(2001) Professor of Mathematics. B.S. 1995, National University of Mexico; Ph.D. 2001, Rutgers University.

(2003) Professor of Mathematics. B.S. 1993, M.S. 1995, Ph.D. 1999, Novosibirsk State University.

(2007) Professor of Mathematics. B.S. 2000, M.A. 2000, Ph.D. 2004, University of California, Los Angeles.

(1987) Professor Emeritus of Mathematics. B.A. 1973, Bard College; Ph.D. 1982, Rutgers University.

(2000) Professor Emeritus of Mathematics. M.A. 1984, University of Santiago de Compostela; Ph.D. 1991, Washington University.

(1970) Professor Emeritus of Mathematics. B.S. 1964, National Taiwan University; Ph.D. 1970, California Institute of Technology.

(1975) Professor Emeritus of Mathematics. B.S. 1966, Case Institute of Technology; M.S. 1967, Ph.D. 1970, Stanford University.

The field of complex systems is relatively young and evolving, encompassing a wide range of disciplines in the sciences, engineering, computer science, and mathematics. In this context, a “complex system” is defined as an engineered or natural system that is characterized by dynamical properties and unobservable interactions that may not be apparent from observations of …

(1982) Professor Emeritus of Mathematics. B.A. 1971, M.S. 1975, California State University, Northridge.

Prerequisite: Consent of the graduate advisor. This course provides essential mathematical tools for the study of complex systems. Topics include vector calculus, linear algebra and aspects of differential equations and partial differential equations.

Prerequisite: Consent of the graduate advisor. This course introduces physical approaches to dealing with complex, many-body systems. Two distinct and complementary frameworks are presented: analytical mechanics and statistical physics. Core concepts include Lagrangian and Hamiltonian formulations of mechanics, phase space, nonlinear dynamics, chaos, fractals, free energy, entropy, partition functions and statistical ensembles.

Prerequisite: Consent of the graduate advisor. The first part of the course will cover nonlinear chemical kinetics, control of chemical reactions, self-assembly at microscopic and macroscopic levels, and development of new techniques for materials synthesis. In the second part, quantum chemical models for describing large systems and their interaction with the surroundings will be introduced.

Prerequisite: Consent of the graduate advisor. The course will explore how to analyze biology from a systems-level point of view. Students will explore design principles in biology, including plasticity, exploratory behavior, weak-linkage, constraints that deconstrain, robustness, (non)optimality and evolvability.

Prerequisite: Consent of the graduate advisor. Overview of computer science topics relevant to complex systems, including software development, design of algorithms, computer simulation, computer and sensor networks, social networks and agent-based systems.

Prerequisite: Consent of the graduate advisor. This course introduces the principles and methods of complex systems engineering. The course is organized as a progression through the systems engineering processes of analysis, design, implementation and deployment with consideration of verification and validation throughout. Case studies and guest lectures in each phase present best practice in the field …

Prerequisites: Passing preliminary examination and graduate advisor consent. This course provides an overview of complex systems and describes theoretical, numerical and computational approaches to defining, analyzing and solving applied problems in complex systems.

Prerequisites: CPLX 710A, passing preliminary examination and graduate advisor consent. Hands-on activities on complex systems topics. Examples of course project topics include complex networked systems (sensor networks and social networks) and agent-based modeling (genetic programming and evolutionary strategies).

Prerequisites: Passing preliminary examination and graduate advisor consent. Advanced studies in various subjects related to complex systems through special seminars, informal group studies of special problems, or group research on complete problems for analysis and experimentation.

(2007) Professor of Mathematics. M.A. 1998, University of Maryland; Ph.D. 2003, University of California, Los Angeles.

(2003) Professor of Mathematics. M.A. 1984, University of Paris-Sud; Ph.D. 1988, University Paris XI-Orsay and Ecole Polytechnique.

(2020) Assistant Professor of Mathematics. B.S. 2008, Université de l’Atlantique; M.A. 2012, University of Missouri, St. Louis; Ph.D. 2020, University of Illinois at Chicago.

(1987) Professor of Mathematics. B.A. 1978, University of California, Santa Cruz; M.A. 1981, University of California, Los Angeles; Ph.D. 1987, University of Southern California.

(1964) Professor Emeritus of Mathematics. B.A. 1954, M.A. 1959, Ph.D. 1962, University of California, Los Angeles.

(1999) Professor of Mathematics. B.A. 1990, University of California, San Diego; M.A. 1994, Ph.D. 1996, University of Wisconsin.

(2001) Professor of Mathematics. B.S. 1995, National University of Mexico; Ph.D. 2001, Rutgers University.

(1968) Professor Emeritus of Mathematics. B.A. 1953, Ph.D. 1964, University of California, Berkeley.

(1964) Professor Emeritus of Mathematics. B.A. 1960, Occidental College; Ph.D. 1964, California Institute of Technology.

(1998) Professor of Mathematics. B.A. 1985, University of Rochester; M.S. 1987, University of Chicago; Ph.D. 1996, University of Texas.

(1968) Professor Emeritus of Mathematics and Engineering. B.S. 1954, M.S. 1957, Ph.D. 1968, University of California, Los Angeles; Professional Engineer, State of California.

(1970) Professor Emeritus of Mathematics. B.S. 1963, M.S. 1964, University of Chicago; Ph.D. 1970, University of California, Los Angeles.

(1962) Professor Emeritus of Mathematics. B.A. 1939, Bedagogical Institute, Baku, Russia; M.S. 1942, Engineering Institute, Moscow, Russia; Ph.D. 1950, University of Tuebengen, Germany.

(2016) Associate Professor of Mathematics. B.S. 2007, University of Science and Technology of China; Ph.D. 2012, Wayne State University.

