Jacobson density theorem, Wedderburn-Artin theorem.
Prerequisite: MAS 5312.
Catalog Program Pages Referencing MAS 6331
MAS 6332 Algebra II 3 Credits
Grading Scheme: Letter Grade
Algebra II
Prerequisite: MAS 6331.
Catalog Program Pages Referencing MAS 6332
MAS 7215 Theory of Numbers I 3 Credits
Grading Scheme: Letter Grade
Introduction to theory of numbers; theorems on divisibility; congruence, number-theoretic functions; primitive roots and indices; quadratic reciprocity law; Diophantine equations and continued functions.
Prerequisite: 2 of MAA 6407, MAA 6617, MAS 6332.
Catalog Program Pages Referencing MAS 7215
MAS 7216 Theory of Numbers II 3 Credits
Grading Scheme: Letter Grade
Theory of Numbers II
Prerequisite: MAS 7215.
Catalog Program Pages Referencing MAS 7216
MAS 7396 Advanced Topics in Algebra I 3 Credits, Max 6 Credits
Grading Scheme: Letter Grade
Current topics in algebra.
Prerequisite: MAA 6407, MAA 6617, MAS 6332 or MTG 6347.
Catalog Program Pages Referencing MAS 7396
MAS 7397 Topics in Algebra II 3 Credits
Grading Scheme: Letter Grade
Topics in Algebra II
Catalog Program Pages Referencing MAS 7397
MAT 6905 Individual Work 3 Credits, Max 9 Credits
Grading Scheme: Letter Grade
Individual Work
Catalog Program Pages Referencing MAT 6905
MAT 6910 Supervised Research 1-5 Credits, Max 5 Credits
Grading Scheme: S/U
Supervised Research
Catalog Program Pages Referencing MAT 6910
MAT 6932 Special Topics in Mathematics 3 Credits, Max 9 Credits
Grading Scheme: Letter Grade
Special Topics in Mathematics
Prerequisite: consent of graduate adviser, who should be consulted well in advance of registration.
Catalog Program Pages Referencing MAT 6932
MAT 6971 Research for Master's Thesis 1-15 Credits
Grading Scheme: S/U
Research for Master's Thesis
Catalog Program Pages Referencing MAT 6971
MAT 7979 Advanced Research 1-12 Credits
Grading Scheme: S/U
Research for doctoral students before admission to candidacy. Designed for students with a master's degree in the field of study or for students who have been accepted for a doctoral program. Not appropriate for students who have been admitted to candidacy.
Catalog Program Pages Referencing MAT 7979
MAT 7980 Research for Doctoral Dissertation 1-15 Credits
Grading Scheme: S/U
Research for Doctoral Dissertation
Catalog Program Pages Referencing MAT 7980
MHF 5107 Introduction to Set Theory 3 Credits
Grading Scheme: Letter Grade
Basic axioms and concepts of set theory, axiom of choice, Zorn's lemma, Schroder-Bernstein theorem, cardinal numbers, ordinal numbers, and the continuum hypothesis.
Catalog Program Pages Referencing MHF 5107
MHF 5207 Foundations of Mathematics 3 Credits
Grading Scheme: Letter Grade
Models and proofs. Foundations of the real and natural number systems. Algorithms. Turing Machines, undecidability and independence. Examples and applications in algebra, analysis, geometry, and topology.
Catalog Program Pages Referencing MHF 5207
MHF 6306 Mathematical Logic I 3 Credits
Grading Scheme: Letter Grade
Languages, models, and theories; Godel's completeness and incompleteness theorems; formal number theory and axiomatic set theory; applications to other areas of mathematics.
Catalog Program Pages Referencing MHF 6306
MHF 6307 Mathematical Logic 2 3 Credits
Grading Scheme: Letter Grade
The three sub-areas Model theory, computability theory, and set theory will be covered. Specific topics may include axiomatization of set theory, transfinite recursion and cardinal arithmetic, Goedel's constructible universe, Cohen's method of forcing, Turing degrees, and Post's problem.
Prerequisite: MHF 6306.
Catalog Program Pages Referencing MHF 6307
MTG 5316 Introduction to Topology I 3 Credits
Grading Scheme: Letter Grade
Basic axioms and concepts of point-set topology, compactness, connectedness, separation axioms, metric spaces, metrization. Tietze extension theorem. Urysohn lemma, Tychonoff theorem, fundamental group.
Catalog Program Pages Referencing MTG 5316
MTG 5317 Introduction to Topology II 3 Credits
Grading Scheme: Letter Grade
Introduction to Topology II
Prerequisite: MTG 5316.
Catalog Program Pages Referencing MTG 5317
MTG 6256 Differential Geometry I 3 Credits
Grading Scheme: Letter Grade
Foundations of the theory of smooth manifolds, vector fields, and differential forms. Topics chosen from a list including differential topology, Lie groups, symplectic geometry, Riemannian geometry, and applications to physics.
Prerequisite: consent of instructor.
Catalog Program Pages Referencing MTG 6256
MTG 6257 Differential Geometry II 3 Credits
Grading Scheme: Letter Grade
Differential Geometry II
Prerequisite: MTG 6256.
Catalog Program Pages Referencing MTG 6257
MTG 6346 Topology I 3 Credits
Grading Scheme: Letter Grade
A basic introduction to advanced topology. Topics covered include general topology, algebraic topology, homotopy theory and topology of manifolds.
Prerequisite: MTG 5317.
Catalog Program Pages Referencing MTG 6346
MTG 6347 Topology II 3 Credits
Grading Scheme: Letter Grade
Topology II
Prerequisite: MTG 6346.
Catalog Program Pages Referencing MTG 6347
MTG 6401 Ergodic Theory and Dynamical Systems I 3 Credits
Grading Scheme: Letter Grade
Periodic points, recurrence, nonwandering and chain recurrent sets, topological conjugacy, minimal sets. Topological entropy, metric entropy. Measure preserving transformations, ergodicity, mixing. Birkhoff's ergodic theorem. Bernouilli shifts. Anosov diffeomorphisms, structural stability, hyperbolic sets. Basic sets, symbolic dynamics, Markov partitions. Lyapunov exponents, KAM (Kolmogorov, Arnold, Moser) theory.
Prerequisite: MTG 5317, MAA 6617, or consent of instructor.
Catalog Program Pages Referencing MTG 6401
MTG 6402 Ergodic Theory and Dynamical Systems II 3 Credits
Grading Scheme: Letter Grade
Continuation of MTG 6401.
Prerequisite: MTG 6401.
Catalog Program Pages Referencing MTG 6402
MTG 7396 Advanced Topics in Topology I 3 Credits, Max 6 Credits
Grading Scheme: Letter Grade
Topics change yearly.
Prerequisite: MTG 6347.
Catalog Program Pages Referencing MTG 7396
MTG 7397 Advanced Topics in Topology II 3 Credits
Grading Scheme: Letter Grade
Discussion of advanced topics in topology and its applications.
Prerequisite: MTG 7396.