Mathematics Catalog Course List

MATH 451. Introduction to Differential Geometry 3 cr.
Applies calculus to curves and surfaces in three dimensional Euclidean space.
Prerequisites: MATH 280 and MATH 391, or consent of instructor.

MATH 452. Foundations of Geometry 3 cr.
Topics in projective, axiomatic Euclidean or non-Euclidean geometries.
Prerequisite: either MATH 280, MATH 330, or MATH 331, or consent of instructor.

MATH 453. Introduction to Topology 3 cr.
Introduction topological spaces and metric spaces, with connections to analysis, geometry, and the classification of surfaces.
Prerequisite: MATH 332 or consent of instructor.

MATH 454. Mathematical Logic 3 cr.
Propositional calculus and the first order predicate calculus, including Gödel's completeness theorem for the latter, and additional topics at the option of the instructor.
Prerequisite: MATH 330 or MATH 331 or consent of instructor.

MATH 455. Elementary Number Theory 3 cr.
Covers primes, congruences and related topics.
Prerequisite: grade of C or better in MATH 331 or consent of instructor

MATH 459. Survey of Geometry 3 cr.
Basic concepts of Euclidean geometry, ruler and compass constructions. May include topics in non-Euclidean geometry.
Prerequisite: C or better in MATH 279. For nonmath majors.

MATH 466. Lattice Theory 3 cr.
Introduction of partially ordered sets distributive, modular, and Boolean lattices.
Prerequisite: MATH 330 or MATH 331 or consent of instructor .

MATH 471. Complex Variables 3 cr.
A first course in complex function theory, with emphasis on applications.
Prerequisite: MATH 391 or both MATH 392 and MATH 291

MATH 472. Fourier Series and Boundary Value Problems 3 cr.
Fourier series and methods of solution of the boundary value problems of applied mathematics.
Prerequisite: MATH 392.

MATH 473. Calculus of Variations and Optimal Control 3 cr.
Euler’s equations, conditions for extreme, direct methods, dynamic programming, and the Pontryagin maximal principle.
Prerequisite: MATH 392.

MATH 480. Vector Spaces and Matrix Algebra 3 cr.
Matrices, determinants, vector spaces, characteristic values, canonical forms; applications.
Prerequisite: any 300-level course with a MATH or STAT prefix.

MATH 481. Modern Algebra 1 3 cr.
Introduction to basic concepts of groups, rings and fields, and selected other topics.
Prerequisite: grade of C or better in MATH 331 or consent of instructor.

MATH 482. Modern Algebra 11 3 cr.
Introduction to theory of modules with special emphasis on vector spaces and linear transformations.
Prerequisite: MATH 481 or consent of instructor.

MATH 491. Introduction to Real Analysis 1 3 cr.
Rigorous discussion of the topics introduced in calculus: sequences, series, limits, continuity, differentiation.
Prerequisite: grade of C or better in MATH 332 or consent of instructor.

MATH 492. Introduction to Real Analysis 11 3 cr.
Continuation of MATH 491. Integration, metric spaces and selected topics.
Prerequisite: MATH 491 or consent of instructor.

MATH 501. Introduction to Differential Geometry 3 cr.
Same as MATH 451 with additional assignments for graduate students.

MATH 502. Foundations of Geometry 3 cr.
Same as MATH 452 with additional assignments for graduate students.

MATH 503. Introduction to Topology 3 cr.
Same as MATH 453 with additional assignments for graduate students.

MATH 504. Mathematical Logic 3 cr.
Same as MATH 454 with additional assignments for graduate students.

MATH 505. Elementary Number Theory 3 cr.
Same as MATH 455 with additional assignments for graduate students.

MATH 506. Lattice Theory 3 cr.
Same as MATH 466 with additional assignments for graduate students.

MATH 511. Fundamentals of Elementary Mathematics 1 3 cr. (3+1P)
Topics from real numbers, geometry, measurement, and algorithms, incorporating calculator technology. Intended for K-8 teachers. As part of course students mentor MATH 111 undergraduates. Does not fulfill degree requirements for M.S. in mathematics.

MATH 512. Fundamentals of Elementary Mathematics 11 3 cr. (3+1P)
Real numbers, geometry, and statistics, incorporating calculator technology. Intended for K-8 teachers. Students serve as mentors to MATH 112 undergraduates. Does not fulfill degree requirements for M.S. in mathematics.