(2021) Associate Professor of Mathematics. B.S. 2009, National Taiwan University; M.A. 2012, Ph.D. 2017, University of Wisconsin-Madison.

(1998) Professor Emeritus of Mathematics. M.A. 1986, Ph.D. 1989, University of California, Los Angeles.

(2012) Professor of Mathematics. A.B. 1997, Princeton University; Ph.D. 2005, California Institute of Technology.

(1988) Professor Emeritus of Mathematics. B.A., B.S. 1975, M.A. 1976, University of California, Santa Barbara; Ph.D. 1981, Cornell University.

(2013) Professor of Mathematics. B.S. 2000, Huazhong Normal University; M.S. 2003, Huazhong University of Science and Technology; Ph.D. 2008, University of Western Ontario.

(1987) Professor Emeritus of Mathematics. B.A. 1979, McGill University; M.S. 1981, Ph.D. 1984, University of Iowa.

(2016) Associate Professor of Mathematics. B.S. 2003, University of Sydney; B.S. 2004, Australian National University; Ph.D. 2010, Stanford University.

(1983) Professor Emeritus of Mathematics. B.A. 1967, Manhattanville College; M.S. 1977, California State University, Northridge; Ph.D. 1990, New York University.

Corequisites: MATH 103 and MATH 103L. This is a credit/no credit pre-baccalaureate math class designed to support students in the algebra intensive GE Math course, the Business Math course, MATH 103. It provides just-in-time remediation for the MATH 103 lecture meetings, allowing students to have the prerequisites at their fingertips. May be repeated once for …

Corequisites: MATH 102 and MATH 102L. This is a credit/no credit pre-baccalaureate math class designed to support students in the algebra intensive GE Math course for the Calculus sequence. It provides just in time remediation for the MATH 102 lecture meetings, allowing students to have the prerequisites at their fingertips. May be repeated once for …

Corequisites: MATH 141 and MATH 141L. This is a credit/no credit pre-baccalaureate math class designed to support students in the Introductory Statistics course. It provides just-in-time remediation for the MATH 141 lecture meetings, allowing students to have the prerequisites at their fingertips. May be repeated once for credit. 2 hours per week. (Credit/No Credit only)

Prerequisites: Listed in Table 1. A preparation for the algebra necessary for calculus. This course is intended for computer science, engineering, mathematics, and natural science majors. It builds on student’s familiarity with linear, quadratic, and rational expressions to achieve fluent proficiency in analyzing the local and global behavior of functions involving such expressions. Not open …

Corequisite: MATH 102. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 102. This course is designed to give students additional exposure to pre-calculus topics beyond what can be done in lecture. The active learning approach to problem solving practiced in this lab class enhances the lecture experience and strengthens the skills …

Prerequisites: Listed in Table 1. Concepts and applications of algebra and calculus to business. Topics include functions, systems of equations, matrices, the derivative and business-related topics in calculus. Available for General Education, Basic Skills Area 2 Mathematical Concepts and Quantitative Reasoning.

Corequisite: MATH 103. This a Credit/No Credit hybrid enrichment laboratory that is designed to give students additional exposure to the applications of college algebra to business and economics beyond what can be done in lecture. The active learning approach to problem solving practiced in the lab class enhances the lecture experience and strengthen the skills …

Prerequisites: Listed in Table 1. A preparation for the trigonometric, exponential, and logarithmic functions used in calculus. This course is intended for computer science, engineering, mathematics, and natural science majors. This course builds on student’s familiarity with exponential, logarithmic, and trigonometric expressions to achieve proficiency in analyzing the local and global behavior of functions involving …

Corequisite: MATH 105. All students in MATH 105 are encouraged to enroll in this course. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 105. This course will include a self-paced, modular online component. 3 hours lab per week. (Credit/No Credit only)

Prerequisites: Listed in Table 1. Mathematics applicable to problems in non-calculus based physics. Sets, inequalities; functions and graphs: polynomial, rational, exponential, logarithmic, trigonometric; introduction to vectors, angular velocity, and parametric equations. This course is not open to students who have credit in MATH 105 or MATH 255A. Available for General Education, Basic Skills Area 2 Mathematical …

Prerequisite: Multiple Measures Placement in GE-level Mathematics. General Education course intended to acquaint the student with basic mathematical ideas. Available for General Education, Basic Skills Area 2 Mathematical Concepts and Quantitative Reasoning.

Prerequisite: Multiple Measures Placement in GE-level Mathematics. Methods for displaying, describing and producing data. Normal distribution. Correlation and regression. Sampling distributions and probability. Statistical inference for means and proportions. Hybrid (part online) or fully online sections only. Available for General Education, Basic Skills Area 2 Mathematical Concepts and Quantitative Reasoning. (Cross-listed with MATH 140BUS, MATH 140SCI, …

Prerequisite: Multiple Measures Placement in GE-level Mathematics. Methods for displaying, describing and producing data. Normal distribution. Correlation and regression. Sampling distributions and probability. Statistical inference for means and proportions. Applications to business. Open to students in the College of Business and Economics. Students who are exploratory majors may enroll in this course. Available for General Education, …

Prerequisite: Multiple Measures Placement in GE-level Mathematics. Methods for displaying, describing and producing data. Normal distribution. Correlation and regression. Sampling distributions and probability. Statistical inference for means and proportions. Applications to STEM fields. Open to all students except those in the College of Business, College of Social and Behavioral Sciences, and CADV (Child and Adolescent …

Prerequisite: Multiple Measures Placement in GE-level Mathematics or concurrent enrollment in MATH 091S. Corequisite: MATH 141L. Basic statistical concepts and reasoning, including methods for displaying, summarizing, interpreting, and producing data. The normal model and variability in random samples. Statistical inference for means and proportions. The linear model: correlation and regression. This course is intended for students majoring in the social …

Corequisite: MATH 141. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 141 that is designed to give students additional exposure to the applications of statistical concepts and tools beyond what can be done in lecture. The active learning approach to problem solving practiced in this lab class enhances the lecture experience …

Prerequisites: Listed in Table 1. Limits, derivatives, and applications of differentiation. Definite and indefinite integrals. The fundamental theorem of calculus and applications of integration. Available for General Education, Basic Skills Area 2 Mathematical Concepts and Quantitative Reasoning.

