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Course Criteria
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3.00 Credits
The rise and development of the non-Euclidean geometries with intensive study of plane hyperbolic geometry. Offered occasionally. Pre-requisite: MATH 142.
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3.00 Credits
Complex number system and its operations, limits and sequences, continuous functions and their properties, derivatives, conformal representation, curvilinear and complex integration, Cauchy integral theorems, power series and singularities. Fall semester. Pre-requisite: MATH 244.
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3.00 Credits
This course is a continuation of MATH 451. Topics covered include series, residues and poles, conformal mapping, integral formulas, analytic continuation, and Riemann surfaces. Spring semester. Pre-requisite: MATH 451.
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3.00 Credits
Bifurcation in one-dimensional flows. Two-dimensionalflows, fixed points and linearization, conservative systems, index theory, limit cycles. Poincare-Bendixson theory, bifurcations. Chaos, the Lorenz equation, discrete maps, fractals, and strange attractors. Pre-requisite: MATH 355.
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3.00 Credits
Fourier series, Fourier Intergrals, the heat equation, Staum-Liouville problems, the wave equation, the potential equation, problems in several dimensions, Laplace transforms numerical methods. Pre-requisite: MATH 355.
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3.00 Credits
Classical cryptographic systems, public key cryptography, symmetric block ciphers, implementation issues. Related and supporting mathematical concepts and structures. Pre-requisite: MATH 143
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0.00 Credits
Required for graduating seniors.
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0.00 - 6.00 Credits
Prior permission of sponsoring professor and chair required.
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3.00 Credits
Prerequisite: an advanced undergraduate course in analysis. Set theory, real line, separation properties, compactness, metric spaces, metrization. (Offered every Spring semester.)
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3.00 Credits
Introduction to algebraic number theory. Topics will include primes, Chinese remainder theorem, Diophantine equations, algebraic numbers and quadratic residues. Additional topics will vary from year to year. Prerequisite: MATH 411
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