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Course Criteria
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3.00 Credits
Prerequisite: MATH 240. An overview of groups, rings, integral domains, and fields; detailed study of several groups; and exploration of properties of integers and polynomials. Topics may include an introduction to computer algebra and Boolean algebra.
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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. Not open to students who have completed MATH350 and MATH351. 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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