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Course Criteria
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3.00 Credits
Infinite sets, Cantor’s diagonal argument, first order logic, formal and informal proofs, combinatorics, Boolean algebra, lattices, and graphs. Prerequisites: MATH 251 and MATH 330. 3 credits.
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3.00 Credits
Matrices, linear systems of equations, linear programming, least-squares approximations, determinants, eigenvalues and eigenvectors, matrix inversion, elimination, iteration and other algorithms, precision and error analysis, of computational cost of algorithms. Emphasizes the practical methods using computer algorithms. Credit not awarded for both MATH 330 and MATH 365. Prerequisites: MATH 182 and CS 117 or CS 135. 3 credits.
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3.00 Credits
Introduction to logic, set algebra and Boolean algebra, with applications to the theory of computing machines. Prerequisite: MATH 251 or MATH 330. 3 credits.
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3.00 Credits
First order linear and non-linear differential equations, second and higher order differential equations with constant coefficients, Laplace transforms and applications, Gaussian elimination and eigenvalue problems, solutions of systems of differential equations. Prerequisite: MATH 283. 3 credits.
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3.00 Credits
Topics include line and surface integrals, complex functions, complex integration, power series, Laurent series, calculus of residues, conformal mappings, linear fractional transformations, probability theory, random variables, random samplings, sample mean and variance. Prerequisite: MATH 283 or equivalent. 4 credits.
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3.00 Credits
Formalization, proofs, and models of quantificational logic; axiomatics; application to mathematical theories, including set theory. Prerequisite: MATH 451. 3 credits.
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3.00 Credits
Sets, functions, groups, quotient groups, homomorphism theorems, Abelian groups, rings, polynomial rings, division rings, Euclidean domains, fields and vector spaces. Prerequisites: MATH 251 and MATH 330. 3 credits each.
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3.00 Credits
Topics include divisibility, arithmetic functions, congruences, quadratic residues, primitive roots, Diophantine equations, continued fractions, algebraic numbers, partitions. Prerequisite: MATH 330. 3 credits. 404 College of Sciences
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3.00 Credits
Topics include finite and infinite sets, axiomatic study of real numbers, topology of Cartesian spaces, sequences of functions, continuous functions, differentiation of functions of one variable. Prerequisites: MATH 251, MATH 330 and MATH 283 or equivalent. 3 credits.
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3.00 Credits
Topics include uniform continuity and fixed point theorems, sequences of continuous functions, approximation theorems, Riemann-Stieltjes integral, uniform convergence and infinite integrals, series of functions, differentiation in Rn. Prerequisite: MATH 457. 3 credits.
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