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MATH 447: Non-Euclidean Geometry
3.00 Credits
Saint Louis University-Main Campus
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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MATH 447 - Non-Euclidean Geometry
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MATH 451: Introduction to Complex Variables
3.00 Credits
Saint Louis University-Main Campus
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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MATH 451 - Introduction to Complex Variables
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MATH 452: Complex Variables II
3.00 Credits
Saint Louis University-Main Campus
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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MATH 452 - Complex Variables II
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MATH 455: Nonlinear Dynamics and Chaos
3.00 Credits
Saint Louis University-Main Campus
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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MATH 455 - Nonlinear Dynamics and Chaos
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MATH 457: Partial Differential Equations
3.00 Credits
Saint Louis University-Main Campus
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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MATH 457 - Partial Differential Equations
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MATH 465: Cryptography
3.00 Credits
Saint Louis University-Main Campus
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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MATH 465 - Cryptography
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MATH 495: Senior Residency
0.00 Credits
Saint Louis University-Main Campus
Required for graduating seniors.
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MATH 495 - Senior Residency
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MATH 498: Advanced Independent Study
0.00 - 6.00 Credits
Saint Louis University-Main Campus
Prior permission of sponsoring professor and chair required.
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MATH 498 - Advanced Independent Study
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MATH 502: Metric Spaces
3.00 Credits
Saint Louis University-Main Campus
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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MATH 502 - Metric Spaces
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MATH 503: Number Theory
3.00 Credits
Saint Louis University-Main Campus
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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MATH 503 - Number Theory
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