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Course Criteria
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3.00 Credits
Prerequisite: MATH240 and MATH241; or equivalent. Credit will be granted for only one of the following: MATH402 or MATH403. Integers; groups, rings, integral domains, fields.
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3.00 Credits
Prerequisite: MATH403. Algebraic and transcendental elements, Galois theory, constructions with straight-edge and compass, solutions of equations of low degrees, insolubility of the quintic equation, Sylow theorems, fundamental theorem of finite Abelian groups.
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3.00 Credits
Prerequisite: MATH240 or MATH461. An abstract treatment of finite dimensional vector spaces. Linear transformations and their invariants.
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3.00 Credits
Prerequisite: MATH141 or permission of department. Integers, divisibility, prime numbers, unique factorization, congruences, quadratic reciprocity, Diophantine equations and arithmetic functions.
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3.00 Credits
Prerequisites: MATH240 and MATH241, with grade of C or better; and permission of department. First semester of a year course. Subjects covered during the year are: sequences and series of numbers, continuity and differentiability of real valued functions of one variable, the Riemann integral, sequences of functions and power series. Functions of several variables including partial derivatives, multiple integrals, line and surface integrals. The implicit function theorem.
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3.00 Credits
Prerequisite: MATH410 and permission of department. Credit will be granted for only one of the following: MATH411 or MATH412. Continuation of MATH410.
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3.00 Credits
Prerequisite: MATH410 and permission of department. Credit will be granted for only one of the following: MATH411 or MATH412. Analysis in several variables, and applications, from a computational perspective.
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3.00 Credits
Prerequisites: MATH410 and MATH240; or equivalent. Existence and uniqueness theorems for initial value problems. Linear theory: fundamental matrix solutions, variation of constants formula, Floquet theory for periodic linear systems. Asymptotic orbital and Lyapunov stability with phase plane diagrams. Boundary value theory and series solutions.
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3.00 Credits
Prerequisite: MATH141 and MATH240; or permission of department. Familiarity with MATLAB is also required. Introduces students to the mathematical concepts arising in signal analysis from the applied harmonic analysis point of view. Topics include applied linear algebra, Fourier series, discrete Fourier transform, Fourier transform, Shannon Sampling Theorem, wavelet bases, multiresolution analysis, and discrete wavelet transform.
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3.00 Credits
Prerequisite: MATH241, MATH246, STAT400, MATH240 or MATH461; and permission of department. Also offered as AMSC420. Credit will be granted for only one of the following: AMSC420, MAPL420, or MATH420. The course will develop skills in mathematical modeling through practical experience. Students will work in groups on specific projects involving real-life problems that are accessible to their existing mathematical backgrounds. In addition to the development of mathematical models, emphasis will be placed on the use of computational methods to investigate these models, and effective oral and written presentation of the results.
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