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Course Criteria
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3.00 Credits
Course Level: Undergraduate/Graduate This course develops the foundations of mathematical analysis by focusing on the real numbers as a complete ordered field, infinite sequences and series, limits and continuity, and key theorems of the differential and integral calculus. Usually offered every fall. Prerequisite: MATH-503 or permission of instructor.
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3.00 Credits
Course Level: Undergraduate/Graduate This course presents the fundamental concepts and techniques of measure theory. It includes Borel sets, measures, measurable sets and functions, integrals as measures, Lp soaces, modes of convergence, and decomposition ans generation of measures (including product measure). Usually offered alternate springs. Prerequisite: MATH-503 and MATH-520 or permission of instructor.
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3.00 Credits
Course Level: Undergraduate/Graduate Topological spaces, continuity, compactness, connectedness, and metric spaces. Usually offered alternate falls. Prerequisite: MATH-503 or permission of instructor.
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3.00 Credits
Course Level: Undergraduate/Graduate Complex functions, Cauchy's theorem and integral formulae, Taylor and Laurent series, residue calculus and contour integration, and conformal mapping. Usually offered every spring. Prerequisite: MATH-500 and MATH-503.
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3.00 Credits
Course Level: Undergraduate/Graduate Fourier series, orthonormal systems, wave equation, vibrating strings and membranes, heat equation, Laplace's equation, harmonic and Green functions. Usually offered alternate springs (odd years). Prerequisite: MATH-321.
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3.00 Credits
Course Level: Undergraduate/Graduate Computer arithmetic and error analysis in computation, matrix decomposition methods in solving systems of linear equations and linear least squares problems, polynomial approximation and polynomial data fitting, iterative algorithms for solving nonlinear equations, and numerical differentiation and integration. Usually offered alternate falls (even years). Prerequisite: CSC-280, MATH-310, and MATH-500, or permission of instructor.
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3.00 Credits
Course Level: Undergraduate/Graduate This course surveys aspects of historical development of mathematics from ancient to modern times and examines the ideological, social, and cultural forces which shaped this development. By providing historical continuity, the course interrelates and unifies the major subject areas such as algebra, calculus and analysis, geometry, number theory, probability, set theory, and the foundation of mathematics. Usually offered alternate springs. Prerequisite: Calculus I-III. Note: Strongly recommended for students in the mathematics education program.
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3.00 Credits
Course Level: Undergraduate/Graduate Topics vary by section, may be repeated for credit with different topic. Topics include foundations/set theory/logic, matrix theory, algebraic topology, measure and integration, functional analysis, ring theory, modern geometry, and advanced modern linear algebra. Usually offered every spring.
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3.00 Credits
Course Level: Undergraduate/Graduate Curriculum construction and program design, instructional effectiveness, and methods and technology for teaching mathematics. Different approaches for students with a variety of mathematical and cultural backgrounds. Required of all students in mathematics education. Usually offered every fall. Prerequisite: MATH-223.
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1.00 - 6.00 Credits
Course Level: Undergraduate/Graduate Prerequisite: permission of instructor and department chair.
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