MTH 501 RESEARCH (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 503 THESIS (116)
This course is repeatable for a maximum of 999 credits.
PREREQS:
Departmental approval required.

MTH 505 READING AND CONFERENCE (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 506 PROJECTS (116)
Graded P/N.
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 507 SEMINAR (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 508 WORKSHOP (116)
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 510 OCCUPATIONAL INTERNSHIP (312)
Planned and supervised training experience at selected government, industrial, or business placement sites. Must be followed by a onehour postinternship seminar. Consult departmental head advisor. Graded P/N.
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 511 REAL ANALYSIS (3)
Topological concepts in metric, normed, and innerproduct spaces. Properties of continuous functions, including the StoneWeierstrass theorem. Introduction to function spaces, contraction mappings, fixed points, and applications. Lebesgue measure and integration in one and several variables, basic convergence theorems, Lebesgue spaces, Fubini's theorem, and applications to Fourier transforms and probability. All courses used to satisfy MTH prerequisites must be completed with B+ or better.
PREREQS:
MTH 312 and MTH 341

MTH 512 REAL ANALYSIS (3)
Topological concepts in metric, normed, and innerproduct spaces. Properties of continuous functions, including the StoneWeierstrass theorem. Introduction to function spaces, contraction mappings, fixed points, and applications. Lebesgue measure and integration in one and several variables, basic convergence theorems, Lebesgue spaces, Fubini's theorem, and applications to Fourier transforms and probability. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 411 or MTH 511

MTH 513 REAL ANALYSIS (3)
Topological concepts in metric, normed, and innerproduct spaces. Properties of continuous functions, including StoneWeierstrass theorem. Introduction to function spaces, contraction mappings, fixed points, and applications. Lebesgue measure and integration in one and several variables, basic convergence theorems, Lebesgue spaces, Fubini's theorem, and applications to Fourier transforms and probability. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 412 or MTH 512

MTH 520 MODELS AND METHODS OF APPLIED MATHEMATICS (3)
Discrete and continuous mathematical models and methods for analysis, including linear analysis, equilibrium and minimum principles, calculus of variations, principal component analysis and orthogonal expansions, asymptotic and Fourier analysis, least squares, constrained and unconstrained optimization, inverse problems, and Monte Carlo techniques. Particular models and methods covered may vary annually. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
(MTH 256 or MTH 256H) and MTH 341 and junior standing or above.

MTH 524 DYNAMICAL SYSTEMS THEORY AND APPLICATIONS (3)
Theory, models, and problems for discrete and/or continuous dynamical systems. Depending on term, the emphasis may be toward deterministic or stochastic systems. Topics generally include stability theory, periodic behavior, and chaotic systems. Models selected from biology, economics, fluid dynamics, and electrical and mechanical systems. May be repeated once for credit with a different topic. All courses used to satisfy MTH prerequisites must be completed with C or better.
This course is repeatable for a maximum of 6 credits.
PREREQS:
MTH 341MTH 342, MTH 311MTH 312, MTH 361 or consent of instructor.

MTH 525 DYNAMICAL SYSTEMS THEORY AND APPLICATIONS (3)
Theory, models, and problems for discrete and/or continuous dynamical systems. Depending on term, the emphasis may be toward deterministic or stochastic systems. Topics generally include stability theory, periodic behavior, and chaotic systems. Models selected from biology, economics, fluid dynamics, and electrical and mechanical systems. May be repeated once for credit with a different topic. All courses used to satisfy MTH prerequisites must be completed with C or better.
This course is repeatable for a maximum of 6 credits.
PREREQS:
MTH 341 and MTH 342 and MTH 311 and MTH 312 and MTH 361 or consent of instructor.

