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Course Criteria
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2.00 Credits
Directed group study of mathematical modeling techniques. Open to undergraduate students only. Class members are expected to participate in the annual Mathematical Competition in Modeling. Total credit limited to 8 units. 2 seminars. Prerequisite: Consent of instructor.
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2.00 - 3.00 Credits
Directed group mathematical research in support of volunteer community service projects. Total credit limited to 8 units. 2 seminars. Prerequisite: consent of instructor and consent of department chair.
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1.00 - 4.00 Credits
Individual investigation, research, studies, or surveys of selected problems. Total credit limited to 8 units. Prerequisite: Junior standing and consent of department chair.
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4.00 Credits
Theory of curves and surfaces in space. Topics such as Frenet formulas, curvature, geodesics, Cartan structural equations, Gauss-Bonnet Theorem. 4 lectures. Prerequisite: MATH 304 or consent of instructor.
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4.00 Credits
Complex vector spaces, unitary and self-adjoint matrices, Spectral Theorem, Jordan canonical form. Selected topics in linear programming, convexity, numerical methods, and functional analysis. 4 lectures. Prerequisite: MATH 306 or consent of instructor.
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4.00 Credits
Elementary analytic functions and mappings. Cauchy's Integral Theorem; Poisson's Integral Formula. Taylor and Laurent series, theory of residues, and the evaluation of integrals. Harmonic functions, conformal mappings. 4 lectures . MATH 40 8 prerequisite: MATH 242, or MATH 241 and MATH 244, or consent of instructor . MATH 40 9 prerequisite: MATH 408.
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4.00 Credits
Introduction to concepts and methods basic to real analysis. Topics such as the real number system, sequences, continuity, uniform continuity and differentiation. 4 lectures. Prerequisite: MATH 306 or consent of instructor.
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4.00 Credits
A continuation of Introduction to Analysis I covering such topics as integration, infinite series, uniform convergence and functions of several variables. Highly recommended for students planning to enter graduate programs or secondary teaching and those interested in applied mathematics. 4 lectures. MATH 413 prerequisite: MATH 412 or consent of instructor. MATH 414 prerequisite: MATH 413.
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4.00 Credits
Qualitative theory of ordinary differential equations: Existence and Unique-ness Theorem, phase portraits, limit sets, stability of fixed points and periodic orbits, energy functions, Poincaré-Bendixson Theorem, Poincaré maps, bifurcations, attractors, chaos. 4 lectures. Prerequisite: MATH 206 and MATH 242, or MATH 241 and MATH 244, or consent of instructor.
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4.00 Credits
Discrete dynamical systems: iteration, stability of fixed points and periodic points, bifurcations, conjugacy, symbolic dynamics, transitivity, limit sets, attractors, chaos, sensitive dependence, Lyapunov exponents, Stable Manifold Theorem, geometric horseshoe, Markov partitions, fractals. 4 lectures. Prerequisite: MATH 206 and MATH 242, or MATH 241 and MATH 244, or consent of instructor.
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