| Math 500 [ 3 ] Computing in the Mathematics Curriculum |
| Description: Use of computers and graphing utilities in the mathematics classroom. Introduction to hardware and commercial software. Applications of selected programming languages to the teaching of mathematics. |
| Prerequisite: 162 or 181. Restriction: College of Education graduate students |
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| Math 501 [ 4 ] Advanced Calculus I |
| Description: Rigorous treatment of calculus in one variable. Definition and topology of real numbers, sequences, limits, functions, continuity, differentiation and integration. Students will learn how to read, understand and construct mathematical proofs. |
| Prerequisite: 264 and two courses at the 300+ level. Restriction: College of Education graduate students.
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| Math 502 [ 3 ] Advanced Calculus II |
| Description: Generalization of 401/501 to several variables and metric spaces: sequences, limits, compactness and continuity on metric spaces; interchange of limit operations; series, power series; partial derivatives; fixed point, implicit and inverse function theorems; multiple integrals. |
| Prerequisite: 501. Restriction: College of Education graduate students. |
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| Math 503 [ 3 ] Calculus for Teachers |
| Description: A penetrating look at functions, derivatives, integrals, and the Fundamental Theorem of Calculus that makes explicit how topics in the secondary school curriculum come to fruition in this fundamental subject. |
| Prerequisite: Restriction: permission of instructor. |
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| Math 504 [ 3 ] Introductory Numerical Analysis: Numerical Linear Algebra |
| Description: (Also offered as CS 575.) Direct and iterative methods of the solution of linear systems of equations and least squares problems. Error analysis and numerical stability. The eigenvalue problem. Descent methods for function minimization, time permitting. |
| Prerequisite: 464, 514 |
| Semesters offered: Spring |
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| Math 505 [ 3 ] Introductory Numerical Analysis: Approx. & Diff. Equations |
| Description: (Also offered as CS 576.) Numerical approximation of functions. Interpolation by polynomials, splines and trigonometric functions. Numerical integration and solution of ordinary differential equations. An introduction to finite difference and finite element methods, time permitting. |
| Prerequisite: 316 or 401 |
| Semesters offered: Fall |
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| Math 506 [ 3 ] College Geometry |
| Description: An axiomatic approach to fundamentals of geometry, both Euclidean and non-Euclidean. Emphasis on historical development of geometry. |
| Prerequisite: Restriction: College of Education graduate students. |
| Semesters offered: Spring |
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| Math 507 [ 3 ] Mathematics from a Historical Perspective |
| Description: A survey of mathematical developments prior to 1800; emphasis on problem solving techniques; comparison of older and more modern methods. |
| Prerequisite: 163. Restriction: College of Education graduate students. |
| Semesters offered: Fall |
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| Math 508 [ 3 ] Theory and Practice of Problem Solving |
| Description: An experience in mathematical invention and discovery at the level of high school geometry and algebra that includes a deeper look at sequences, series, and recursions. |
| Prerequisite: 180 or 162. Corequisite: 306. Restriction: College of Education graduate students. |
| Semesters offered: Offered upon demand |
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| Math 509 [ 3 ] Applications of Mathematics |
| Description: An experience in mathematical invention and discovery at the level of high school geometry and algebra that includes a deeper look at sequences, series, and recursions. |
| Prerequisite: 181 or 163. Restriction: College of Education graduate students. |
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| Math 510 [ 3 ] Introduction to Analysis I |
| Description: Real number fields, sets and mappings. Basic point set topology, sequences, series, convergence issues. Continuous functions, differentiation, Riemann integral. General topology and applications: Weierstrass and Stone-Weierstrass approximation theorems, elements of Founier Analysis (time permitting). |
| Prerequisite: 321, 401. |
| Semesters offered: Fall |
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| Math 511 [ 3 ] Introduction to Analysis II |
| Description: Continuation of 510. Differentiation in R^n. Inverse and implicit function theorems, integration in R^n, differential forms and Stokes theorem. |
| Prerequisite: 510.
