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MTH Graduate Courses, Corvallis Campus

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Top MTH 501 RESEARCH (1-16)  Offered in current or future terms
This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 503 THESIS (1-16)  Offered in current or future terms
This course is repeatable for a maximum of 999 credits. PREREQS: Departmental approval required.

Top MTH 505 READING AND CONFERENCE (1-16)  Offered in current or future terms
This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 506 PROJECTS (1-16)  Offered in current or future terms
Graded P/N. This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 507 SEMINAR (1-16)  Offered in current or future terms
This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 508 WORKSHOP (1-16) 
This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 510 OCCUPATIONAL INTERNSHIP (3-12)  Offered in current or future terms
Planned and supervised training experience at selected government, industrial, or business placement sites. Must be followed by a one-hour post-internship seminar. Consult departmental head advisor. Graded P/N. This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 511 REAL ANALYSIS (3)  Offered in current or future terms
Topological concepts in metric, normed, and inner-product spaces. Properties of continuous functions, including the Stone-Weierstrass 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

Top MTH 512 REAL ANALYSIS (3)  Offered in current or future terms
Topological concepts in metric, normed, and inner-product spaces. Properties of continuous functions, including the Stone-Weierstrass 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

Top MTH 513 REAL ANALYSIS (3)  Offered in current or future terms
Topological concepts in metric, normed, and inner-product spaces. Properties of continuous functions, including Stone-Weierstrass 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

Top MTH 520 MODELS AND METHODS OF APPLIED MATHEMATICS (3)  Offered in current or future terms
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.

Top MTH 524 DYNAMICAL SYSTEMS THEORY AND APPLICATIONS (3)  Offered in current or future terms
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-MTH 342, MTH 311-MTH 312, MTH 361 or consent of instructor.

Top MTH 525 DYNAMICAL SYSTEMS THEORY AND APPLICATIONS (3)  Offered in current or future terms
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.

Top MTH 527 INTRODUCTION TO MATHEMATICAL BIOLOGY (3)  Offered in current or future terms
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

Top MTH 528 STOCHASTIC ELEMENTS IN MATHEMATICAL BIOLOGY (3)  Offered in current or future terms
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)

Top MTH 531 GENERAL TOPOLOGY AND FUNDAMENTAL GROUPS (3)  Offered in current or future terms
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.

Top MTH 532 GENERAL TOPOLOGY AND FUNDAMENTAL GROUPS (3)  Offered in current or future terms
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.

Top MTH 534 INTRODUCTION TO DIFFERENTIAL GEOMETRY (3)  Offered in current or future terms
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)

Top MTH 535 DIFFERENTIAL GEOMETRY (3) 
Differentiable 2-manifolds; 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.

Top MTH 537 GENERAL RELATIVITY (3)  Offered in current or future terms
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.

Top MTH 540 COMPUTATIONAL NUMBER THEORY (3)  Offered in current or future terms
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

Top MTH 541 APPLIED AND COMPUTATIONAL ALGEBRA (3)  Offered in current or future terms
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.

Top MTH 542 APPLIED AND COMPUTATIONAL ALGEBRA (3)  Offered in current or future terms
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.

Top MTH 543 ABSTRACT LINEAR ALGEBRA (3)  Offered in current or future terms
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

Top MTH 551 NUMERICAL LINEAR ALGEBRA (3)  Offered in current or future terms
Computation of solutions of linear systems using direct and iterative methods; least-squares 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.

Top MTH 552 NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS (3)  Offered in current or future terms
Numerical solution of initial-value problems using Runge-Kutta methods and linear multistep methods; introduction to boundary-value 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.

Top MTH 553 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS (3)  Offered in current or future terms
Numerical solution of boundary value problems and initial-boundary 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.

Top MTH 563 PROBABILITY I (3)  Offered in current or future terms
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.

Top MTH 564 PROBABILITY II (3)  Offered in current or future terms
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.

Top MTH 565 PROBABILITY III (3)  Offered in current or future terms
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.

