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MATH 5280: Partial Differential Equations
3.00 Credits
University of Minnesota-Twin Cities
Introduction, emphasizing use of Fourier series, Green's functions, and other classical techniques.
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MATH 5280 - Partial Differential Equations
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MATH 5327: Advanced Linear Algebra
3.00 Credits
University of Minnesota-Twin Cities
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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MATH 5327 - Advanced Linear Algebra
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MATH 5330: Theory of Numbers
3.00 Credits
University of Minnesota-Twin Cities
Properties of integers, primes, divisibility, congruences, and quadratic reciprocity. Computational aspects include factoring algorithms and RSA cryptosystem. (offered alt yrs)
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MATH 5330 - Theory of Numbers
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MATH 5365: Graph Theory
3.00 Credits
University of Minnesota-Twin Cities
Finite graphs, including trees, connectivity, traversability, planarity, colorability, labeling, and matchings.
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MATH 5365 - Graph Theory
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MATH 5366: Enumerative Combinatorics
3.00 Credits
University of Minnesota-Twin Cities
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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MATH 5366 - Enumerative Combinatorics
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MATH 5371: Abstract Algebra I
3.00 Credits
University of Minnesota-Twin Cities
Introduction to groups and rings and their applications.
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MATH 5371 - Abstract Algebra I
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MATH 5372: Abstract Algebra II
3.00 Credits
University of Minnesota-Twin Cities
Polynomial rings, divisibility in integral domains, field extensions, finite fields, special topic, and applications.
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MATH 5372 - Abstract Algebra II
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MATH 5384: Algebraic Coding Theory
3.00 Credits
University of Minnesota-Twin Cities
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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MATH 5384 - Algebraic Coding Theory
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MATH 5810: Linear Programming
3.00 Credits
University of Minnesota-Twin Cities
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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MATH 5810 - Linear Programming
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MATH 5830: Numerical Analysis:Approximation and Quadrature
3.00 Credits
University of Minnesota-Twin Cities
Error analysis, interpolation and approximation, numerical integration, solution of nonlinear systems. (offered alt yrs)
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MATH 5830 - Numerical Analysis:Approximation and Quadrature
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