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MATH 416: Combinatorics
3.00 Credits
University of South Dakota
Pigeon hole principle, principle of inclusion-exclusion, other algebraic counting techniques, combinatorial designs, matchings, and graph theory. Note Registration restriction: Instructor consent Credits: 3
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MATH 416 - Combinatorics
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MATH 417: Matrix Theory
3.00 Credits
University of South Dakota
Theory of matrices, including matrix operations, transpose, conjugate transpose, determinants, linear spaces, bases, linear transformations, eigenspaces, hermitian matrices, normal matrices, and definite matrices. Prerequisites and Corequisites Course prerequisite: MATH 412 Credits: 3
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MATH 417 - Matrix Theory
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MATH 421: Complex Analysis
3.00 Credits
University of South Dakota
The algebra of complex numbers; complex functions; contour integration and Cauchy integral theorems; Taylor and Laurent series and the residue theorem; the evaluation of real definite integrals; elementary mapping problems. Prerequisites and Corequisites Course prerequisite: MATH 225 Credits: 3
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MATH 421 - Complex Analysis
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MATH 423: Advanced Calculus I
3.00 Credits
University of South Dakota
A theoretical treatment of Calculus that covers: limits; continuity and differentiability of functions of a single variable and of several variables; convergence of sequences and series; integration; and applications. Prerequisites and Corequisites Course prerequisites: MATH 225 and 351, or Instructor consent Credits: 3
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MATH 423 - Advanced Calculus I
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MATH 424: Advanced Calculus II
3.00 Credits
University of South Dakota
This is a continuation of MATH 423. Prerequisites and Corequisites Course prerequisite: MATH 423 Credits: 3
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MATH 424 - Advanced Calculus II
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MATH 432: Partial Differential Equations
3.00 Credits
University of South Dakota
Fourier series, partial differential equations, Frobenius series, Bessel functions, and transform methods. Prerequisites and Corequisites Course prerequisites: MATH 225 and 321 Credits: 3
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MATH 432 - Partial Differential Equations
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MATH 450: History of Mathematics
3.00 Credits
University of South Dakota
A general presentation of historical topics in mathematics including contributions to mathematics from ancient civilizations; developments leading to the creation of modern geometries, calculus and modern algebra; and contributions of outstanding mathematicians. Prerequisites and Corequisites Course prerequisite: MATH 125 or Instructor consent Credits: 3
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MATH 450 - History of Mathematics
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MATH 471: Numerical Analysis I
3.00 Credits
University of South Dakota
Analysis of rounding errors, numerical solutions of nonlinear equations, numerical differentiation, numerical integration, interpolation and approximation, numerical methods for solving linear systems. Prerequisites and Corequisites Course prerequisite: MATH 225 Cross-listed: CSC 471 Credits: 3
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MATH 471 - Numerical Analysis I
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MATH 472: Numerical Analysis II
3.00 Credits
University of South Dakota
Solution of nonlinear equations. Computational methods of linear algebra, theory of matrices in numerical analysis, special eigenvalue problems and computational algorithms. Finite difference interpolations, numerical solutions to ordinary and partial differential equations, boundary value problems. Prerequisites and Corequisites Course prerequisite: MATH 471 Cross-listed: CSC 472 Credits: 3
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MATH 472 - Numerical Analysis II
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MATH 475: Operations Research
3.00 Credits
University of South Dakota
An introductory overview of the field of operations research including topics from linear programming, simplex methods, network models, nonlinear programming, game theory, Markov Chains, introduction to dynamic programming, queuing theory and simulation. Prerequisites and Corequisites Course prerequisites: STAT 281 and MATH 125 or Instructor consent Cross-listed: CSC 475, STAT 475 Credits: 3
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MATH 475 - Operations Research
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