Top MTH 567 ACTUARIAL MATHEMATICS (3)  Offered in current or future terms
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.

Top MTH 574 NUMBER SYSTEMS AND OPERATIONS IN K-8 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 K-8. 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.

Top MTH 575 COMPARING GEOMETRIES IN K-8 MATHEMATICS (3) 
Key ideas and topics in Euclidean and non-Euclidean geometries critical for the mathematics content knowledge of elementary teachers in grades K-8. 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.

Top MTH 576 ALGEBRA AND FUNCTION IN K-8 MATHEMATICS (3) 
Key ideas and topics in algebra and function concepts critical for the mathematics content knowledge of elementary teachers in grades K-8. 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.

Top MTH 578 PROBABILITY AND DATA ANALYSIS IN K-8 MATHEMATICS (3) 
Key ideas and topics in probability, data analysis, and statistics critical for the mathematics content knowledge of elementary teachers in grades K-8. 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.

Top MTH 581 APPLIED ORDINARY DIFFERENTIAL EQUATIONS (3)  Offered in current or future terms
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))

Top MTH 582 APPLIED PARTIAL DIFFERENTIAL EQUATIONS (3)  Offered in current or future terms
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.

Top MTH 583 COMPLEX VARIABLES (3)  Offered in current or future terms
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)

Top MTH 590 TOPICS IN SECONDARY MATHEMATICS (3)  Offered in current or future terms
Key ideas and topics in discrete mathematics critical for the mathematics content knowledge of middle and high school teachers in grades 6-12. 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.

Top MTH 591 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)  Offered in current or future terms
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

Top MTH 592 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)  Offered in current or future terms
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

Top MTH 593 ALGEBRA AND GEOMETRIC TRANSFORMATIONS (3)  Offered in current or future terms
Geometric transformations as real, complex, and matrix functions, invariants and genealogy of geometric transformations, extensions to transformations of the sphere and of three-dimensional 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

Top 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 6-12. 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.

Top MTH 595 COMPARING GEOMETRIES IN SECONDARY MATHEMATICS (3) 
Key ideas and topics in Euclidean and non-Euclidean geometries critical for the mathematics content knowledge of middle and high school teachers in grades 6-12. 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.

Top 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 6-12. 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.

Top 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 6-12. 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.

Top MTH 599 SPECIAL TOPICS (0-16)  Offered in current or future terms
Topics may vary. This course is repeatable for a maximum of 18 credits. PREREQS: Instructor approval required.

Top MTH 601 RESEARCH (1-16)  Offered in current or future terms
PREREQ: Departmental approval required. This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 603 THESIS (1-16)  Offered in current or future terms
PREREQ: Departmental approval required. This course is repeatable for a maximum of 999 credits. PREREQS: Departmental approval required.

Top MTH 605 READING AND CONFERENCE (1-16)  Offered in current or future terms
PREREQ: Departmental approval required. This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 606 SPECIAL PROJECTS (1-16)  Offered in current or future terms
Graded P/N. This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 607 SEMINAR (1-16)  Offered in current or future terms
PREREQ: Departmental approval required. This course is repeatable for a maximum of 16 credits. PREREQS: Departmental approval required.

Top MTH 611 COMPLEX ANALYSIS (3)  Offered in current or future terms
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.

Top MTH 612 COMPLEX ANALYSIS (3)  Offered in current or future terms
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

Top 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

Top MTH 619 TOPICS IN ANALYSIS (1-12)  Offered in current or future terms
May be repeated for credit. This course is repeatable for a maximum of 12 credits.

Top MTH 621 PARTIAL DIFFERENTIAL EQUATIONS (3)  Offered in current or future terms
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 year-long 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 senior-level analysis or instructor consent. MTH 621, MTH 622, MTH 623 must be taken in order.

Top MTH 622 PARTIAL DIFFERENTIAL EQUATIONS (3)  Offered in current or future terms
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 year-long 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.