Corequisite: MATH 150A. All students in MATH 150A are encouraged to enroll in this course. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 150A. This course will include a self-paced, modular online component. 3 hours lab per week. (Credit/No Credit only)

Prerequisites: Listed in Table 1. Techniques of integration and improper integrals. Sequences and series. Power series and Taylor polynomials. Parametric and polar coordinates. Vectors and solid geometry.

Corequisite: MATH 150B. All students in MATH 150B are encouraged to enroll in this course. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 150B. This course will include a self-paced, modular online component. 3 hours lab per week. (Credit/No Credit only)

Prerequisites: Multiple Measures Placement in GE-level Mathematics, or credit in MATH 093 or MATH 196QR or MATH 196S or equivalent. Language of sets, systems of numeration, nature of numbers and fundamentals of operations, relations and functions, domain of integers, and field of rational and real numbers. Designed primarily for students intending to teach in elementary …

Prerequisite: Completion of MATH 210 with a grade of “C” or better. Univariate and bivariate data analysis; probability and probability distributions; design of studies and concepts of inferential statistics; applications to procedures used to evaluate teaching and learning. Not available for credit toward a Mathematics major or minor.

Prerequisite: Completion of MATH 150B with a grade of “C” or better. Continuation of MATH 150B. Solid analytic geometry and space curves. Partial differentiation and applications. Multiple integrals. Line integrals and independence of path. Vector calculus including the divergence theorem and Stokes’ theorem.

Prerequisites: Listed in Table 1. Knowledge of trigonometry is assumed. First semester of a brief course in calculus. Topics include calculus of functions of one real variable, techniques of differentiation, applications to graphing, optimization problems, and an introduction to integration. Applications to life sciences are emphasized. Not open for credit to students who have successfully …

Corequisite: MATH 255A. All students in MATH 255A are encouraged to enroll in this lab. This course will include a self-paced, modular outline component. 3 lab hours per week. (Credit/No Credit only)

Prerequisites: Listed in Table 1. Second semester of a brief course in calculus. Topics include techniques of integration, introduction to differential equations, applications of calculus in probability, elements of multivariable calculus, and linear algebra. Applications to life sciences are emphasized. Not open for students who have successfully completed MATH 150AB.

Corequisite: MATH 255B. All students in MATH 255B are encouraged to enroll in this course. This course will include a self-paced, modular online component. 3 lab hours per week. (Credit/No Credit only)

Prerequisite: Completion of MATH 150B with a grade of “C” or better. Systems of linear equations, matrices, determinants, eigenvalues, vector spaces and linear transformations, as well as introduction to inner products on Rn and spectral theorem for symmetric matrices.

Prerequisite: Completion of MATH 150B with a grade of “C” or better. Recommended Corequisite or Preparatory: MATH 250. First order equations. Explicit solution methods, existence and uniqueness for initial value problems. Higher order linear equations. Undetermined coefficients and variation of parameters. Laplace transforms and transform solution methods. Linear first-order systems. Emphasis on engineering applications. Not …

Prerequisite: Completion of MATH 210 with a grade of “C” or better. Second course for students intending to teach in elementary or junior high school. Geometry as a system; congruence and similarity through construction with straightedge and compass; transformational geometry; the nature of measurement, precision and accuracy. Not available for credit toward the major or …

Recommended Corequisite or Preparatory: MATH 310. Problem solving using models and simulation in mathematics appropriate for the elementary-school classroom. 2 hours of activities per week. (Credit/No Credit only)

Prerequisites: Completion of MATH 210 and MATH 310 with grades of “C” or better, or instructor consent. Topics selected from: abstract algebra and applied algebra using elementary mathematical models. Not available for credit toward the Mathematics major or minor.

Prerequisite: Completion of MATH 150B with a grade of “C” or better. The goal of this course is to help students transition from a primarily computational mode of doing mathematics to a more conceptual mode. The emphasis will be on proofs, which are taught in the context of elementary number theory, combinatorics and analysis; the …

Prerequisites: ECE 320 or PHIL 230; Completion of MATH 150B with a grade of “C” or better. Propositional calculus, predicate calculus, set algebra, relations, functions, mappings, fields and number systems.

Prerequisites: Multiple Measures Placement in GE-level Mathematics, or credit in MATH 093 or MATH 196QR or MATH 196S. Completion of the lower division writing requirement; Upper division standing. A course designed to give students an appreciation of the diversity of mathematics and the spirit in which it is employed in various applications. The character and …

Prerequisite: Completion of MATH 150B with a grade of “C” or better. Sample spaces, probability rules, independence, conditional probability, Bayes Theorem, discrete random variables (binomial, Poisson, geometric, negative binomial), continuous random variables (normal, gamma, exponential, uniform), expectations, moment generating functions, joint, conditional and marginal distributions and conditional expectations, linear combinations of random variables, sampling distributions, …

Prerequisites: Completion of MATH 250 and MATH 262 with a grade of “C” or better. Not open to students who have credit for MATH 280. First-order equations and explicit solution methods. The Picard-Lindelöf existence and uniqueness theorem. Higher order linear equations. Undetermined coefficients and variation of parameters. Power series solutions. Linear systems and eigenvector methods. Linearization …

Prerequisites: Completion of MATH 262 and MATH 320 with a grade of “C” or better. Survey course in abstract algebra. Introduction to groups, rings, fields and vector spaces.