MTH 527 INTRODUCTION TO MATHEMATICAL BIOLOGY (3)
Modeling and mathematical analysis of biological processes using first principles at scales ranging from the molecular to the population level. Deterministic models are studied in both discrete and continuous time and analyzed using linearization principles, linear and nonlinear stability techniques, phase plane methods, and methods from partial differential equations. Results obtained from mathematical analysis will be qualitatively interpreted and applied to the biological process under investigation. All courses used to satisfy MTH prerequisites must be completed with a C or better.
PREREQS:
(MTH 256 or MTH 256H) and MTH 341

MTH 528 STOCHASTIC ELEMENTS IN MATHEMATICAL BIOLOGY (3)
An introduction to stochastic modeling of biological processes. The stochastic models covered may include Markov processes in both continuous and discrete time, urn models, branching processes, and coalescent processes. The biological applications may include genetic drift, population dynamics, genealogy, demography, and epidemiology. Mathematical results will be qualitatively interpreted and applied to the biological process under investigation.
PREREQS:
MTH 341 and (MTH 361 or MTH 463 or MTH 563)

MTH 531 GENERAL TOPOLOGY AND FUNDAMENTAL GROUPS (3)
Topological spaces and maps. Separation axioms, compactness, convergence, extension theorems, metrizability and compactification. Product spaces and simplicial complexes. Definition and basic properties of the fundamental group functor, with applications to the theory of covering spaces. Selected topics from dimension theory, manifold theory, and other areas of topology. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 531 and MTH 532 must be taken in order.

MTH 532 GENERAL TOPOLOGY AND FUNDAMENTAL GROUPS (3)
Topological spaces and maps. Separation axioms, compactness, convergence, extension theorems, metrizability and compactification. Product spaces and simplicial complexes. Definition and basic properties of the fundamental group functor, with applications to the theory of covering spaces. Selected topics from dimension theory, manifold theory, and other areas of topology. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 531 and MTH 532 must be taken in order.

MTH 534 INTRODUCTION TO DIFFERENTIAL GEOMETRY (3)
Curves and surfaces in Euclidean space; geodesics; curvature; introduction to tensor algebra and differential forms; selected applications. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
(MTH 255 or MTH 255H) and MTH 342 and (MTH 311 recommended)

MTH 535 DIFFERENTIAL GEOMETRY (3)
Differentiable 2manifolds; curvature; geodesics; tensor algebra and the algebra of exterior differential forms with emphasis on Euclidean space; differentiation of tensors and forms; integration of forms; selected applications. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
(MTH 434 or MTH 534) or instructor approval required.

MTH 537 GENERAL RELATIVITY (3)
Geometry of special relativity. Tensor analysis, metrics, geodesics, curvature. Einstein field equations, cosmological models, black holes. Selected topics such as global structure, conserved quantities, spinors. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 434 [C] or MTH 534 [C]
and
MTH 311 is recommended.

MTH 540 COMPUTATIONAL NUMBER THEORY (3)
Development of the number theory used in some basic tests of primality and methods of factoring integers. Applications to cryptology. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 231 or MTH 343 or MTH 355

MTH 541 APPLIED AND COMPUTATIONAL ALGEBRA (3)
Applications of fundamental algebraic systems to topics such as factorization of polynomials, finding roots of polynomials, error correcting codes. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 343 and (MTH 342 or MTH 440 or MTH 540) or instructor approval required.

MTH 542 APPLIED AND COMPUTATIONAL ALGEBRA (3)
Applications of fundamental algebraic systems to topics such as factorization of polynomials, finding roots of polynomials, error correcting codes. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
(MTH 441 or MTH 541) or instructor approval required.

MTH 543 ABSTRACT LINEAR ALGEBRA (3)
Abstract vector spaces. Linear transformations, eigenvalues and eigenvectors, the Jordan canonical form, inner product spaces. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 342 and MTH 343

MTH 551 NUMERICAL LINEAR ALGEBRA (3)
Computation of solutions of linear systems using direct and iterative methods; leastsquares solution of overdetermined systems; computation of eigenvalues and eigenvectors. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 341 and programming experience or instructor approval required. MTH 342 and MTH 351 are recommended.

MTH 552 NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS (3)
Numerical solution of initialvalue problems using RungeKutta methods and linear multistep methods; introduction to boundaryvalue problems. Analysis of stability, accuracy, and implementation of methods. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
(MTH 256 or MTH 256H) and (MTH 306 or MTH 306H or MTH 341) and programming experience required and junior standing required. MTH 351 or MTH 451 or MTH 551 recommended.