Top MTH 623 PARTIAL DIFFERENTIAL EQUATIONS (3)  Offered in current or future terms
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 year-long 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.

Top MTH 627 ADVANCED PARTIAL DIFFERENTIAL EQUATIONS (3)  Offered in current or future terms
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.

Top 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.

Top MTH 634 ALGEBRAIC TOPOLOGY (3)  Offered in current or future terms
Simplicial and singular homology, products, and cohomology; applications to fixed-point 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.

Top MTH 635 ALGEBRAIC TOPOLOGY (3)  Offered in current or future terms
Simplicial and singular homology, products, and cohomology; applications to fixed-point 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

Top MTH 636 ALGEBRAIC TOPOLOGY (3)  Offered in current or future terms
Simplicial and singular homology, products, and cohomology; applications to fixed-point and separation theorems. Topics selected from homotopy, manifold and obstruction theory. Normally offered alternate years. PREREQS: MTH 532 and MTH 635

Top MTH 644 ABSTRACT ALGEBRA I (3)  Offered in current or future terms
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.

Top MTH 645 ABSTRACT ALGEBRA II (3)  Offered in current or future terms
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.

Top MTH 649 TOPICS IN ALGEBRA AND NUMBER THEORY (3)  Offered in current or future terms
May be repeated for credit. This course is repeatable for a maximum of 27 credits.

Top MTH 654 NUMERICAL ANALYSIS (3)  Offered in current or future terms
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. Course-specific prerequisites may be announced.

Top MTH 655 NUMERICAL ANALYSIS (3)  Offered in current or future terms
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. Course-specific prerequisites may be announced.

Top MTH 656 NUMERICAL ANALYSIS (3)  Offered in current or future terms
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. Course-specific prerequisites may be announced.

Top MTH 657 TOPICS IN APPLIED MATHEMATICS (1-12)  Offered in current or future terms
Previous topics have included turbulence, financial mathematics and probability methods in partial differential equations. This course is repeatable for a maximum of 12 credits.

Top MTH 658 TOPICS IN MATHEMATICAL MODELING (1-12)  Offered in current or future terms
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.

Top MTH 659 TOPICS IN NUMERICAL ANALYSIS (1-12)  Offered in current or future terms
May be repeated for credit. This course is repeatable for a maximum of 12 credits.

Top MTH 664 PROBABILITY THEORY (3)  Offered in current or future terms
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.

Top MTH 665 PROBABILITY THEORY (3)  Offered in current or future terms
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

Top MTH 669 TOPICS IN STOCHASTIC PROCESSES (1-12)  Offered in current or future terms
Previous topics have included Markov processes, martingales, branching processes, and stochastic differential equations. This course is repeatable for a maximum of 12 credits.

Top MTH 674 DIFFERENTIAL GEOMETRY OF MANIFOLDS (3)  Offered in current or future terms
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.

Top MTH 675 DIFFERENTIAL GEOMETRY OF MANIFOLDS (3)  Offered in current or future terms
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

Top MTH 676 TOPICS IN TOPOLOGY (3)  Offered in current or future terms
May be repeated for credit. This course is repeatable for a maximum of 27 credits.

Top MTH 679 TOPICS IN GEOMETRY (1-12)  Offered in current or future terms
May be repeated for credit. This course is repeatable for a maximum of 12 credits.

Top MTH 680 MODERN APPROACHES TO CALCULUS (3) 
Alternative approaches to calculus instruction based on the availability of computers and calculators. Applications of symbolic-graphical 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.

Top MTH 682 TEACHING AND LEARNING PROBABILITY AND STATISTICS (3)  Offered in current or future terms
Experimental, activity-based 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.

Top 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.

Top 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.

Top MTH 689 TOPICS IN MATHEMATICS EDUCATION (1-12)  Offered in current or future terms
Topics may vary. This course is repeatable for a maximum of 12 credits.

Top MTH 699 SPECIAL TOPICS (1-16) 
May be repeated for credit. This course is repeatable for a maximum of 16 credits.



 
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