MATH 303 Themes for Society (3) Descriptive overviews of selected areas of mathematics which play a visible role in the modern world. Topics include management science and operations research, political science, statistics, computer science, biology, and some late 20th Century advancements in pure mathematics. Credit may not count toward the mathematical science major. Prerequisite: MATH 120. May not be taken by students who have received credit for MATH 302A.

MATH 304 Women and Mathematics (3) Examination of the social phenomena that have led to the small number of women in the mathematical profession. Exploration of the controversy concerning research on the comparative mathematical ability of boys and girls. Study of the lives, times, and works of women mathematicians. May not be taken by students who have received credit for MATH 302B.

MATH 306 Statistical Vignettes (3) Basic statistics and practical applications from the perspective of users in real situations. Topics may include: language and terminology, distributions, sampling, tests of significance, computerization of standard techniques, issues on uses and abuses of statistics, statistics in the social sciences, statistics in the business world. May be repeated for credit as topics change for a total of six (6) units. Credit may not be counted toward the mathematical sciences major. Prerequisite: MATH 120.

MATH 330 Introduction to the History of Mathematics (3) Major currents in the evolution of mathematical thought from early civilization to modern times. Prerequisite: MATH 160.

MATH 340 Statistics (3) Descriptive statistics; probability review; central tendency and dispersion; tests for variance, analysis of variance; random sampling, confidence intervals; simple nonparametric tests; univariate and joint distributions. Credit may not be counted toward the mathematical sciences major. Prerequisite: MATH 140 or MATH 240.

MATH 350 Foundations for Theoretical Mathematics (3) A bridge course between computation-driven mathematics and theoretical mathematics. Designed to provide an introduction to the understanding of mathematical arguments, a firm foundation in major ideas involving elementary logic, set theory, relations, functions, graph theory, and cardinality which are needed for advanced work, a guide for students to think and to express themselves mathematically, and a sufficient introduction to some of the ideas of modern algebra (e.g., matrix algebra, permutation groups, and modular arithmetic) and basic analysis (e.g., completeness in the reals, accumulation points) to capture some of their flavor and spirit. Prerequisite: MATH 160 with a minimum grade of C.

MATH 356 Mathematical Models (3) Construction, development, and study of mathematical models for real situations. Subjects from graph and network problems, enumeration problems, value and utility theory, conflict resolution, discrete optimization, simulation, Markov chains, computer applications. Prerequisite: MATH 162 or 350.

MATH 360 Foundations of Analysis (3) A classical treatment of the basic concepts of calculus of one variable: the real number system, limits, continuity, differentiability, the Riemann integral, sequences and series of numbers and functions. Prerequisite: MATH 350.

MATH 362 Differential Equations (3) Analysis and application of ordinary differential equations: linear and nonlinear equations, existence and uniqueness theorems, analytic methods, qualitative analysis of solutions, numerical methods. Combines theoretical ideas along with hands-on experience using appropriate computer software. May not be taken for credit by students who have received credit for MATH 364. Prerequisite: Calculus with Applications II with a grade of C or better.

MATH 370 Discrete Mathematics (3) Designed to provide some of the terminology, concepts, and techniques of several areas of discrete mathematics, especially some of those applicable in computer science. Elementary combinatorics, graphs and digraphs, trees, algebraic structures, Boolean algebra and computer logic, finite-state machines, groups and codes. Prerequisite: MATH 160.

MATH 372 Introduction to Number Theory (3) Divisibility, Euclidean algorithm, unique factorization, congruences, and quadratic reciprocity. May also cover some of the following: included primitive roots and indices, continued fractions, sum of squares, introduction to Diophantine equations, prime numbers, pseudo-primes, the prime number theorem, and factorization and primality-testing algorithms. Prerequisite: MATH 350 or consent of instructor.

MATH 374 Linear Algebra (3) Systems of linear equations, vector spaces, independence, bases, dimension, orthogonality, least squares, determinants, eigenvalues and eigenvectors, positive definiteness, computation, linear programming. This course will combine theoretical ideas with hands-on experience using appropriate computer software packages. Prerequisite: MATH 350 or 370.

MATH 398 Tutorial on Mathematical Methods (1) Designed to develop the skill to present clear, correct mathematical argument and exposition. Corequisite: Concurrent enrollment in an upper-division theoretical mathematics course or consent of discipline advisor.

MATH 404 Non-Statistical Mathematics in the Social Sciences (3) Themes involving applications of Mathematics in the social sciences such as: proportional representation, voting rules and aggregation of individual preferences, spatial models of election competition, power in weighted voting systems, power indices in politics, balance theory and social inequalities, measurement theory, game theory, static models of animal dominance, rumor and information networks. Prerequisite: MATH 120.

MATH 410 Modern Geometry (3) Critical review of the foundations and basic structure of plane and solid Euclidean geometry, non-Euclidean geometries, incidence and affine geometries; convexity and applications. Prerequisite: MATH 160.