MTH 553 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS (3)
Numerical solution of boundary value problems and initialboundary value problems using finite difference and finite element methods. Analysis of stability, accuracy, and implementation of methods. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
(MTH 452 or MTH 552) or instructor approval required.

MTH 563 PROBABILITY I (3)
An introduction to probability theory; topics covered include: the axioms of probability, probability spaces and models, independence, random variables; densities, distributions, expectation, and variance; probability inequalities, the law of large numbers, and the binomial central limit theorem. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 312 or instructor approval required.

MTH 564 PROBABILITY II (3)
Transformations of random variables; sums of independent random variables, generating functions, characteristic functions, the central limit theorem and other weak limit theorems. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
(MTH 463 or MTH 563) and MTH 341 or instructor approval required.

MTH 565 PROBABILITY III (3)
Random variables, central limit theorem; distributions of standard statistics; Markov chains, continuous and discontinuous stochastic processes. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
(MTH 464 or MTH 564) or instructor approval required.

MTH 567 ACTUARIAL MATHEMATICS (3)
Foundations of actuarial science from the point of view of mathematical models that arise in the design and management of insurance systems. Most models will be life insurance based. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
(MTH 463 or MTH 563) or ST 421.

MTH 574 NUMBER SYSTEMS AND OPERATIONS IN K8 MATHEMATICS (3)
Key ideas and topics in number systems, operations, place value, and algorithms critical for the mathematics content knowledge of elementary teachers in grades K8. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 390 or instructor approval required.

MTH 575 COMPARING GEOMETRIES IN K8 MATHEMATICS (3)
Key ideas and topics in Euclidean and nonEuclidean geometries critical for the mathematics content knowledge of elementary teachers in grades K8. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 390 or instructor approval required.

MTH 576 ALGEBRA AND FUNCTION IN K8 MATHEMATICS (3)
Key ideas and topics in algebra and function concepts critical for the mathematics content knowledge of elementary teachers in grades K8. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 390 or instructor approval required.

MTH 578 PROBABILITY AND DATA ANALYSIS IN K8 MATHEMATICS (3)
Key ideas and topics in probability, data analysis, and statistics critical for the mathematics content knowledge of elementary teachers in grades K8. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 390 or instructor approval required.

MTH 581 APPLIED ORDINARY DIFFERENTIAL EQUATIONS (3)
Linear and nonlinear systems of ordinary differential equations, elementary stability theory, higher order equations, boundary value problems, series solution of ordinary differential equations.
PREREQS:
(MTH 256 or MTH 256H) and (((MTH 253 or MTH 253H) and MTH 341) or (MTH 306 or MTH 306H))

MTH 582 APPLIED PARTIAL DIFFERENTIAL EQUATIONS (3)
Partial differential equations, Bessel's and Legendre's equations, Fourier analysis, separation of variables, transform methods.
PREREQS:
MTH 480 or MTH 481 or MTH 581 or instructor approval required.

MTH 583 COMPLEX VARIABLES (3)
Introduction to the complex differential and integral calculus: Cuachy's theorem and formula, the residue calculus, power series and Laurent series, harmonic functions, conformal mapping, and applications.
PREREQS:
(MTH 256 or MTH 256H) and (MTH 253 or MTH 306 or MTH 306H)

MTH 590 TOPICS IN SECONDARY MATHEMATICS (3)
Key ideas and topics in discrete mathematics critical for the mathematics content knowledge of middle and high school teachers in grades 612. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 390 or instructor approval required.

