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Course Criteria
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3.00 Credits
Introduction, emphasizing use of Fourier series, Green's functions, and other classical techniques.
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3.00 Credits
Vector spaces over fields, subspaces, linear transformations, matrix representations, change of basis, inner-product spaces, singular value decomposition, eigenspaces, diagonalizability, annihilating polynomials, Jordan form.
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3.00 Credits
Properties of integers, primes, divisibility, congruences, and quadratic reciprocity. Computational aspects include factoring algorithms and RSA cryptosystem. (offered alt yrs)
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3.00 Credits
Finite graphs, including trees, connectivity, traversability, planarity, colorability, labeling, and matchings.
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3.00 Credits
Permutations, combinations, binomial coefficients, inclusion-exclusion, recurrence relations, ordinary and exponential generating functions, Catalan numbers, selected topics from designs, finite geometries, Polya's enumeration formula.
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3.00 Credits
Introduction to groups and rings and their applications.
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3.00 Credits
Polynomial rings, divisibility in integral domains, field extensions, finite fields, special topic, and applications.
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3.00 Credits
Introduction to linear error-correcting codes using binary vector spaces and finite fields. Hamming codes, Golay codes, linear codes in general, cyclic codes, BCH codes, and their encoding/decoding. (offered alt yrs)
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3.00 Credits
Motivation problems, modeling, theory of simplex method, duality and sensitivity analysis, large-scale problems, complexity, and Karmarkar algorithm. (offered alt yrs)
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3.00 Credits
Error analysis, interpolation and approximation, numerical integration, solution of nonlinear systems. (offered alt yrs)
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