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MATH 430: Advanced Linear Algebra
4.00 Credits
Eastern Washington University
SPRING-EVEN YEARS Prerequisites: MATH 225 and 231. Advanced study of linear algebra, including the structure theory of linear transformations, the Cayley- Hamilton Theorem and multilinear algebra.
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MATH 430 - Advanced Linear Algebra
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MATH 431: Introduction to Modern Algebra I
4.00 Credits
Eastern Washington University
FALL Prerequisites: MATH 225, 231. Sets, groups, cyclic and permutation groups, Lagrange's Theorem, quotient groups and the isomorphism theorems.
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MATH 431 - Introduction to Modern Algebra I
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MATH 432: Introduction to Modern Algebra II
4.00 Credits
Eastern Washington University
Prerequisite: MATH 431. Basic theory of rings and ideals. Polynomial rings, principal ideal domains and unique factorization domains. Modules.
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MATH 432 - Introduction to Modern Algebra II
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MATH 433: Introduction to Modern Algebra III
4.00 Credits
Eastern Washington University
SPRING-ODD YEARS Prerequisite: MATH 432. Field theory. Splitting fields, Galois groups, fundamental Theorem of Galois Theory. Applications to classical problems of Euclidean constructibility and solvability by radicals.
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MATH 433 - Introduction to Modern Algebra III
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MATH 445: Numerical Analysis II
4.00 Credits
Eastern Washington University
SPRING-EVEN YEARS Prerequisite: Junior or higher standing; MATH 345. The course combines numerical linear algebra with calculus to derive methods of scientific computing: numerical differentiation and integration, existence, uniqueness, stability and numerical approximation of solutions of nonlinear systems and of ordinary or partial differential equations, splines and fast Fourier or wavelet transforms. The course also includes such applications to the engineering and the sciences as the design and analysis of algorithms to compute special functions, computed geometric design, fluid dynamics, heat diffusion or financial Black-Scholes models, image processing or nonlinear regression.
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MATH 445 - Numerical Analysis II
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MATH 447: Differential Equations
4.00 Credits
Eastern Washington University
WINTER-ODD YEARS Prerequisites: MATH 225, 231 and 347. Advanced study of differential equations including power series solutions, systems, numerical solutions and partial differential equations.
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MATH 447 - Differential Equations
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MATH 460: Continuous Functions
4.00 Credits
Eastern Washington University
FALL Prerequisites: MATH 225 and 231. This course develops the topology of the n-dimensional real Euclidean space. Topics include the completeness of the real numbers, topological spaces, continuity and properties preserved by continuous functions, compactness and connectedness. Homework and examinations in MATH 460 focus more on designing proofs new to the student than they do in MATH 360.
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MATH 460 - Continuous Functions
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MATH 461: Advanced Calculus I
4.00 Credits
Eastern Washington University
Prerequisites: MATH 241 and 360 or 460. This course applies notions from linear algebra and continuous functions to develop the calculus of functions of several variables. Topics include differentiability, the derivative as a linear transformation, extreme value problems and the implicit and inverse function theorems.
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MATH 461 - Advanced Calculus I
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MATH 462: Advanced Calculus II
4.00 Credits
Eastern Washington University
SPRING Prerequisite: MATH 461. This course builds on topics introduced in MATH 461 to treat integration. Topics include line integrals, exterior algebra and a general form of Stoke's Theorem, with selected applications to algebra, topology and fluid dynamics if time permits.
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MATH 462 - Advanced Calculus II
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MATH 470: Foundations of Geometry
4.00 Credits
Eastern Washington University
SPRING-ODD YEARS Prerequisite: MATH 225 and 231 or concurrent enrollment. A treatment of plane Euclidean and projective geometries, including the theory of conics, utilizing analytic methods and linear algebra.
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MATH 470 - Foundations of Geometry
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