MTH 591 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)
Ordered fields, number systems (natural, integer, rational, real, and complex), fundamental theorems of arithmetic and algebra, algebraic and transcendental numbers, constructible points and numbers and the classical geometric constructions, Polya's problem solving heuristics and strategies. Intended primarily for prospective mathematics teachers. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 341

MTH 592 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)
Major results of Euclidean geometry, axiom systems for Euclidean geometry, dependency tree of Euclidean theorems, groups of geometric transformations with applications to symmetries of plane and solid objects, Euler's formula, tilings and tesselations, isometries and similitudes of the plane (translations, rotations, reflections, glide reflections, dilations). Intended primarily for prospective mathematics teachers. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 491 or MTH 591

MTH 593 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)
Geometric transformations as real, complex, and matrix functions, invariants and genealogy of geometric transformations, extensions to transformations of the sphere and of threedimensional space, selected applications chosen from fractals, analysis of frieze and crystallographic patterns, problem solving, groups of symmetries, computer graphics, and the use of dynamic geometry software. Intended primarily for prospective mathematics teachers. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 492 or MTH 592

MTH 594 NUMBER SYSTEMS AND OPERATIONS IN SECONDARY MATHEMATICS (3)
Key ideas and topics in number systems, operations, place value, and algorithms critical for the mathematics content knowledge of middle and high school teachers in grades 612. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 390 or instructor approval required.

MTH 595 COMPARING GEOMETRIES IN SECONDARY MATHEMATICS (3)
Key ideas and topics in Euclidean and nonEuclidean geometries critical for the mathematics content knowledge of middle and high school teachers in grades 612. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 390 or instructor approval required.

MTH 596 ALGEBRA AND FUNCTION IN SECONDARY MATHEMATICS (3)
Key ideas and topics in algebra and function concepts critical for the mathematics content knowledge of middle and high school teachers in grades 612. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 390 or instructor approval required.

MTH 598 PROBABILITY AND DATA ANALYSIS IN SECONDARY MATHEMATICS (3)
Key ideas and topics in probability, data analysis, and statistics critical for the mathematics content knowledge of middle and high school teachers in grades 612. Based on the recommendations of The Mathematical Education of Teachers by the Conference Board of the Mathematical Sciences. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 390 or instructor approval required.

MTH 599 SPECIAL TOPICS (016)
Topics may vary.
This course is repeatable for a maximum of 18 credits.
PREREQS:
Instructor approval required.

MTH 601 RESEARCH (116)
PREREQ: Departmental approval required.
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 603 THESIS (116)
PREREQ: Departmental approval required.
This course is repeatable for a maximum of 999 credits.
PREREQS:
Departmental approval required.

MTH 605 READING AND CONFERENCE (116)
PREREQ: Departmental approval required.
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 606 SPECIAL PROJECTS (116)
Graded P/N.
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 607 SEMINAR (116)
PREREQ: Departmental approval required.
This course is repeatable for a maximum of 16 credits.
PREREQS:
Departmental approval required.

MTH 611 COMPLEX ANALYSIS (3)
Basic theory of analytic functions of a complex variable, including Cauchy's theorem, residue theorem, analytic continuation, conformal mappings, entire, and meromorphic functions. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
(MTH 411 or MTH 511). MTH 611 and MTH 612 must be taken in order.

MTH 612 COMPLEX ANALYSIS (3)
Basic theory of analytic functions of a complex variable, including Cauchy's theorem, residue theorem, analytic continuation, conformal mappings, entire, and meromorphic functions. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 611

MTH 614 FUNCTIONAL ANALYSIS (3)
Topological vector spaces, generalized functions, operator theory. Normally offered alternate years. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 513

MTH 619 TOPICS IN ANALYSIS (112)
May be repeated for credit.
This course is repeatable for a maximum of 12 credits.

MTH 621 PARTIAL DIFFERENTIAL EQUATIONS (3)
Partial differential equations of physics, including those of potential theory, wave propagation, and heat flow, treated by classical means, generalized functions and variational principles. Square summable function methods and integral equations. This course is the first in a yearlong sequence of MTH 621, MTH 622, MTH 623. All courses used to satisfy MTH prerequisites must be completed with C or better.
This course is repeatable for a maximum of 6 credits.
PREREQS:
6 credits of seniorlevel analysis or instructor consent. MTH 621, MTH 622, MTH 623 must be taken in order.