MATH 513. Fundamentals of Algebra and Geometry 3 cr. (3+1P)
Algebra and metric geometry, incorporating calculator technology. Intended for K-8 teachers. Students serve as mentors to MATH 313 undergraduates. Does not fulfill degree requirements for M.S. in mathematics.

MATH 514. Math and Science with Technology 3 cr.
Experiments involving measurements, primarily in physics; actual outcomes are compared with theoretical results. Intended for teachers grade 3 through 12. Students serve as mentors to MATH 314 undergraduates. Does not fulfill degree requirements for M.S. in mathematics.
Prerequisite: MATH 511 and MATH 512 or consent of instructor.

MATH 517. Complex Variables 3 cr.
Same as MATH 471 with additional work for graduate students.

MATH 518. Fourier series and Boundary Value Problems 3 cr.
Same as MATH 472 with additional work for graduate students.

MATH 519. Calculus of Variations and Optimal Control 3 cr.
Same as MATH 473 with additional work for graduate students.

MATH 525. Modern Algebra 1 3 cr.
Same as MATH 481 with additional work for graduate students.

MATH 526. Modern Algebra 11 3 cr.
Same as MATH 482 with additional work for graduate students.

MATH 527. Introduction to Real Analysis 1 3 cr.
Same as MATH 491 with additional work for graduate students.

MATH 528. Introduction to Real Analysis 11 3 cr.
Same as MATH 492 with additional work for graduate students.

MATH 530. Special Topics 1-3 cr.
Specific subjects to be announced in the Schedule of Classes. May be for unlimited credit with the approval of department

MATH 531. Ordinary Differential Equations 3 cr.
Linear systems; existence and uniqueness theorems for general systems, equilibria and stability; stable, unstable and center manifolds; bifurcations.
Prerequisites: MATH 392 and MATH 491, or consent of instructor.

MATH 532. Partial Differential Equations 3 cr.
The basic equations of mathematical physics. Elliptic, hyperbolic, and parabolic equations. Characteristic surfaces. Well-posed problems.
Prerequisite: MATH 518 or equivalent.

MATH 533. Linear Programming 3 cr.
Linear programming problem formulation, simplex method, theory of linear programming, dual problem, transportation problem, and postoptimality analysis.
Prerequisite: I E 531 or MATH 480 or consent of instructor. Same as I E 533.

MATH 534. Nonlinear Programming 3 cr.
Classical optimization, Lagrange multipliers and Kuhn-Tucker theory, convex simplex algorithm, and quadratic convergence.
Same as I E 534.

MATH 535. Discrete Optimization 3 cr.
Discrete optimization, networks and graphs, integer programming, integer nonlinear programming, dynamic programming.
Prerequisite: I E 533 or MATH 533 or consent of instructor. Same as I E 535.

MATH 540. Directed Reading 1-6 cr.
May be repeated for a maximum of 6 credits.
Graded S/U.

MATH 541. Topology I 3 cr.,
Topological spaces, connectedness, compactness, Tychonoff’s theorem, separation axioms, Tietze's extension theorem, Urysohn's metrizabon theorerti, elementary homotopytheory, the fundamental group, the Seifert-van Kampen theorem.
Prerequisites: MATH 525 and MATH 528, or consent of instructor.

MATH 542. Topology II 3 cr.,
Covering spaces and their classification, CW-complexes, singular and cellular homology, Brouwer’s fixed point theorem, and other applications.
Prerequisites: MATH 541 or consent of instructor.

MATH 550. Complexity 3 cr.
Covers polynomially bounded, NP-complete, exponentially hard, and undecidable problems; reducibility.
Prerequisite: MATH 450/C S 450 or MATH510/C S 510. Same as C S 550.

MATH 555. Differentiable Manifolds 3 cr.
Differentiable structures, tangent bundles, vector fields and differential equations, differential forms, integration, and topics chosen by the instructor.
Prerequisites: MATH 526 and MATH 528, or consent of instructor.

MATH 557. Axiomatic Set Theory 3 cr.
A detailed study of Zermelo-Fraenkel and Bernays set theories.
Prerequisite: MATH 454.

MATH 561. The Role of History in the Teaching Mathematics 3 cr.
In-depth study of selected mathematical topics through examination of their historical development, with emphasis on studying original sources. Pedagogical aspects of using history and original sources in teaching mathematics. Research and preparation of classroom materials based on original sources.

MATH 573. Numerical Linear Algebra 3 cr.
An advanced course in matrix theory, centered on a study of algorithms for finding eigenvalues and eigenvectors, inverting matrices, and solving linear systems - in particular the large, sparse linear systems which arise in solving partial differential equations by finite differences.
Prerequisites: MATH 480 or MATH 482 or equivalent. Some computing experience is desirable.

