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Course Criteria
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4.00 Credits
A one-semester calculus summary for students in the life sciences. Topics include limits, derivatives, maxima and minima, curve sketching, integrals, areas, and numerical techniques. Applications are included from a variety of fields. Prerequisite: MS101.
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3.00 Credits
A one-semester calculus course for business students. Topics include limits, derivatives, maxima and minima, curve sketching, integrals, and optimization techniques. Applications include marginal analysis. Prerequisite: MS101.
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3.00 Credits
An introduction to matrices and linear algebra. Topics include determinants, Gauss-Jordan elimination, vectors in Euclidean n-space, dot product, norms, linear mappings, eigenvalues and eigenvectors. Applications from such fields as archeology, demography, game theory, cryptography, and fractal geometry are introduced. Prerequisite: MS101. The continuation is MS345.
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4.00 Credits
This course prepares the student to confront the elements of advanced theoretical mathematics: to understand mathematical statements, to read and write proofs, and to appreciate the processes of mathematical creation. Topics include elementary logic, set theory, functions, relations, and induction. Prerequisite: MS201.
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3.00 Credits
A rigorous approach to the concepts underlying calculus, building on the fundamental idea of the limit within the real number system. Topics include introductory topology of the real line, limits, and convergence of sequences and infinite series. The continuation is MS401.
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3.00 Credits
An introduction to the basic algebraic structures of groups, rings, and fields. Topics include permutation groups, integers modulo n, cosets, the Lagrange theorem, group-homomorphisms, polynomial rings, and integral domains. The continuation is MS405.
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3.00 Credits
This course is a study of equations involving derivatives. Topics include first and second order differential equations, existence and uniqueness of solutions, separation of variables, variation of parameters, linear and non-linear systems, solution by generalized eigenvectors, phase portraits, linear approximations, potential functions, gradient and Hamiltonian systems, limit cycles and chaotic systems, and mathematical modeling with differential equations. Prerequisite: MS203.
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3.00 Credits
This course studies elementary properties of integers including divisibility, factorization, and primality, with applications to RSA and public key cryptography. Topics include Diophantine equations, congruences, the Chinese Remainder Theorem, divisibility tests, theorems of Fermat, Wilson, and Euler, residue classes, quadratic residues, quadratic reciprocity, continued fractions, multiplicative functions, and a brief introduction to analytic number theory.
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3.00 Credits
The continuation of MS245. This course is an axiomatic theory of vector spaces. Topics include general vector spaces, inner product spaces, linear mappings, the Rank-Nullity Theorem, representations of mappings, diagonalization of mappings. Prerequisite: MS245.
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3.00 Credits
An introduction to the development and use of mathematical models, including topics such as model construction and fitting, regression and empirical modeling, difference equations and dynamical systems, and probabilistic modeling and Monte Carlo simulation. Prerequisite: CS100 or CS101. Cross-listed as CS350. MS351 Operations Research (3). An introduction to deterministic optimization. Topics include linear programming and the simplex method, the transportation problem, goal programming, network analysis, dynamic programming, and game theory.
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