Corequisite: MATH 320 or MATH 326. This is a one-semester introduction to combinatorics. Topics include enumerative combinatorics (inclusion-exclusion, generating functions, Polya’s Theorem, etc.) and combinatorial structures (graphs, designs, etc.).

Prerequisite or Corequisite: MATH 320. One of the goals of this course is to help students write rigorous proofs of results of plane Euclidean geometry. It is also expected that students visualize and develop geometric intuition through the use of dynamic geometry software. The content includes history, axiomatic structure and theorems of plane Euclidean geometry, …

Corequisite: MATH 262. This course gives students an introduction to basic numerical techniques and to programming using some of the common software packages used in mathematics. Students apply these techniques in projects from different branches of mathematics. (This course does not replace a rigorous course in numerical analysis.) 2 hours lecture, 2 hours lab.

Prerequisites: Multiple Subject Candidates—MATH 210 and MATH 310 or corequisite with MATH 310. Single Subject Candidates—MATH 150A, MATH 150B; Junior standing. Field experience course designed to give the prospective teacher an appreciation of a quality mathematics program in public schools. Requirements include 45 hours of participation in an assigned school and regular group meetings to discuss …

Prerequisites: Completion of MATH 262 and MATH 340 with a grade of “C” or better. Point estimation, bias and mean squared error, optimality theory for estimates, maximum likelihood estimation, confidence intervals, test of hypotheses, power, and optimality theory for tests. Available for graduate credit.

Prerequisite: Completion of MATH 440A with a grade of “C” or better. Chi-square goodness of fit tests, simple and multiple linear regression, 1- and 2-way analysis of variance, and statistical analysis using the computer. Available for graduate credit.

Prerequisite: Completion of MATH 340 with a grade of “C” or better, or MATH 440A with a grade of “C” or better. Topics selected from statistics and/or probability, such as nonparametric statistics, multivariate statistics, experimental design, decision theory and advanced probability theory.

Prerequisites: MATH 250, MATH 262, and MATH 340 all with grades of “C” or better. This course focuses on more advanced but essential topics in probability theory and stochastic processes. Topics include joint probability distributions, functions of random variables, conditional probabilities, expectations and variances, probability inequalities, stochastic convergence, multivariate normal distribution, quadratic forms, random walks, …

Prerequisite: MATH 340. This course will cover the fundamental concepts of statistical model building, including inference, applied linear regression, multiple regression, prediction and variable selection, nonlinear and nonparametric regression, principal component analysis and factor analysis. Software and coding will be used to apply the theory to examples and real data sets, but no previous coding …

Prerequisite: MATH 444 or MATH 440A or graduate standing with approval from the coordinator/instructor. This course will cover concepts of linear models and prediction models including generalized linear models, supervised and unsupervised learning such as classification techniques and clustering. It also includes missing data techniques and concepts of time-series analysis. Software and coding will be …

Prerequisite: Completion of MATH 320 with a grade of “C” or better. Brief exposure to real numbers including completeness, Bolzano Weierstrass theorem, countability of subsets; continuity and differentiability of real valued functions on the real line; the inverse function theorem on R; integration; the fundamental theorem of calculus; improper Riemann integration; infinite series; uniform convergence; …

Prerequisite: Completion of MATH 450A with a grade of “C” or better. Topics include topology on R^n, continuity and differentiability of functions from domains in R^m to R^n, Taylor’s formula, the inverse and implicit function theorems, integration of functions on Jordan regions, iterated integrals, the change of variables theorem, curves and surfaces in R^n, and …

Prerequisite: Completion of MATH 450A with a grade of “C” or better. Complex numbers, analytic functions, complex integration, Cauchy’s Theorem, power series, calculus of residues and conformal mappings. Available for graduate credit.

Prerequisite: Completion of MATH 360 with a grade of “C” or better. Second course in abstract algebra. Group theory, rings and modules, and field extensions. Available for graduate credit.

Prerequisites: Completion of MATH 262 and MATH 320 with a grade of “C” or better. Recommended Corequisite or Preparatory: MATH 360. This course covers vector spaces and linear transformations from a more theoretical perspective than that covered in MATH 262. The course begins with a review of abstract vector spaces, including the invariance of dimension …

Prerequisite: Completion of MATH 320 with a grade of “C” or better. Recommended Corequisite or Preparatory: MATH 360. Euclidean algorithm and the unique factorization theorem, congruences, primitive roots and indices, quadratic residues and the law of quadratic reciprocity, and distribution of primes. Available for graduate credit.

Prerequisite: Completion of MATH 351 with a grade of “C” or better, or MATH 280 with a grade of “C” or better. Orthogonal functions, Laplace’s equation, Poisson’s equation, Bessel’s equation, self-adjoint operators, Sturm-Liouville theory, Fourier series, separation of variables applied to the heat equation and wave equation, nonhomogeneous problems, Green’s functions for time-independent problems, and …

Prerequisites: COMP 110/L; Completion of MATH 262 with a grade of “C” or better. Techniques of applied mathematics, solution of equations, interpolation, numerical integration and numerical solution of differential equations. Available for graduate credit.

Prerequisites: Completion of MATH 150B and MATH 262 with a grade of “C” or better; Some computer programming experience. Computer-oriented study of seminumerical and non-numerical algorithms. Sorting, tree searching, generation of combinatorial structures, algorithm proof techniques, best algorithms and programming complexity. Available for graduate credit.

