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Course Criteria
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3.00 Credits
Pr., MATH 2660. Mathematics of the integers, divisibility, primes, unique factorization, congruences and residues, Dio- phantine problems and number theoretic functions.
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3.00 Credits
Pr., MATH 2660. An introduction to algebraic structures. Binary operations, groups, subgroups, groups of permutations, cyclic groups, normal subgroups, quotient groups, homomorphisms and isomorphisms, rings, integral domains, fields.
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3.00 Credits
Pr., MATH 4310. A continuation of MATH 4310. Ideals and quotient rings, ring homomorphisms, rings of polynomials, factorization, Euclidean rings, extension fields, selected additional topics.
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3.00 Credits
Pr., MATH 2660, knowledge of a computer programming language. Use of models and simulation for solving problems in applied mathematics. Techniques of setting up, solving, and interpreting models as well as an introduction to selected standard models.
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3.00 Credits
Pr., MATH 1620. Axiomatic devel- opment of plane geometry. Emphasis on the development of proofs by students.
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3.00 Credits
Pr., MATH 2630, permission of instructor. Metric spaces, continuity, sequences, equivalent metrics, topological spaces and homeo- morphisms, products, connectedness and compactness. Offered when there is sufficient demand.
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3.00 Credits
Pr., MATH 2660, significant fluency in a pro- gramming language, familiarity with FORTRAN. Number systems and error propagation, solutions of nonlinear equations, acceleration of convergence, polynomial and spline interpolation, numerical integration and differentiation, efficient direct solution of systems of linear equations, PLU factorization of matrices, and matrix norms and condition numbers.
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3.00 Credits
Pr., MATH 4600. Iterative solutions of large systems of linear equations, numerical solutions of eigenvalue problems for linear systems, numerical solutions of boundary value problems for ordinary differential equations, numerical solution of systems of ordinary differential equations and least square approximation. Offered when there is sufficient demand.
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3.00 Credits
Pr., MATH 2630. Basic probability theory, combinatorics, random variables, special distributions, and applications to scientific and engineering data.
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3.00 Credits
Pr., MATH 4670. A continuation of MATH 4670 Mathematical Statistics I. Moment-generating functions and the use of moments, Central Limit Theorem, derivation of probability density func- tions of sample statistics, sampling, estimation and hypothesis testing, and correlation and regression. Offered when there is sufficient demand.
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