MTH 622 PARTIAL DIFFERENTIAL EQUATIONS (3)
Partial differential equations of physics, including those of potential theory, wave propagation, and heat flow, treated by classical means, generalized functions and variational principles. Square summable function methods and integral equations. This course is the first in a yearlong sequence of MTH 621, MTH 622, MTH 623. All courses used to satisfy MTH prerequisites must be completed with C or better.
This course is repeatable for a maximum of 6 credits.
PREREQS:
MTH 621 [C]
and
/or instructor consent.

MTH 623 PARTIAL DIFFERENTIAL EQUATIONS (3)
Partial differential equations of physics, including those of potential theory, wave propagation, and heat flow, treated by classical means, generalized functions and variational principles. Square summable function methods and integral equations. This course is the third one in yearlong sequence. All courses used to satisfy MTH prerequisites must be completed with C or better.
This course is repeatable for a maximum of 6 credits.
PREREQS:
MTH 621 [C] and MTH 622 [C]
and
/or instructor consent.

MTH 627 ADVANCED PARTIAL DIFFERENTIAL EQUATIONS (3)
Advanced theory including existence proofs and distributional approach. Normally offered fall term in odd years. All courses used to satisfy MTH prerequisites must be completed with C or better.
This course is repeatable for a maximum of 6 credits.
PREREQS:
MTH 413 or MTH 513 or instructor consent.

MTH 628 ADVANCED PARTIAL DIFFERENTIAL EQUATIONS (3)
Advanced theory including existence proofs and distributional approach. Normally offered winter term in even years. All courses used to satisfy MTH prerequisites must be completed with C or better.
This course is repeatable for a maximum of 6 credits.
PREREQS:
MTH 627 or consent of instructor.

MTH 634 ALGEBRAIC TOPOLOGY (3)
Simplicial and singular homology, products, and cohomology; applications to fixedpoint and separation theorems. Topics selected from homotopy, manifold and obstruction theory. Normally offered alternate years. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 532. MTH 634, MTH 635, MTH 636 must be taken in order.

MTH 635 ALGEBRAIC TOPOLOGY (3)
Simplicial and singular homology, products, and cohomology; applications to fixedpoint and separation theorems. Topics selected from homotopy, manifold and obstruction theory. Normally offered alternate years. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 532 and MTH 634

MTH 636 ALGEBRAIC TOPOLOGY (3)
Simplicial and singular homology, products, and cohomology; applications to fixedpoint and separation theorems. Topics selected from homotopy, manifold and obstruction theory. Normally offered alternate years.
PREREQS:
MTH 532 and MTH 635

MTH 644 ABSTRACT ALGEBRA I (3)
Group theory, rings and fields, Galois theory. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
Graduate standing in mathematics or a related field, or instructor approval required. MTH 443 or MTH 543 is recommended.

MTH 645 ABSTRACT ALGEBRA II (3)
Group theory, rings and fields, Galois theory. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
Graduate standing in mathematics or a related field, or instructor approval required. MTH 644 is recommended.

MTH 649 TOPICS IN ALGEBRA AND NUMBER THEORY (3)
May be repeated for credit.
This course is repeatable for a maximum of 27 credits.

MTH 654 NUMERICAL ANALYSIS (3)
Advanced topics in numerical analysis, such as finite volume methods and finite element methods for partial differential equations, numerical methods for inverse problems, and image processing. All courses used to satisfy MTH prerequisites must be completed with C or better.
This course is repeatable for a maximum of 12 credits.
PREREQS:
Familiarity with numerical methods and graduate standing, or instructor's consent. Coursespecific prerequisites may be announced.

MTH 655 NUMERICAL ANALYSIS (3)
Advanced topics in numerical analysis, such as finite volume methods and finite element methods for partial differential equations, numerical methods for inverse problems, and image processing. All courses used to satisfy MTH prerequisites must be completed with C or better.
This course is repeatable for a maximum of 12 credits.
PREREQS:
Familiarity with numerical methods and graduate standing, or instructor's consent. Coursespecific prerequisites may be announced.