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| Semesters offered: Spring |
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| Math 512 [ 3 ] Introduction to Ordinary Differential Equations |
| Description: Linear systems. Existence and uniqueness theorems, flows, linearized stability for critical points, stable manifold theorem. Gradient and Hamiltonian systems. Limit sets, attractors, periodic orbits, Floquet theory and the Poincare Map. Introduction to perturbation theory. |
| Prerequisite: Math 314, or 321, 316, 401. |
| Semesters offered: Fall |
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| Math 513 [ 3 ] Introduction to Partial Differential Equations |
| Description: Classification of partial differential equations; properly posed problems; separation of variables, eigenfunctions and Green's functions; brief survey of numerical methods and variational principles. |
| Prerequisite: Math 312, 313, 314 or 321, one of 311 or 402. |
| Semesters offered: Spring |
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| Math 514 [ 3 ] Applied Matrix Theory |
| Description: Determinants; theory of linear equations; matrix analysis of differential equations; eigenvalues, eigenvectors and canonical forms; variational principles; generalized inverses. |
| Prerequisite: 314 or 321. |
| Semesters offered: Fall |
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| Math 519 [ (3, no limit) ] Selected Topics in Number Theory |
| Description: (Credit: 3, no limit.) |
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| Math 520 [ 3 ] Abstract Algebra I |
| Description: Theory of groups, permutation groups, Sylow theorems. Introduction to ring theory, polynomial rings. Principal ideal domains. |
| Prerequisite: Math 322. |
| Semesters offered: Fall |
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| Math 521 [ 3 ] Abstract Algebra II |
| Description: Continuation of 520. Module theory, field theory, Galois theory. |
| Prerequisite: Math 321, 520 |
| Semesters offered: Spring |
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| Math 527 [ 3 ] Probability |
| Description: Mathematical models for random experiments, random variables, expectation. The common discrete and continuous distributions with application. Joint distributions, conditional probability and expectation and independence. Laws of large numbers and the central limit theorem. Moment generating functions. |
| Prerequisite: 264 or equivalent |
| Semesters offered: Fall |
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| Math 530 [ 3 ] Algebraic Geometry I |
| Description: Basic theory of complex affine and projective varieties. Smooth and singular points, dimension, regular and rational mappings between varieties, Chow's Theorem. |
| Prerequisite: Math 431, 521, 561 |
| Semesters offered: Alternate Falls |
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| Math 531 [ 3 ] Algebraic Geometry II |
| Description: Continuation of 530. Degree of a variety and linear systems. Detailed study of curves and surfaces. |
| Prerequisite: Math 530. |
| Semesters offered: Alternate Springs |
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| Math 532 [ 3 ] Algebraic Topology I |
| Description: Introduction to homology and cohomology theories. Homotopy theory, CW complexes. |
| Prerequisite: Math 431, 521. |
| Semesters offered: Alternate Falls |
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| Math 533 [ 3 ] Algebraic Topology II |
| Description: Continuation of 532. Duality theorems, universal coefficients, spectral sequence. |
| Prerequisite: Math 532 |
| Semesters offered: Alternate Springs |
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| Math 534 [ 3 ] Introduction to Differential Geometry |
| Description: Elementary theory of surfaces, differential forms, integral geometry, Riemannian geometry. |
| Prerequisite: 311 or 402. |
| Semesters offered: Offered Upon Demand |
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| Math 535 [ 3 ] Foundations of Topology |
| Description: Basic point set topology. Separation axioms, metric spaces, topological manifolds, fundamental group and covering spaces. |
| Prerequisite: 401 |
| Semesters offered: Fall |
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| Math 536 [ 3 ] Introduction to Differentiable Manifolds |
| Description: Concept of a manifold, differential structures, vector bundles, tangent and cotangent bundles, embedding, immersions and submersions, transversality, Stokes' theorem. |
| Prerequisite: Math 511. |
| Semesters offered: Alternate Springs |
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| Math 537 [ 3 ] Riemannian Geometry I |
| Description: Theory of connections, curvature, Riemannian metrics, Hopf-Rinow theoreom, geodesics. Riemannian submanifolds. |
| Prerequisite: Math 536. |
| Semesters offered: Alternate Falls |
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| Math 538 [ 3 ] Riemannian Geometry II |
| Description: Continuation of MATH 537 with emphasis on adding more structures. Riemannian submersions, Bochner theorems with relation to topology of manifolds, Riemannian Foliations, Complex and Kaehler geometry, Sasakian and contact geometry. |