MATH 577. Numerical Analysis I 3 cr.
Topics may include interpolation, differential equations, nonlinear equations, optimization.
Prerequisites: MATH 480 and 527, or consent of instructor.

MATH 581. Theory of Fields 3 cr.
Elements of the theory of algebraic and transcendental extensions. Galois theory. Also selected advanced topics in algebra.
Prerequisite: MATH 526 or consent of instructor.

MATH 582. Commutative and Noncommutative Algebra 3 cr.
Theory of modules, rings and modules of fractions, theory of Noetherian rings, Hilbert Basis Theorem, theory of noncommutative rings, Wedderburn Theorems.
Prerequisite: MATH 581.

MATH 583. Algebraic Number Theory 3 cr.
Number fields and number rings, prime decomposition in number rings, ideal theory and the ideal class group, and selected other topics.

MATH 584. Representation Theory 3 cr.
Topics from representation theory of finite or infinite groups.
Prerequisite: consent of instructor. May be repeated for a maximum of 9 credits.

MATH 585. Universal Algebra 3 cr.
Basics of universal algebra and category theory. Theorems of Birkhoff and Tarski relating equational classes, free algebras and their construction through homomorphisms, subalgebras and products. Further topics from model theory, sheaf theory and representation by subdirect products.
Prerequisite: consent of instructor. May be repeated for a maximum of 6 credits.

MATH 586. Nonlinear Dynamics I 3 cr.
Same as PHYS 586.

MATH 591. Complex Analysis I 3 cr.
Rigorous treatment of complex differentiation and integration, properties of analytic functions, series and Cauchy's integral representations.
Prerequisites: MATH 517 and MATH 528, or consent of instructor.

MATH 592. Complex Analysis II 3 cr.
Harmonic functions, product representations, conformal mappings, Riemann's mapping theorem, Riemann surfaces, and selected other topics.
Prerequisite: MATH 591 or consent of instructor.

MATH 593. Measure and Integration 3 cr.
Measure spaces, measurable functions, extension and decomposition theorems for measures, integration on measure spaces, absolute continuity, iterated integrals.
Prerequisite: MATH 528 or consent of instructor.

MATH 594. Real Analysis 3 cr.
Differentiation, Lp spaces, Banach spaces, measure and topology, other selected topics.
Prerequisite: MATH 593.

MATH 598. Special Research Programs 1-3 cr.
Individual analytical or experimental projects. Maximum of 3 credits per semester. More than 3 credits total requires approval of graduate committee. Six credits maximum.

MATH 599. Master’s Thesis var. cr.
Thesis.

MATH 600. Doctoral Research var. cr.
Research.

MATH 601. Special Topics 1-3 cr.
Specific subjects to be announced in the Schedule of Classes. May be repeated for unlimited credit with the approval of department

MATH 620. Applications od Tensor Analysis 3 cr.
Same as PHYS 620.
MATH 643. Topology III 3 cr.
Topics may include higher homotopy groups, fibrations, cohomology operations and obstruction theory, spectral sequences, or others chosen by instructor.
Prerequisites: MATH 542 or consent of instructor. May be repeated for a maximum of 9 credits.

MATH 655. Topics in Differential Geometry 3 cr.
Representation theory of Lie groups, Riemannian geometry, or another topic chosen by instructor. Content varies.
Prerequisite: MATH 555 or consent of instructor. May be repeated for a maximum of 9 credits.

MATH 683. Homological Algebra 3 cr.
Basic topics in homological algebra and category theory.
Prerequisite: MATH 582 or consent of instructor. May be repeated for a maximum of 9 credits.

MATH 686. Nonlinear Dynamics II 3 cr.
Same as PHYS 686.

MATH 695. Introduction to Functional Analysis I 3 cr.
Banach spaces. The three basic principles: uniform boundedness principle, closed graph/open mapping theorems, Hahn-Banach theorem.
Prerequisites: MATH 541 and MATH 594, or consent of instructor.

MATH 696. Introduction to Functional Analysis II 3 cr.
Continuation of MATH 695. Topics selected from topological vector spaces, Hilbert space, spectral theory, Banach algebras, and distribution theory.
Prerequisite: MATH 695 or consent of instructor.

MATH 698. Selected Topics var. cr.

MATH 700. Doctoral Dissertation var. cr.
Dissertation.