Prerequisites: MATH 340 with a grade of “C” or better, and MATH 351 with a grade of “C” or better, or graduate standing. Applications of mathematical techniques to solve selected problems in ecology, biology, economics, finance, social sciences, life sciences, physical sciences and engineering. Models discussed include deterministic, stochastic, optimization, static, and dynamic ones. Emphasis …

Prerequisite: Senior standing. A course where prospective teachers see high-school level mathematics from a more advanced perspective, where there is considerably more emphasis on issues of pedagogy than in other content courses, and where students will see connections between the mathematics they have learned and some of the activities that they will themselves be engaged …

Prerequisite: Junior standing in the major. Students will study current topics in mathematical and/or statistical literature and will prepare written summaries and give oral presentations to the class. Students will be active participants in all seminars by asking questions and providing written critiques and summaries of the presentations of other students.

Prerequisite: Junior standing in the major. Students will gain practical experience in the profession by either participating in an internship doing mathematical/statistical work at an outside organization or by doing directed research within the department. All students are expected to work a minimum of 8 hours per week on this assignment and meet with the …

Prerequisites: Senior standing and instructor consent.

See Independent Study under courses of study.

Prerequisite: MATH 450A. Metric spaces, topological spaces, compactness, completeness and connectedness. Introduction to function spaces, with emphasis on the uniform topology.

Prerequisite: MATH 440A. General linear model in matrix form, simple and multiple regression analysis, transformations, variable selection, multicollinearity, analysis of variance, robust regression, logistic regression, principal components and factor analysis. Statistical software utilized.

Prerequisites: MATH 340, MATH 450A and MATH 462. Hogg-Craig Theorem, Cochran Theorem, convergence in probability and distribution, Cramer-Wold Theorem, Continuous Mapping Theorem, Weak-Law-of-Large-Numbers, Lindberg-Feller Central Limit Theorem (CLT), Lyapunov CLT, Regular Exponential families, Neyman-Factorization Criterion, the substitution principle, asymptotic relative efficiency, the method of the moments, the MLE and its asymptotic efficiency, Uniformly Minimum Variance …

Prerequisite: MATH 440A or MATH 541. One, two and K sample location methods, the histogram estimator, kernel density estimation, the choice of the smoothing parameter, other density estimators: orthogonal basis, penalized maximum likelihood, nonparametric regression: Nadaraya-Watson, choice of smoothing parameter, k-nn, splines, bootstrap.

Prerequisite: MATH 440A or MATH 541. Multivariate normal distribution, multivariate data analysis, inference about a mean vector including Hotelling’s T2 and the likelihood ratio statistic, Wishart distribution, MANOVA, classification and discriminant analysis, principal components, factor analysis, canonical correlation, multidimensional scaling. Applications and use of statistical software.

Prerequisite: MATH 340. Markov chains, first step analysis, recurrent and transient states, stationary and limiting distributions, random walks, branching processes, Poisson and birth and death processes, renewal theory, martingales, introduction to Brownian motion and related Gaussian processes.

Prerequisite: MATH 552. Operations on sets and events, sigma algebras, probability measures, Lebesgue measure, measurable maps and random variables, independence, Borel-Cantelli lemmas, zero-one laws, integration with respect to a probability measure, convergence theorems for integral, product spaces, and Fubini’s theorem. Laws of large numbers, convergence in distribution, and the central limit theorem.

Prerequisite: MATH 440A or MATH 541. Time series, stationary and nonstationary time series models, seasonal and nonseasonal time series models, trends, ARIMA (Box-Jenkins) models, smoothing methods, estimation, diagnostic checking, forecasting techniques, spectral domain, periodogram, filtering, spectral density.

Prerequisite: MATH 440A or MATH 541. Inference and measures of association for categorical data, generalized linear model, logistic and Poisson regression, logit, probit and loglinear models, analysis of matched pairs.

Prerequisite: MATH 440A or MATH 541. Methods for generating random variables, Monte Carlo methods, Monte Carlo Integration and variance reduction, bootstrap and jackknife, optimization and solving nonlinear equations, EM algorithms, Fisher scoring method, and Markov Chain Monte Carlo methods.

Prerequisite: MATH 440A or MATH 541 or consent of instructor. This series will cover topics in probability and statistics not covered elsewhere in the program, as chosen by individual instructors. Up to two different courses within this series may be taken for credit. Course Title MATH 549A Bayesian Statistics MATH 549B Linear Models MATH 549C …

Prerequisites: MATH 450B and MATH 501. Differentiable forms and exterior derivatives on R^n; line integrals on R^n; differentiable manifolds and differentiable forms; Stokes’ theorem and applications; additional topics as time permits.

Prerequisite: MATH 501. Introduction to measure theory and Lebesgue integration, and their application to probability theory. Monotone and dominated convergence theorems, Fubini’s theorem, Fourier analysis and Banach spaces.

Prerequisite: MATH 460. Graduate course in abstract algebra. Group theory, Galois theory and other topics.

Prerequisite: MATH 450B. The local theory of regular curves in R3 and Frenet formulas. Regular surfaces in R3, the first and second fundamental forms, Gaussian and mean curvatures, and the Egregium Gauss theorem. Geodesics and the Gauss-Bonnet theorem.

Prerequisite: MATH 462. Methods for solving large linear problems and eigenvalue problems are presented at an advanced level. Direct methods such as LU factorization, Cholesky factorization and the Least Squares method, and Iterative methods, such as the Jacobi, Gauss-Seidel, SOR and conjugate Gradient methods, are discussed in detail. Eigenvalue problems are solved via power iteration, …

Prerequisite: MATH 581 or consent of instructor. The course will cover topics in numerical analysis which are important in many applications and which are not covered elsewhere in the program. Part A usually covers numerical methods in optimization, Part B covers numerical methods for ordinary differential equations, and Part C covers numerical solution of partial …

Prerequisite: Senior or graduate standing in the Mathematics Department. Students will read about advanced topics in the recent literature in Mathematics and report on them in a lecture. This course may be taken up to two times with the consent of the advisor. (Credit/No Credit only)

Prerequisite: MATH 552 or consent of instructor. This course is devoted to a variety of important topics in applied mathematics that are not covered elsewhere in the program. In particular, Part A will cover the mathematical theory of partial differential equations, Part B covers mathematical optimization and operations research, and Part C covers mathematical biology.

