| Math 401 [ 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 402 [ 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 405 [ 3 ] Linear & Integer Programming |
| Description: Linear Programming: conversion of problems to linear programs, geometrical interpretation, simplex method and duality, degeneracy and cycling. Interger programming by use of cutting planes. Advanced topics: sparse matrix implementation, problems with special methods of solution. |
| Prerequisite: 314, CS 151L |
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| Math 406 [ 3 to ] Topics in the History of Math |
| Description: Selected topics in the history of mathmatics; in depth treatment of great mathmatical thinkers and great themes in the history of mathematics |
| Prerequisite: 264 and 305 |
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| Math 412 [ 3 ] Nonlinear Dynamics and Chaos |
| Description: Qualitative study of linear and nonlinear ordinary differential equations and discrete time maps including stability analysis, bifucations, fractal structures and chaos; applications to biology, chemistry, physics, and engineering. |
| Prerequisite: 264 and (314 r 321) or 316 |
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| Math 415 [ 3 ] History and Philosophy of Mathematics |
| Description: (Also offered as PHIL 415.) A historical survey of principal issues and controversies on the nature of mathematics. Emphasis varies from year to year. |
| Prerequisite: 163 or 181 or 356 |
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| Math 421 [ 3 ] Modern Algebra II |
| Description: Theory of fields, algebraic field extensions and Galois theory for fields of characteristic zero. |
| Prerequisite: 322 or 422. |
| Semesters offered: spring |
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| Math 422 [ 3 ] Modern Algebra for Engineers |
| Description: Groups, rings and fields. (This course will not be counted in the hours necessary for a mathematics major.) |
| Prerequisite: Math 264. |
| Semesters offered: Fall |
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| Math 431 [ 3 ] Introduction to Topology |
| Description: Metric spaces, topological spaces, continuity, algebraic topology. |
| Prerequisite: Math 401. |
| Semesters offered: Fall |
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| Math 434 [ 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 439 [ (1-3, no limit) ] Topics in Mathematics |
| Description: (Credit: 1-3, no limit.) |
| Semesters offered: Offered Upon Demand |
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| Math 441 [ 3 ] Probability |
| Description: Also offered as STAT 461/561.) Mathematical models for random experiments, random variables, expectation. The common discrete and continuous distributions with application. Joint distributions, conditional probability and expectation, independence. Laws of large numbers and the central limit theorem. Moment generating functions. |
| Prerequisite: Math 264. |
| Semesters offered: Fall |
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| Math 449 [ 3 ] Topics in Probability |
| Description: May be repeated for credit, no limit. |
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| Math 461 [ 4 ] Introductory Real Analysis for Engineers |
| Description: Continuity, differentiability and integrability for functions of one real variable. (This course will not be counted in the hours nescessary for a mathematics major.) |
| Prerequisite: 264 |
| Semesters offered: Fall Spring |
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| Math 462 [ 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: 314, or 321, 316, 401 |
| Semesters offered: Fall |
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| Math 463 [ 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, and 314 or 321, one of 311 or 402. |
| Semesters offered: Spring |
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| Math 464 [ 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 466 [ 3 ] Mathematical Methods in Science & Engineering |
| Description: Special functions and advanced mathematical methods for solving differential equations, difference equations and integral equations. |
| Prerequisite: 311 and 312 and 313 and 316 |
| Semesters offered: Spring |
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| Math 471 [ 3 ] Introduction to Scientific Computing |
| Description: (Also offered as CS 471.) Introduction to scientific computing fundamentals, exposure to high performance programming language and scientific computing tools, case studies of scientific problem solving techniques. |
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| Math 472 [ 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 499 [ (1-3 to a maximum of 6) ] Individual Study |
| Description: (Credit: 1-3 to a maximum of 6.) Guided study, under the supervision of a faculty member, of selected topics not covered in regular courses. |
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