1996-1997 Academic Catalog

Science Mathematics CHEM-451,452,453 Physical Chemistry I,II,III 4 hours autumn and winter quarters 3 hours spring quarter A study of the properties of chemical systems, including the fundamentals of thermodynamics, chemical dynamics, and quantum mechanics. Autumn and Winter quarters: three lectures and one three-hour laborat01y per week. Spring quarter: three lectures. Prerequisite: CHEM-254 Quantitative Analysis or PHYS-273 General Physics. (Fee: $35) (odd years) CHEM-454 Advanced Inorganic Chemistry 5 hours Modern concepts of the strncture of matter, nature of the chemical bond, complex ions, and the periodic properties of the elements. Prerequisite: CHEM-254 Quantitative Analysis. (even years) CHEM-455 Topics in Chemistry 2-5 hours Topics of special interest are selected by the chemistry faculty from the areas of modern chemistry. May be repeated once for credit. Prerequisite: CHEM-153 General Chemistry or equivalent; permission of instructor. Mathematics MATH-281 Analytic Geometry and Calculus I-A,W 5 hours First course of a tln·ee-course sequence covering basic concepts of analytic geometty and single variable calculus. Includes limits, derivatives, applications of the 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 II-W,Sp 5 hours The second course of a tln·ee-course sequence covering the basic concepts of analytic geometry and single variable calculus. Includes calculus-based development of the 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 Geometry and Calculus I. MATH-283 Analytic Geometry and Calculus III-A,Sp 5 hours Third course of a three-course sequence covering basic concepts of analytic geometty 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 algorithms. Forms an eight-hour sequence with MATH-356 Discrete Mathematics: Combinatorics. Prerequisite: MATH-303 Logic and Methods of Proof. (odd years) MATH-356 Disc.-ete 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 combin– ations, generating functions, partitions, and recutTence relations. Prerequisite: MATH-303 Logic and Methods of Proof. (odd years) MATH-360 Number Theory-A 5 hours An introduction to most of the topics of elementaiy 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 reason– ing will develop the theories considered in the courses. Prerequisite: MATH-303 Logic and Methods of Proof. (odd years) MATH-374 Complex Variables 5 hours Introduction to complex arithmetic, differentiation: analytic functions, Cauchy-Riemann equations, harmonic functions, elementaiy functions and their mapping propetiies, integration: Cauchy's Theorem, Cauchy's Integral Formula, Taylor and Laurent series, poles, residues, and the residue theorem. Prerequisite: MATH-388 Advanced Calculus I. (odd years) MATH-384 Probability and Statistics-W 5 homs 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 Geomet1y 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 III. 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 determinants. Prerequisite: MATH-283 Analytic Geometry and Calculus III. MATH-389 Advanced Calculus II-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. Prerequisite: 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 II; MATH-303 Logic and Methods of Proof. (even years) MATH-411 Applied Statistics 3 hours Topics chosen from the following: regression analysis, queuing theory, invent01y theory, decision analysis, simulation, quality control, and reliability theory. Prerequisite: MATH-384 Probability and Statistics. MATH-441 Euclidean and Non-Euclidean Geometries-Sp 5 hours Rigorous treatment of the foundations of Euclidean geometry; an introduction to hyperbolic geomet1y with emphasis on its Euclidean models. Prerequisite: MATH-303 Logic and Methods of Proof. (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 theo1y, separation axioms, covering properties, compactness, connectedness, metrifability, and complete metric spaces. Prerequisite: MATH-303 Logic and Methods of Proof. (even years) MATH-461,462 Abstract Algebra I,II-A,W 4 hours Introduction to sets and logic, and the development of algebraic systems, groups, rings, integral domains, fields, and Galois the01y. Prerequisite: MATH 303 Logic and Methods of Proof. (even years) MATH-471,472 Real Variables I,Il-A,W 4 hours Introduction to the real number system's algebraic, order, complete– ness, and cardinality properties, the topology of Cartesian spaces R" and functions including continuity and uniform continuity, connectedness, convexity, compactness, various types of conver– gence, limits, differentiability, Riemann and Lebesgue integration, measurability, and L spaces. Prerequisite: MATH-389 Advanced Calculus II. P (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 of instrnctor.