MTH 656 NUMERICAL ANALYSIS (3)
Advanced topics in numerical analysis, such as finite volume methods and finite element methods for partial differential equations, numerical methods for inverse problems, and image processing. All courses used to satisfy MTH prerequisites must be completed with C or better.
This course is repeatable for a maximum of 12 credits.
PREREQS:
Familiarity with numerical methods and graduate standing, or instructor's consent. Coursespecific prerequisites may be announced.

MTH 657 TOPICS IN APPLIED MATHEMATICS (112)
Previous topics have included turbulence, financial mathematics and probability methods in partial differential equations.
This course is repeatable for a maximum of 12 credits.

MTH 658 TOPICS IN MATHEMATICAL MODELING (112)
Mathematical treatment of topics of current interest in the physical and biological sciences and technology. May be repeated for credit when topic varies.
This course is repeatable for a maximum of 12 credits.
PREREQS:
Instructor approval required.

MTH 659 TOPICS IN NUMERICAL ANALYSIS (112)
May be repeated for credit.
This course is repeatable for a maximum of 12 credits.

MTH 664 PROBABILITY THEORY (3)
General theory of probability measures and random variables, including weak convergence, characteristic functions, central limit theory, conditional expectations, martingales. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 411 or MTH 511 or equivalent.

MTH 665 PROBABILITY THEORY (3)
General theory of probability measures and random variables, including weak convergence, characteristic functions, the central limit theorem, and the Brownian motion process. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 664

MTH 669 TOPICS IN STOCHASTIC PROCESSES (112)
Previous topics have included Markov processes, martingales, branching processes, and stochastic differential equations.
This course is repeatable for a maximum of 12 credits.

MTH 674 DIFFERENTIAL GEOMETRY OF MANIFOLDS (3)
Differentiable manifolds, tangent bundles, vector fields and flows, submanifolds, Riemannian metrics, differential forms, integration on manifolds. Selected topics such as foliations, Lie groups, and de Rham cohomology. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 341 and (MTH 411 or MTH 511). MTH 674 or MTH 675 must be taken in order.

MTH 675 DIFFERENTIAL GEOMETRY OF MANIFOLDS (3)
Differentiable manifolds, connections in linear bundles, Riemannian manifolds and submanifolds. Selected topics such as variational theory of geodesics, harmonic forms, and characteristic classes. Normally offered alternate years. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 674

MTH 676 TOPICS IN TOPOLOGY (3)
May be repeated for credit.
This course is repeatable for a maximum of 27 credits.

MTH 679 TOPICS IN GEOMETRY (112)
May be repeated for credit.
This course is repeatable for a maximum of 12 credits.

MTH 680 MODERN APPROACHES TO CALCULUS (3)
Alternative approaches to calculus instruction based on the availability of computers and calculators. Applications of symbolicgraphical calculators, spreadsheets, symbolic algebra systems, and graphics packages to the teaching of calculus. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
MTH 253 and instructor approval required.

MTH 682 TEACHING AND LEARNING PROBABILITY AND STATISTICS (3)
Experimental, activitybased approaches to introductory probability and statistics are explored. Topics include computer simulations, exploratory data analysis, misuses of statistics, and misconceptions of probability. All courses used to satisfy MTH prerequisites must be completed with C or better.
PREREQS:
Instructor approval required.

MTH 684 COMPUTERS AND MATHEMATICS (3)
A variety of mathematical problems are investigated with a laboratory approach using microcomputers and a wide variety of software. Problems may be taken from number theory, calculus, geometry, probability, and elementary numerical analysis.
PREREQS:
Ability to program in either BASIC or PASCAL and instructor approval required.

MTH 685 ADVANCED PROBLEM SOLVING (3)
Mathematical problem solving using the heuristic approach of George Polya. Problems may be taken from a variety of areas, including number theory, calculus, geometry, probability, abstract and linear algebra.
PREREQS:
Instructor approval required.

MTH 689 TOPICS IN MATHEMATICS EDUCATION (112)
Topics may vary.
This course is repeatable for a maximum of 12 credits.

MTH 699 SPECIAL TOPICS (116)
May be repeated for credit.
This course is repeatable for a maximum of 16 credits.