MATH 420 Differential Geometry of Curves and Surfaces (3) Explores the basic concepts of the local geometry of curves and surfaces. The Frenet-Serret Theorem and its consequences will be examined in detail. The idea of curvature of geometric objects will be explored leading up to the concepts of geodesic, minimal surface and Riemannian curvature. Subject matter will be chosen from the global theory of both curves and surfaces. The isoparametric inequality, four-vertex theorem, Fenchel's Theorem, Theorem of Turning Tangents, the Gauss-Bonnet Theorem, and an introduction to the theory of manifolds may be studied. Prerequisites: MATH 260 and 264.

MATH 421 Calculus on Manifolds (3) The generalization of multivariable calculus to the setting of manifolds. The inverse and implicit function theorems, differential forms, integration on manifolds, the general version of Stokes' theorem. May also include an introduction to global invariants such as De Rham cohomology. Prerequisites: MATH 260, 264, or MATH 360, 374.

MATH 440 Mathematical Statistics (3) Basic concepts of probability. Data collection: random sampling and experimental design; data organization and description: tables and graphs, univariate descriptive statistics, bivariate descriptive statistics; probability: random variables, standard distributions, computer simulation; statistical inference: tests of significance, point estimation methods, confidence intervals, inference in simple linear regression. This course will combine theoretical ideas with hands-on experience using appropriate computer software packages. Prerequisite: MATH 162.

MATH 460 Introduction to Complex Analysis (3) Complex numbers, analytic functions, complex integration, residues and poles, power series, applications. Prerequisite: MATH 260.

MATH 462 Introduction to Probability (3) Axioms and basic properties, random variables, univariate probability functions and density functions, moments, standard distributions, Laws of Large Numbers, and Central Limit Theorem. Emphasis will be placed on applications. This course will combine theoretical ideas with hands-on experience using appropriate computer software packages. Prerequisites: MATH 260, or MATH 162 and 350.

MATH 464 Numerical Analysis and Computing (3) Computer arithmetic, solution of a single algebraic equation, solution of systems of equations interpolating polynomials, numerical integration, numerical solution of ordinary differential equations; error analysis and computational effort of numerical algorithms. This course will combine theoretical ideas with hands-on laboratory experience. Also offered as CS 464. Students may not receive credit for both. Prerequisites: CS 111 or equivalent and MATH 162.

MATH 470 Introduction to Abstract Algebra (3) An introduction to the theory of groups, rings, and fields. Additional subjects may include finite fields, field extensions, modules, the structure theorem of finitely generated abelian groups, semi-groups, partially ordered sets, Boolean algebras, finite-state machines, and coding theory. Prerequisite: MATH 350 or consent of instructor.

MATH 472 Introduction to Graph Theory (3) Fundamental concepts of undirected and directed graphs, trees, connectivity and traversability, planarity, colorability, networks, matchings; emphasis on modern applications. Prerequisite: MATH 350 or consent of instructor.

MATH 474 Introduction to Combinatorics (3) Introduction of the basic tools of combinatorics and their applications. Permutations, combinations, occupancy problems, generating functions, recurrences, inclusion/exclusion, graph theory, pigeonhole principle, experimental design, coding theory. Prerequisite: MATH 350 or consent of instructor.

MATH 480 Introduction to Optimization, I (3) Model-formulation, model-building, applications, as well as interpretation of software output of linear decision problems: convexity, linear programming, optimal assignment, transportation, network models, goal programming, integer programming; graphical methods, simplex methods, branch-and-bound methods, traveling salesman problem. Combines theoretical ideas with laboratory experience. Prerequisite: MATH 264 or MATH 374 or consent of instructor.

MATH 482 Introduction to Optimization, II (3) Theory and numerical methods for solving unconstrained and constrained nonlinear optimization problems: optimization of functions of several variables, nonlinear least squares, nonlinear programming, quadratic programming; quasi-Newton techniques, secant methods, classical line searches, method of feasible directions, method of steepest descent. Combines theoretical ideas with laboratory experience. Knowledge of a programming language is required. Prerequisite: MATH 260, 264 or MATH 374, or consent of instructor.

MATH 490 Senior Seminar (3) Presentation and discussion of selected topics in mathematical sciences in order to supplement available offerings. Prerequisites: Twelve (12) units of upper-division mathematics and consent of discipline advisor.

MATH 495 Internship in Mathematics (1-3) Faculty-sponsored academic internship in business, industrial, government, research firm, or university labs and centers. Prerequisite: Consent of instructor.

MATH 498 Individual Study in Mathematics (1-3) Individually directed reading and study in mathematical sciences literature. May be repeated for a maximum of three (3) units. Prerequisites: Twelve (12) units of upper-division in Mathematics and consent of instructor.

MATH 499 Independent Research in Mathematics (1-3) Designed for students capable of independent and original research. May be repeated for a maximum of three (3) units. Prerequisites: Twelve (12) units of upper-division mathematics and consent of instructor.

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