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Course Criteria
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3.00 Credits
Prerequisites: Mathematics 254. Linear codes, perfect and related codes, cyclic linear codes, BCH codes, burst error-correcting codes.
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3.00 Credits
Prerequisites: Mathematics 245 and 254. Fundamental of discrete probability and information theory: joint and conditional distributions, Bayes' theorem, entropy, channel capacity. Noiseless coding theorem and data compression algorithms: Huffman codes, arithmetic coding, Ziv-Lempel codes. Information theory in error correction coding and cryptography.
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3.00 Credits
Prerequisites: Mathematics 252 and 337. Boundary value problems for heat and wave equations: eigenfunction expansions, Sturm-Liouville theory and Fourier series. D'Alembert's solution to wave equation; characteristics. Laplace's equation, maximum principles, Bessel functions.
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3.00 Credits
Prerequisites: Mathematics 252. Analytic functions, Cauchy-Riemann equations, theorem of Cauchy, Laurent series, calculus of residues, and applications.
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3.00 Credits
Prerequisites: Mathematics 254 or 342A. Scalar and vector fields; gradient, divergence, curl, line and surface integrals: Green's, Stokes' and divergence theorems. Green's identities. Applications to potential theory or fluid mechanics or electromagnetism.
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3.00 Credits
Prerequisites: Mathematics 245 and 254; or 342A. Completeness of the real numbers and its consequences, sequences of real numbers, continuity, differentiability and integrability of functions of one real variable.
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3.00 Credits
Prerequisites: Mathematics 534A. Series and sequences of functions and their applications, functions of several variables and their continuity, differentiability and integrability properties.
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3.00 Credits
Prerequisites: Mathematics 337. Theory of ordinary differential equations: existence and uniqueness, dependence on initial conditions and parameters, linear systems, stability and asymptotic behavior, plane autonomous systems, series solutions at regular singular points.
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3.00 Credits
Prerequisites: Minimum grade of C in Mathematics 151; Mathematics 254 or 342A, 342B. One- and two-dimensional iterated maps, equilibria and their stability, sensitive dependence on initial conditions, Lyapunov exponents, horseshoe maps, period doubling, chaotic attractors, Poincare maps, stable/unstable manifolds, bifurcations. Applications in biology, chemistry, physics, engineering, and other sciences.
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3.00 Credits
Prerequisites: Mathematics 254 or 342A; and Computer Science 106 or 107 or 205. Solution of equations of one variable, direct methods in numerical linear algebra, least squares approximation, interpolation and uniform approximation, quadrature.
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