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Course Criteria
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3.00 Credits
Topics include finite differences, interpolation, numerical integration and differentiation, solutions of equations of one variable, linear systems, and numerical solutions of ordinary differential equations. Prerequisites: MTH 2220, 2227 and 3331, or permission of instructor.
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3.00 Credits
The real number system, completeness, limits, continuity, sequences, differentiation, and the Riemann integral. Prerequisites: MTH 2227 and 3318.
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3.00 Credits
Sequences and series of functions, series, and a continuation of the integral to include the Fundamental Theorem of Calculus. Prerequisite: MTH 4424.
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3.00 Credits
Complex numbers, elementary functions and their mappings, complex limits and power series, analytic functions, integrals, contour integrals, and Cauchy integral formula. Prerequisites: MTH 2227 and 3318 or permission of instructor.
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3.00 Credits
Divisibility, congruencies, prime numbers, Fermat’s theorem, Diophantine equations, number theoretic functions. Prerequisites: MTH 2227 and 3318.
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3.00 Credits
Properties of the integers, modular arithmetic. Elementary theory of groups, finite groups, subgroups, cyclic groups, permutation groups. Group isomorphisms and homomorphisms. Prerequisites: MTH 2227, 3318, and 3331, or permission of instructor.
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3.00 Credits
Elementary theory of rings, polynomial rings, divisibility, unique factorization domains. Integral domains, ideals, factor rings, divisibility in integral domains. Elementary theory of fields. Extension fields. Prerequisite: MTH 4441.
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3.00 Credits
Probability theory, sample spaces, random variables, mutual exclusion, independence, conditional probability, permutations and combinations, common discrete and continuous distributions, expected value, mean, variance, multivariate distributions, covariance, Central Limit Theorem. Prerequisite: MTH 2227 or permission of instructor.
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3.00 Credits
Fundamentals of the theory of statistics, the Central Limit Theorem, point estimation, sufficiency, consistency, hypothesis testing, sampling distributions, confidence intervals, linear regression models, interpretation of experimental results, Bayesian
Estimation. Prerequisite: MTH 4451.
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3.00 Credits
An introduction to metric and topological spaces and associated topics, separation axioms, compactness, and connectedness. Prerequisites: MTH 2227 and 3318.
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