1999-2000 Academic Catalog

Mathematics MATH-281 Analytic Geometry and Calculus 1-A,W 5 hours First course of a three-course sequence covering basic concepts of analytic geometry and single variable calculus. Includes limits, derivatives, applications ofthe derivative, and single variable integration with introduction to numeric integration techniques. Prerequisite: GSCI-185 Precalculus or equivalent; permission of instructor. MATH-282 Analytic Geometry and Calculus H-W,Sp 5 hours The second course of a three-course sequence covering the basic concepts of analytic geometry and single variable calculus. Includes calculus-based development ofthe logarithmic and exponential functions along with other transcendental functions, applications of integration, additional integration techniques, sequences, series, and expansion of functions into Taylor and power series. Prerequisite: MATH-281 Analytic GeometrJ1 and Calculus I. MATH-283 Analytic Geometry and Calculus HI-A,Sp 5 hours Third course of a three-course sequence covering basic concepts of analytic geometry and single variable calculus. Includes conic sections, plane curves, parametric equations, polar coordinates, vectors and geometry in three-space, vectors, and vector calculus. Prerequisite: MATH-282 Analytic Geometry and Calculus II. MATH-303 Logic and Methods of Proof-A 5 hours Introduction to formal mathematical logic; emphasis on preparing students for the abstraction of upper-division courses. Special attention is given to the development of students' skills with a variety of methods of proof, using examples from numerous areas. Prerequisite: MATH-282 Analytic Geometry and Calculus II. MATH-355 Discrete Mathematics: Graph Theory-W 4 hours Introduction to the basic concepts of graph theory and discrete mathematics problem-solving. Topics covered include elements of graph theory, covering circuits, graph coloring, trees and searching, and network alg01ithms. Forms an eight-hour sequence with MATH- 356 Discrete Mathematics: Combinatorics. Prerequisite: MATH-303 Logic and Methods ofProof (odd years) MATH-356 Discrete Mathematics: Combinatorics-Sp 4 hours Study of combinatorial reasoning, focusing on enumeration. Intended to develop a proficiency in methods of enumerative problem solving. Topics chosen from areas such as counting methods for arrangements and selections, permutations and combinations, generating functions, partitions, and recmTence relations. Prerequisite: MATH-303 Logic andMethods ofProof (odd years) MATH-360 Number Theory-A 5 hours Introduction to most of the topics of elementary number theory such as modular arithmetic, prime factorizations, linear diophantine equations, the Chinese remainder theorem, quadratic reciprocity, Pythagorean triples, number theoretic functions, and related topics. Concrete examples will illustrate the concepts and abstract reasoning will develop the theories considered in the courses. Prerequisite: MATH-303 Logic and Methods ofProof (odd years) MATH-374 Complex Variables 5 hours Introduction to complex arithmetic, differentiation: analytic functions, Cauchy-Riemann equations, harmonic functions, elemen– tary functions and their mapping properties, integration: Cauchy's Theorem, Cauchy's Integral Formula, Taylor and Laurent series, poles, residues, and the residue theorem. Prerequisite: MATH-283 Analytic Geomefly and Calculus III. (odd years) MATH-384 Probability and Statistics-W 5 hours Probability models, random variables, binomial, T, chi square and F distributions, sample spaces, estimation, and hypotheses tests are studied from theoretical and practical viewpoints. Prerequisite: MATH-283 Analytic Geometry and Calculus III. MATH-387 Differential Equations-A,W 5 hours Study of the standard techniques employed in the solution of differential equations with emphasis on those arising from physical problems. Prerequisite: MATH-283 Analytic Geometry and Calculus II. MATH-388 Advanced Calculus 1-A,W 5 hours each quarter Introduction to differential calculus of several variables, multiple integrals, vector analysis, line integrals, surface integrals, and an abbreviated introduction to linear algebra, matrix algebra, and determi– nants. Prerequisite: MATH-283 Analytic Geometry and Calculus III. MATH-389 Advanced Calculus H-Sp 5 hours Topics in function theory, vector analysis, differential calculus of several variables, vector differential calculus, integral calculus of several variables, vector integral calculus, and infinite series. Prerequi– site: MATH-388 Advanced Calculus I. MATH-394 Linear Algebra-Sp 5 hours Introduction to the algebra of linear equations, including determi– nants, matrices, vector spaces, eigenvalues, eigenvectors, and linear mapping. Prerequisite: MATH-282 Analytic Geometry and Calculus JI. (even years) MATH-411 Applied Statistics 3 hours Topics chosen from the following: regression analysis, queuing theory, inventory theory, decision analysis, simulation, quality control, and reliability theory. Prerequisite: MATH-384 Probability andStatistics. MATH-441 Euclidean and Non-Euclidean Geometries-Sp 5 hours Rigorous treatment of the foundations of Euclidean geometry; an introduction to hyperbolic geometry with emphasis on its Euclidean models. Prerequisite: MATH-303 Logic andMethods ofProof (odd years) MATH-445 Topology-A 5 hours Introduction to elementary point set topology; emphasis on illustrating how the familiar concepts of closed and open intervals, continuity of functions, and various geometrical properties have been generalized from classical mathematics. Topics include: metric spaces, topological space theory, separation axioms, covering properties, compactness, connectedness, metrizability, and complete metric spaces. Prerequisite: MATH-303 Logic and Methods ofProof MATH-461,462AbstractAlgebral,H-A,W 4 hours Introduction to sets and logic, and the development of algebraic systems, groups, rings, integral domains, fields, and other advanced topics. Prerequisite: MATH-303 Logic and Methods ofProof (even years) MATH-471,472 Real Variables I, H-A,W 4 hours Introduction to the real number system's algebraic, order, complete– ness, and cardinality properties, the topology of Cartesian spaces Rn and functions including continuity and uniform continuity, connected– ness, convexity, compactness, various types of convergence, limits, differentiability, and Riemann integration, measurability, and L spaces. Prerequisite: MATH-283 Analytic Geometry and Calcu~us 111; MATH-303 Logic and Methods ofProof (even years) MATH-480 Topics in Mathematics 2-5 hours Some typical topics are complex variables, matrix algebra, vector analysis, numerical analysis, introduction to computer programming, partial differential equations, and mathematical modeling. Prerequisite: permission ofinstructor. MATH-490 Independent Study in Mathematics 1-4 hours Independent research in the various branches ofmathematics and allied fields of application. Submission and approval of a research proposal must precede registration. Prerequisite: major in mathemat– ics and permission ofresearch advisor. MATH-491 Mathematical Methods for Physicists-A,W,Sp 5 hours Advanced mathematical methods used in the solution of physics problems. Topics include curvilinear coordinates, vector analysis, and Fourier, Bessel, and Legendre solutions to partial differential equa– tions. Prerequisite: PHYS-311 Theoretical Mechanics or PHYS-378 Modern Physics I; MATH-387 Differential Equations; MATH-388 Advanced Calculus I.