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Course Criteria
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3.00 Credits
Fundamental calculus of functions of two or more variables. Implicit function theorem, Taylor expansion, line integrals, Green's theorem, surface integrals. Duplicates 4526. Pre: 2224. (3H,3 Credits) II,IV.
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3.00 Credits
Theory of limits, continuity, differentiation, integration, series. This course duplicates 4525. Course involves mathematical proofs; one may benefit by first taking 3034. I,II,III Pre: 2224. (3H,3 Credits)
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3.00 Credits
Computational methods for numerical solution of non-linear equations, differential equations, approximations, iterations, methods of least squares, and other topics. Partially duplicates Math 4554. A grade of C or better required in CS prerequisite 1044 or 1705. II Pre: 2214, 2224, CS 1044 or CS 1705. (3H,3 Credits)
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3.00 Credits
Finite and infinite sets, mathematical induction, functions, equivalence relations, order relations, recurrence relations, discrete dynamical systems. Partially duplicates 2534 and 3034. In order to enroll in 3434, a student must obtain (1) a C or better in each of 1114, 1205, 1206, 1224 and (either 2214 or 2224), or (2) at most one C- and a GPA of at least 2.2 in the courses mentioned in (1). (3H,3 Credits)
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3.00 Credits
Peano postulates, cardinal arithmetic, axiom of choice, well orderings, ordinal arithmetic, continuum hypothesis. Pre: 2224, (3034 or 3134). (3H,3 Credits)
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3.00 Credits
Historical development of mathematics from antiquity to modern times. Senior standing in mathematics required. I. (3H,3 Credits)
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3.00 Credits
An introduction to the theory of groups and rings. Topics include normal subgroups, permutation groups, Sylow's Theorem, Abelian groups, Integral Domains, Ideals, and Polynomial Rings. I,II,III. Pre: 3124. (3H,3 Credits)
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3.00 Credits
Divisibility, congruences, multiplicative functions, primitive roots, quadratic reciprocity. II Pre: 2534 or 3034 or 3134. (3H,3 Credits)
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3.00 Credits
Second course in linear algebra. Similarity invariants, Jordan canonical form, inner product spaces, self-adjoint operators, selected applications. Pre: 3144. (3H,3 Credits)
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3.00 Credits
Advanced topics in discrete mathematics with applications. Includes counting techniques, generating functions, recurrence relations, combinatorial designs, semigroups, words and rewriting rules, matroids, and selected additional topics (e.g., Ramsey theory, Polya theory, Young tableaux). Knowledge of a programming language (e.g., C, fortran, Pascal) required. I. Pre: 3034, 3134. (3H,3 Credits)
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