Prerequisite: Consent of instructor. Specialized topics from a concentrated field of current interest presented at an advanced level.

Selected problems in ecology, biology, economics, finance, social sciences, life sciences, physical sciences and engineering are used to develop advanced techniques of mathematical modeling.

Prerequisite: Consent of instructor. Advanced topics not covered in the previous classes on the subject. Part A covers topics in analysis, Part B covers topics in geometry, and Part C covers topics in topology. May be repeated with the consent of the advisor.

Prerequisites: MATH 501, MATH 455. Topics covered include the general Cauchy theorem, power series and analytic continuation, series and product expansions, conformal mapping and the Dirichlet problem.

Prerequisite: Consent of instructor. Advanced topics not covered in the previous classes on the subject. Part A covers topics in algebra, Part B covers topics in number theory, and Part C covers other topics in discrete mathematics. May be repeated with the consent of the advisor.

Prerequisite: MATH 560 or consent of instructor. Topics covered include modules, localization, integral dependence, chain conditions (Noetherian and Artinian), discrete valuation rings (DVRs) and Dedekind domains.

Prerequisites: MATH 501, MATH 552. This two-semester sequence gives an introduction to Banach and Hilbert spaces and their applications. Fixed Point Theorems and their applications to differential and integral equations and variational principles. Adjoint and self-adjoint operators and spectral theory of linear operators. MATH 680A is a prerequisite for MATH 680B.

Directed Comprehensive Studies

Thesis or Graduate Project

See Independent Study under courses of study.

The Department of Mathematics is dedicated to teaching and research. Our mission is to provide an exciting place for our undergraduate and graduate students to learn and do research in mathematical sciences. The department prepares students for a wide range of career paths, ranging from academia, the insurance industry, engineering, climatology, medicine, law and business. …

Mathematicians today are engaged in a wide variety of activities. Research mathematicians create new theories and techniques. Applied mathematicians use that theory and mathematical modeling to solve problems in economics, science, medicine, engineering, and management. Teachers of mathematics develop new ways to teach mathematical concepts to children and adults. University-level mathematics involves more than algorithms …

The Secondary Teaching option provides preparation for students planning to teach mathematics at the secondary level. Students in this option may enroll in a postbaccalaureate teacher preparation program to earn a Preliminary Single Subject Credential in Mathematics. Alternatively, students who meet the eligibility requirements can enter either the Four-Year Integrated Mathematics (FYI-Math) Teacher Credential Program …

The B.S. degree in Mathematics is designed for students who want to pursue occupational careers involving mathematics or want to prepare for graduate work in mathematics. Double Major Students pursuing either a B.A. or a B.S. degree may combine a second major with Mathematics. In this circumstance, upon approval of an advisor, 6 units of …

The B.S. degree in Mathematics is designed for students who want to pursue occupational careers involving statistics or want to prepare for graduate work in statistics. Double Major Students pursuing either a B.A. or a B.S. degree may combine a second major with Mathematics. In this circumstance, upon approval of an advisor, 6 units of …

The B.S. degree in Mathematics is designed for students who want to pursue occupational careers involving applied mathematics or want to prepare for graduate work in applied mathematics. Double Major Students pursuing either a B.A. or a B.S. degree may combine a second major with Mathematics. In this circumstance, upon approval of an advisor, 6 …

The minor in Mathematics is designed to provide students with mathematical preparation useful for future employment opportunities.

The Department of Mathematics offers a Master of Science degree with three options: Pure Mathematics (Option I), Applied Mathematics (Option II), and Statistics (Option III). Each of the options prepares a student for further graduate work; for higher mathematical work in industry, business and government; and for teaching at community colleges. Option I is primarily …

The Four-Year Integrated Mathematics (FYI-Math) teacher credential program is designed for students who are certain about their career choice. For admission, students must be eligible for a course in Basic Skills Written Communication and for MATH 150A, and they should see a teacher preparation or credential advisor in the Department of Mathematics. Upon entering the program …

The Junior-Year Integrated Mathematics (JYI-Math) teacher credential program begins in the junior year for students who apply and have been accepted to the program. JYI-Math integrates undergraduate subject-matter knowledge with teacher education content and leads to both a B.A. degree in Mathematics and a Preliminary Single Subject Credential in Mathematics. For admission, students must be …

The Department of Mathematics offers a Master of Science degree with three options: Pure Mathematics (Option I), Applied Mathematics (Option II), and Statistics (Option III). Each of the options prepares a student for further graduate work; for higher mathematical work in industry, business and government; and for teaching at community colleges. Option II emphasizes Applied …

The Department of Mathematics offers a Master of Science degree with three options: Pure Mathematics (Option I), Applied Mathematics (Option II), and Statistics (Option III). Each of the options prepares a student for further graduate work; for higher mathematical work in industry, business and government; and for teaching at community colleges. Option III is primarily designed …

The Mathematics Subject Matter Program for the Single Subject Credential consists of 60 units.

