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Course Criteria
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3.00 Credits
4175: Elementary concepts in cryptography; classical cryptosystems; modern symmetric cryptography; public key cryptography; digital signatures, authentication schemes; modular arithmetic, primitive roots, primality testing. At least one mathematics course at or above the 3000 level and facility with either a programming language or a computer algebra system is required. 4176: Discrete logs; pseudoprime tests; Pollard rho factoring; groups; quadratic residues; elliptic curve cryptosystems and factoring; coding theory; quantum cryptography. (3H,3 Credits)
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3.00 Credits
Linear algebra of infinite dimensional spaces, inner product spaces, normed spaces, completeness, orthonormal bases, bounded and unbounded linear operators, adjoints, spectra, compact operators. Pre: (3214 or 4526), (3224 or 4525), (4425 or 4564). (3H,3 Credits)
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3.00 Credits
Real number system, point set theory, limits, continuity, differentiation, integration, infinite series, sequences and series of functions. I,II Pre: 3224 for 4225; 4225 for 4226. (3H,3 Credits)
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3.00 Credits
Analytic functions, complex integration, series representation of analytic functions, residues, conformal mapping, applications Pre: 4525 or 3224. (3H,3 Credits) II.
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3.00 Credits
Solution techniques, linear systems, the matrix exponential, existence theorems, stability, non-linear systems, eigenvalue problems. Pre: 3224 or 4525. (3H,3 Credits)
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3.00 Credits
Survey of basic concepts in chaotic dynamical systems. Includes material on bifurcation theory, conjugacy, stability, and symbolic dynamics. Pre: 3224 or 4525. (3H,3 Credits)
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3.00 Credits
Basic concepts of topological spaces, continuous functions, connected spaces, compact spaces, and metric spaces. I Pre: 3124, 3224. (3H,3 Credits)
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3.00 Credits
Transformational approach to Euclidean geometry including an in-depth study of isometries and their application to symmetry, geometric constructions, congruence, coordinate geometry, and non-Euclidean geometries. I,II. Pre: 1114, 1206. (3H,3 Credits)
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3.00 Credits
Selected topics in geometry for advanced undergraduates. Pre: 1114, 1206. (3H,3 Credits)
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3.00 Credits
Interpolation and approximation, numerical integration, solution of equations, matrices and eigenvalues, systems of equations, approximate solution of ordinary and partial differential equations. Applications to physical problems. Partially duplicates 4554 and 3414. Mathematics majors or minors cannot take both 4404 and 3414. Pre: 4564, ESM 2074. (3H,3 Credits)
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