| Prerequisite: Math 537. |
| Semesters offered: Alternate Springs |
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| Math 539 [ (3, no limit) ] Selected Topics in Geometry and Topology |
| Description: |
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| Math 540 [ 3 ] Stochastic Processes with Applications |
| Description: Markov chains and processes with applications. Classification of states. Decompositions. Stationary distributions. Probability of absorption, the gambler's ruin and mean time problems. Queuing and branching processes. Introduction to continuous time Markov processes. Jump processes and Brownian motion. |
| Prerequisite: Math 527. |
| Semesters offered: Offered Upon Demand |
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| Math 541 [ 3 ] Advanced Probability |
| Description: (Also offered as STAT 567.) A measure theoretic introduction to probability theory. Construction of probability measures. Distribution and characteristic functions, independence and zero-one laws. Sequences of independent random variables, strong law of large numbers and central limit theorem. Conditional expectation. Martingales. |
| Prerequisite: Math 563 |
| Semesters offered: Alternate Springs |
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| Math 542 [ 3 ] Mathematics for Secondary Teachers |
| Description: Topics from secondary mathematics presented from an advanced standpoint and designed to meet the needs of pre- and in-service teachers. Open only to prospective and in-service teachers of mathematics. |
| Prerequisite: 306 and 322 and 327. Restriction College of Education graduate students. |
| Semesters offered: Fall |
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| Math 543 [ (1-3, no limit) ] Topics in Mathematics for Elementary and Middle School Teachers |
| Description: (Credit: 1-3, no limit.) Presents mathematical topics of concern to elementary and mid-school teachers. Open only to in-service and prospective teachers. |
| Prerequisite: Restriction: College of Education graduate students. |
| Semesters offered: Offered upon demand |
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| Math 549 001 [ (3, no limit) ] Selected Topics in Probability Theory |
| Description: Relativistic Classical Electrodynamics and XFELs |
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| Math 550 [ (1-3, no limit) ] Topics in Mathematics for Secondary Teachers |
| Description: (Credit: 1-3, no limit.) Presents mathematical topics of concern to secondary teachers. Open only to in-service and prospective teachers. May be repeated for credit by permission of instructor. |
| Prerequisite: Restriction: College of Education graduate students. |
| Semesters offered: Offered upon demand |
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| Math 551 [ (1-3, no limit) ] Problems |
| Description: (Credit: 1-3, no limit.) |
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| Math 557 [ (3, no limit) ] Selected Topics in Numerical Analysis |
| Description: (Credit: 3, no limit.) (Also offered as CS 557.) Possible topics include approximation theory, two point boundary value problems, quadrature, integral equations and roots of nonlinear equations. |
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| Math 561 [ 3 ] Functions of a Complex Variable I |
| Description: Analyticity, Cauchy theorem and formulas, Taylor and Laurent series, singularities and residues, conformal mapping, selected topics. |
| Prerequisite: Math 311 or 402 |
| Semesters offered: Fall |
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| Math 562 [ 3 ] Functions of a Complex Variable II |
| Description: The Mittag-Leffler theorem, series and product expansions, introduction to asymptotics and the properties of the gamma and zeta functions. The Riemann mapping theorem, harmonic functions and Dirichlet's problem. Introduction to elliptic functions. Selected topics. |
| Prerequisite: Math 561 |
| Semesters offered: Fall |
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| Math 563 [ 3 ] Measure Theory |
| Description: Functions of one and several real variables, measure theory, starting with Lebesque measure and integration. Product measures. Measure on spaces of functions. |
| Prerequisite: Math 401 or 510 |
| Semesters offered: Fall |
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| Math 565 [ 3 ] Harmonic Analysis |
| Description: Fourier analysis on the circle, real line and on compact and locally compact groups. |
| Prerequisite: Math 563 |
| Semesters offered: Offered Upon Demand |
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| Math 568 [ 3 ] Stochastic Differential Equations |
| Description: Basic theory of stochastic differential equations with applications. The presentation will be at a level accessible to scientists, engineers, and applied mathematicians. |
| Prerequisite: Math 316, 441. |
| Semesters offered: Offered Upon Demand |
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| Math 569 [ (3, no limit) ] Selected Topics in Analysis |