This ADT/STAR Act Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.A./General Option 2024 Mathematics, B.A./General Option 2025 Mathematics, B.A./General Option All lower division GE completed. Lower division major requirements of Calculus I, Calculus II, and Calculus III (MATH 150A, MATH 150B, MATH 250) completed as part of the AS-T in Mathematics. …

This 4-Year Degree Road Map applies to the following catalog year(s): 2021 Mathematics, B.A./Four-Year Integrated (FYI) Mathematics Subject Matter Program for the Single Subject Credential Option 2022 Mathematics, B.A./Four-Year Integrated (FYI) Mathematics Subject Matter Program for the Single Subject Credential Option Degree Road Maps are based on successful completion of prerequisites or placement into major …

This 4-Year Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.A./Four-Year Integrated (FYI) Mathematics Subject Matter Program for the Single Subject Credential Option 2024 Mathematics, B.A./Four-Year Integrated (FYI) Mathematics Subject Matter Program for the Single Subject Credential Option Degree Road Maps are based on successful completion of prerequisites or placement into major …

This 4-Year Degree Road Map applies to the following catalog year(s): 2025 Mathematics, B.A./Four-Year Integrated (FYI) Mathematics Subject Matter Program for the Single Subject Credential Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom …

This 4-Year Degree Road Map applies to the following catalog year(s): 2021 Mathematics, B.A./General Option 2022 Mathematics, B.A./General Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report Plan. Refer to the …

This 4-Year Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.A./General Option 2024 Mathematics, B.A./General Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report Plan. Refer to the …

This 4-Year Degree Road Map applies to the following catalog year(s): 2025 Mathematics, B.A./General Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report Plan. YEAR 1: 1st Semester Course Units MATH …

This Transfer Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.A./Junior-Year Integrated (JYI) Mathematics Subject Matter Program for the Single Subject Credential Option 2024 Mathematics, B.A./Junior-Year Integrated (JYI) Mathematics Subject Matter Program for the Single Subject Credential Option 2025 Mathematics, B.A./Junior-Year Integrated (JYI) Mathematics Subject Matter Program for the Single Subject Credential …

This ADT/STAR Act Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.A./Secondary Teaching Option 2024 Mathematics, B.A./Secondary Teaching Option All lower division GE completed. Lower division major requirements of Calculus I, Calculus II, and Calculus III (MATH 150A, MATH 150B, MATH 250) completed as part of the AS-T in Mathematics. Refer to …

This ADT/STAR Act Degree Road Map applies to the following catalog year(s): 2025 Mathematics, B.A./Secondary Teaching Option All lower division GE completed. Lower division major requirements of Calculus I, Calculus II, and Calculus III (MATH 150A, MATH 150B, MATH 250) completed as part of the AS-T in Mathematics. Refer to the Catalog Archives for General Education requirements. Transfer …

This 4-Year Degree Road Map applies to the following catalog year(s): 2021 Mathematics, B.A./Secondary Teaching Option 2022 Mathematics, B.A./Secondary Teaching Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report Plan. Refer …

This Transfer Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.A./Secondary Teaching Option 2024 Mathematics, B.A./Secondary Teaching Option The Transfer Degree Road Map on this page presumes the completion of lower division General Education, Title 5 (United States History and Government), and lower division core requirements for this major. See General Education …

This Transfer Degree Road Map applies to the following catalog year(s): 2025 Mathematics, B.A./Secondary Teaching Option The Transfer Degree Road Map on this page presumes the completion of lower division General Education, Title 5 (United States History and Government), and lower division core requirements for this major. See General Education Rules for more information. Lower …

This Transfer Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.A./General Option 2024 Mathematics, B.A./General Option 2025 Mathematics, B.A./General Option The Transfer Degree Road Map on this page presumes the completion of lower division General Education, Title 5 (United States History and Government), and lower division core requirements for this major. See …

This 4-Year Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.A./Secondary Teaching Option 2024 Mathematics, B.A./Secondary Teaching Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report Plan. Refer …

This 4-Year Degree Road Map applies to the following catalog year(s): 2025 Mathematics, B.A./Secondary Teaching Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report Plan. YEAR 1: 1st Semester Course Units …

This ADT/STAR Act Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.S./Applied Mathematical Sciences Option 2024 Mathematics, B.S./Applied Mathematical Sciences Option 2025 Mathematics, B.S./Applied Mathematical Sciences Option All lower division GE completed. Lower division major requirements of Calculus I, Calculus II, and Calculus III (MATH 150A, MATH 150B, MATH 250) completed as …

This 4-Year Degree Road Map applies to the following catalog year(s): 2021 Mathematics, B.S./Applied Mathematical Sciences Option 2022 Mathematics, B.S./Applied Mathematical Sciences Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report …

This Transfer Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.S./Applied Mathematical Sciences Option 2024 Mathematics, B.S./Applied Mathematical Sciences Option 2025 Mathematics, B.S./Applied Mathematical Sciences Option The Transfer Degree Road Map on this page presumes the completion of lower division General Education, Title 5 (United States History and Government), and lower division …

This ADT/STAR Act Degree Road Map applies to the following catalog years: 2023 Mathematics, B.S./Mathematics Option 2024 Mathematics, B.S./Mathematics Option 2025 Mathematics, B.S./Mathematics Option All lower division GE completed. Lower division major requirements of Calculus I, Calculus II, and Calculus III (MATH 150A, MATH 150B, MATH 250) completed as part of the AS-T in Mathematics. …

This 4-Year Degree Road Map applies to the following catalog year(s): 2021 Mathematics, B.S./Mathematics Option 2022 Mathematics, B.S./Mathematics Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report Plan. Refer to the …

This 4-Year Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.S./Mathematics Option 2024 Mathematics, B.S./Mathematics Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report Plan. Refer to the …

This Transfer Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.S./Mathematics Option 2024 Mathematics, B.S./Mathematics Option 2025 Mathematics, B.S./Mathematics Option The Transfer Degree Road Map on this page presumes the completion of lower division General Education, Title 5 (United States History and Government), and lower division core requirements for this major. See …

This 4-Year Degree Road Map applies to the following catalog year(s): 2025 Mathematics, B.S./Mathematics Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report Plan. YEAR 1: 1st Semester Course Units MATH …

This ADT/STAR Act Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.S./Statistics Option 2024 Mathematics, B.S./Statistics Option 2025 Mathematics, B.S./Statistics Option All lower division GE completed. Lower division major requirements of Calculus I, Calculus II, and Calculus III (MATH 150A, MATH 150B, MATH 250) completed as part of the AS-T in Mathematics. …

