MATH 500 Mathematics and Technology (3) Use of mathematical software in analyzing and solving mathematical problems, and in presenting and teaching Mathematics. Packages used may include Maple, Mathematica, Axiom, MatLab, Gauss, HiQ; course will be updated as new software is developed. Combines theoretical ideas with hands-on laboratory experience. Prerequisites: MATH 350 and CS 302.

MATH 510 Mathematical Communication (3) Discusses organizing and presenting mathematics in both oral and written form. Explores the three aspects of writing in mathematics: how to write expository mathematics, how to write formal mathematics, and writing as a tool for learning mathematics. Prerequisite: MATH 350.

MATH 512 Elements of Calculus (3) Designed for secondary school teachers of high-school calculus. Theoretical emphasis on calculus of functions of one variable; limits, continuity, derivatives, integrals, infinite series, applications. Credit may not be counted towards the mathematical sciences major. Prerequisite: MATH 162.

MATH 520 Algebra (3) Study of algebraic structures and their applications inside and outside of mathematics. Covers some of the following: the theory of rings and ideals, polynomial rings, modules, computational algebra, introduction to commutative algebra, finite fields, number fields, field extensions, Galois theory, associative rings, a review of group theory, group representation theory and its applications, Boolean algebras, semi-groups. Applications to such fields as geometry, discrete math, number theory, algebraic geometry, analysis, physics, circuit design, and coding theory may be discussed. Prerequisite: MATH 470.

MATH 522 Number Theory (3) Computational and theoretical aspects of number theory including some of the following: congruences, reciprocity laws, pseudo-primes, factorization algorithms, primality testing, the prime number theorem, introduction to Diophantine equations, introduction to computational number theory, introduction to algebraic number theory, and introduction to analytic number theory. Applications may include fast fourier analysis, signal processing, coding, and cryptography. Combines theoretical ideas with hands-on laboratory experience and experimentation. Prerequisites: MATH 470 or MATH 520.

MATH 530 Measure Theory (3) Lebesque measure, measurable functions, the Lebesque integral, Fubini's theorem, Lp-spaces, and differentiation. Prerequisite: MATH 360 or consent of instructor.

MATH 540 Concrete Mathematics (3) A blend of continuous and discrete topics including sums, recurrences, elementary number theory, binomial coefficients, generating functions, discrete probability, and asymtotic methods. Prerequisite: MATH 370 or 372 or 470 or 472 or 474.

MATH 542 Algorithmic Graph Theory (3) Introduction to algorithmic complexity; spanning trees; connectivity; planarity; tours; coloring; intractability. Directed graphs: ranking, dominance, voting. Prerequisite: MATH 540 or 644 or consent of instructor.

MATH 550 Geometry (3) Geometric ideas selected from the following fields: Euclidean geometry, non-Euclidean geometry, projective geometry, algebraic geometry, differential geometry, computational geometry, other geometries. Combines theoretical ideas with hands-on laboratory experience. Prerequisites: MATH 374 and MATH 470.

MATH 555 General Topology (3) Topological spaces, open and closed sets, metric spaces, continuity, compactness, connectedness. Other subjects may include separation axioms, fundamental groups, classification of surfaces, completion of metric spaces. Prerequisites: MATH 350 or 360, or consent of instructor.

MATH 561 Computational Linear Algebra (3) Provides a thorough background in the formulation and analysis of algorithms for numerical linear algebra. Includes fundamentals of scientific computation, subspaces, rank-revealing matrix factorizations, numerical solutions of linear systems, linear least squares, regularization, perturbation theory, and iterative methods. Combines theoretical ideas with laboratory experience. Knowledge of computer language is required. Prerequisites: MATH 500 and either MATH 264 or MATH 374, or consent of instructor. May not be taken for credit by students who have received credit for MATH 626.

MATH 562 Mathematical Programming, I (3) Theory and basic techniques for solving optimization problems. Linear programming, optimality conditions, duality, sensitivity analysis, integer programming. Simplex algorithm, dual-simplex and the primal-dual algorithm, Karmarkar's method, cutting plane algorithm. Combines theoretical ideas with laboratory experience. Knowledge of a computer language is required. Prerequisite: MATH 500, and either MATH 264 or MATH 374, or consent of instructor.

MATH 564 Mathematical Programming, II (3) Theory and numerical optimization methods for nonlinear programming. Quasi-Newton secant methods for nonlinear equations and unconstrained minimization, convergence, nonlinear least squares, Broyden's method, methods for problems with special structure, and constrained optimization. Combines theoretical ideas with laboratory experience. Knowledge of a computer language is required. Prerequisites: MATH 500 and either MATH 264 or MATH 374, or consent of instructor.

MATH 570 Mathematical Modeling (3) Mathematical modeling with emphasis on models used in the social, life, and management sciences and their role in explaining and predicting real world phenomena. Combines theoretical ideas with hands-on laboratory experience. Prerequisites: MATH 360, 462, 500, and 540 or consent of instructor.

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