| Description: (Credit: 3, no limit.) |
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| Math 570 [ 3 ] Singular Perturbations [ Additional Information ] |
| Description: Singularly perturbed boundary value problems, layer type expansions and matching. Initial value problems and multi-scaling methods for ordinary and partial differential equations. Phase plane and qualitative ideas. Applications. Perturbations of Hamiltonian systems. |
| Prerequisite: 462, 463 |
| Semesters offered: Alternate Springs |
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| Math 571 [ 3 ] Ordinary Differential Equations |
| Description: Existence and uniqueness of solutions, linear systems, asymptotic behavior of solutions to nonlinear systems, integral manifolds and linearizations, perturbation theory, bifurcation theory, dichotomies for solutions of linear systems. |
| Prerequisite: Math 462 |
| Semesters offered: Alternate Springs |
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| Math 572 [ 3 ] Fourier Analysis and Wavelets |
| Description: Discrete Fourier and Wavelet Transform. Fourier series and integrals. Expansions in series of orthogond wavelets and other functions. Multiresolution and time/frequency analysis. Applications to signal processing and statistics. |
| Prerequisite: 314, 321 or 401 |
| Semesters offered: Offered Upon Demand |
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| Math 573 [ 3 ] Partial Differential Equations |
| Description: Equations of first order, classification of equations and systems, elliptic equations and introduction to potential theory, hyperbolic equations and systems, parabolic equations. |
| Prerequisite: Math 463 |
| Semesters offered: Alternate Falls |
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| Math 576 [ 3 ] Numerical Linear Algebra |
| Description: Selected advanced topics in numerical linear algebra. |
| Prerequisite: Math 504 |
| Semesters offered: Alternate Springs |
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| Math 577 [ 3 ] Numerical Ordinary Differential Equations |
| Description: Numerical methods for initial value and/or boundary value problems. |
| Prerequisite: Math 462, 504, 505. |
| Semesters offered: Offered Upon Demand |
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| Math 578 [ 3 ] Numerical Partial Differential Equations |
| Description: Introduction to the numerical analysis of partial differential equations. |
| Prerequisite: Math 463, 504, 505 |
| Semesters offered: Alternate Falls |
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| Math 579 [ (3, no limit.) ] Selected Topics in Applied Math |
| Description: (Credit: 3, no limit.) |
| Grading: Homework |
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| Math 579 001 [ (3, no limit.) ] Selected Topics in Applied Math [ Additional Information ] |
| Description: Relativistic Classical Electrodynamics and XFELs |
| Grading: Homework |
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| Math 581 [ 3 ] Functional Analysis I |
| Description: Normed vector spaces, including Hilbert and Banach spaces. Linear operators on these spaces, with an emphasis on applications. |
| Prerequisite: Math 510 |
| Semesters offered: Offered Upon Demand |
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| Math 582 [ 3 ] Functional Analysis II |
| Description: Advanced topics in function spaces and linear operators. |
| Prerequisite: Math 581 |
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| Math 583 [ 3 ] Methods of Applied Math I |
| Description: Approximation in Hilbert spaces, basic operator theory, integral equations, distribution theory, Green's functions, differential operators, boundary value problems and nonlinear problems |
| Prerequisite: Math 312, 314, 316, 401. |
| Semesters offered: Alternate Falls |
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| Math 584 [ 3 ] Methods of Applied Math II |
| Description: Eigenfunction expansions for ordinary and partial differential operators, Euler-Lagrange equations, Hamilton's principle, calculus of variations, brief complex variable theory, special functions, transform and spectral theory, asymptotic expansions. |
| Prerequisite: Math 312, 314, 316, and 401. |
| Preparation: Advanced work in applied mathematics and applied science, such as electricity and magnetism, wave propagation, heat transfer, and quantum mechanics. |
| Grading: Homeworks |
| Semesters offered: Alternate Springs |
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| Math 598 [ 1-6 ] Practicum |
| Description: (Credit: 1-6 to a maximum of 6.) Practicum involves a project of an applied nature which may be done in conjunction with an industrial laboratory, a research institution or another department of the University. It is expected the student will become acquainted with a field of application in science or engineering and complete a project of use and interest to workers in that field. A final written report is required. |
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| Math 599 [ 1-6 ] Master's Thesis |
| Description: Offered on a CR/NC basis only. |
|