This 4-Year Degree Road Map applies to the following catalog year(s): 2021 Mathematics, B.S./Statistics Option 2022 Mathematics, B.S./Statistics Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report Plan. Refer to the …

This Transfer Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.S./Statistics Option 2024 Mathematics, B.S./Statistics Option 2025 Mathematics, B.S./Statistics Option The Transfer Degree Road Map on this page presumes the completion of lower division General Education, Title 5 (United States History and Government), and lower division core requirements for this major. See …

This 4-Year Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.S./Applied Mathematical Sciences Option 2024 Mathematics, B.S./Applied Mathematical Sciences Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report …

This 4-Year Degree Road Map applies to the following catalog year(s): 2025 Mathematics, B.S./Applied Mathematical Sciences Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report Plan. YEAR 1: 1st Semester Course …

This 4-Year Degree Road Map applies to the following catalog year(s): 2023 Mathematics, B.S./Statistics Option 2024 Mathematics, B.S./Statistics Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report Plan. Refer to the …

This 4-Year Degree Road Map applies to the following catalog year(s): 2025 Mathematics, B.S./Statistics Option Degree Road Maps are based on successful completion of prerequisites or placement into major required (or major specific) math courses. Please meet with an advisor to develop a custom Degree Progress Report Plan. YEAR 1: 1st Semester Course Units MATH …

(2012) Professor of Mathematics. B.S. 1990, M.S. 1991, Ph.D. 1995, University of Toronto.

(1995) Professor of Mathematics. Diploma 1984, Universität Erlangen; Ph.D. 1989, University of Southern California.

(1990) Professor Emeritus of Mathematics. B.A. 1975, M.A. 1977, Ph.D. 1983, University of Campinas Brazil.

(1961) Professor Emeritus of Mathematics. B.A. 1956, Cornell University; M.A. 1958, University of Pennsylvania.

(2022) Assistant Professor of Mathematics. B.S. 2006, Bahounar University of Kerman; M.B.A. 2011, Multimedia University; Ph.D. 2018, University of Pittsburgh.

(2007) Associate Professor of Mathematics. M.S. 1994, St. Petersburg State University; Ph.D. 2000, Chalmers University of Technology.

(1994) Professor of Mathematics. B.S. 1974, Technical University, Warsaw; M.S. 1976, Warsaw University; Ph.D. 1981, Virginia Polytechnic Institute and State University.

(1970) Professor Emeritus of Mathematics. B.S. 1964, Brown University; Ph.D. 1970, University of Wisconsin.

(1984) Professor Emeritus of Mathematics. B.S. 1977, Brooklyn College; M.A. 1982, Ph.D. 1982, University of Massachusetts.

(1984) Professor Emeritus of Mathematics. B.S. 1977, Brooklyn College; M.A. 1982, Ph.D. 1982, University of Massachusetts.

(1963) Professor Emeritus of Mathematics. B.S. 1956, College of the City of New York; M.S. 1962, New York University; Ph.D. 1969, University of California, Los Angeles.

(1970) Professor Emeritus of Management Science and Professor Emeritus of Mathematics. B.A. 1951, Reed College; M.S. 1954, University of Washington; Ph.D. 1960, University of California, Los Angeles.

(1985) Professor Emeritus of Mathematics. B.A. 1972, M.A. 1974, University of California, San Diego; Ph.D. 1979, University of California, Berkeley.

(1991) Professor Emeritus of Mathematics. B.Tech. 1980, Indian Institute of Technology, Madras; M.S. 1983, Ph.D. 1991, University of California, San Diego.

(2016) Professor of Mathematics. B.S. 2001, M.Sc. 2004, Jordan University of Science and Technology; Ph.D. 2011, University of Alabama at Birmingham.

(1992) Professor of Mathematics. B.A. 1981, M.A. 1985, Ph.D. 1989, University of California, Los Angeles.

(1965) Professor Emeritus of Mathematics. B.S. 1955, M.S. 1957, Oklahoma State University; M.S. 1959, University of Chicago; Ph.D. 1978, University of California, Los Angeles.

(2000) Associate Professor of Mathematics. B.S. 1994, University of Tennessee; M.A. 1997, Ph.D. 1999, University of California, Los Angeles.

(2002) Department Chair of Mathematics; Professor of Mathematics. B.S. 1989, Mount Holyoke College; Ph.D. 1994, University of Pennsylvania.

(2013) Professor of Mathematics. M.S. 1997, Eötvös Loránd University; DEA Math. 1998, Université de la Méditerranée; Ph.D. 2002, Swiss Federal Institute of Technology.

(1971) Professor Emeritus of Mathematics. B.A. 1954, M.A. 1955, Andhra University; M.A. 1969, Ph.D. 1971, University of California, Santa Barbara.

(1990) Professor Emeritus of Mathematics. B.A. 1983, University of California, Berkeley; M.A. 1985, Ph.D. 1990, University of California, Davis.

(1990) Professor Emeritus of Mathematics. B.A. 1970, M.S. 1972, California State University, Northridge; Ph.D. 1977, University of California, Los Angeles.

(1969) Professor Emeritus of Mathematics. B.A. 1964, M.A. 1968, Ph.D. 1969, University of California, Santa Barbara.

(2011) Professor of Mathematics. B.S. 1990, M.S. 1992, Ph.D. 1998, University of Yaounde.

(2018) Associate Professor of Mathematics. B.S. 2006, M.S. 2008, State University of Campinas; Ph.D. 2012, The Pennsylvania State University.

(1973) Professor Emeritus of Mathematics. B.A. 1963, M.S. 1966, Ph.D. 1969, University of California, Los Angeles.