**MATH Information | MATH Programs | MATH Courses**

**Mathematics Courses (MATH)**

Satisfying the Entry-Level Math (ELM) requirement (see “Undergraduate Programs” section of this Catalog) is a prerequisite for all mathematics courses and mathematics education courses except MATH 1 and 10. Please contact the ELM Coordinator in the Department of Mathematics and Statistics for details regarding the ELM test score.

**1. Elementary Algebra and Geometry (3)**

Prerequisite: Appropriate ELM score.

Arithmetic review, elementary algebra, and some basic geometry concepts.

Cannot be taken for credit toward a university degree. Credit/No Credit grading only. Not open for credit to students who are exempt from the ELM or who have not yet taken the ELM but are required to do so. (Lecture 3 hrs.)

**10. Intermediate Algebra (3)
**Prerequisite: Appropriate ELM score.

Polynomial, rational, and radical expressions and equations; rational exponents; solutions and graphs of linear, quadratic, and rational inequalities; systems of linear equations; operations, inverses, and graphs of functions; logarithmic and exponential functions and their applications.

Cannot be taken for credit toward a university degree. Credit/No Credit grading only. Not open for credit to students who have credit in MATH 10E are exempt from the ELM or who have not yet taken the ELM but are required to do so.

(Lecture 3 hrs.)

**10E. Intermediate Algebra (3)
**Prerequisite: Appropriate ELM score. Polynomial, rational, and radical expressions and equations; rational exponents; solutions and graphs of linear, quadratic, and rational inequalities; systems of linear equations; operations, inverses, and graphs of functions; logarithmic and exponential functions and their applications.

Cannot be taken for credit toward a university degree. Credit/No Credit grading only. Not open to students who have credit in MATH 10, are exempt from the ELM or have not yet taken the ELM but are required to do so. (Lecture 2 hrs, activity 2 hrs)

**101. Trigonometry (3)
**Prerequisites: MATH 10 or equivalent.

Trigonometric functions and applications. Complex numbers.

Not open for credit to students with credit in MATH 117 or 122. (Lecture 3 hrs.) (CAN MATH 8)

**103. Mathematical Ideas (3)
**Prerequisites: Three years of high school mathematics, or the equivalent.

Surveys variety of concepts in undergraduate mathematics. Includes elementary logic, numeration systems, rational and real numbers, modular number systems, elementary combinatorics, probability and statistics, using real world examples.

Not open for credit to students with credit in any MATH course numbered greater than 103, or the equivalent. (Lecture 3 hrs.) (CAN MATH 2)

**112. College Algebra (3)
**Prerequisites: Three years of high school mathematics or equivalent.

Linear and quadratic equations and systems: matrices and determinants; theory of equations; polynomial, exponential and logarithmic functions and their graphs; permutations and probability.

Designed for students majoring in a life or social science.

Not open for credit to students with credit in MATH 115, 117, 119A, 120, or 122. (Lecture 3 hrs.)

**114. Finite Mathematics (3)
**Prerequisites: Three years of high school mathematics including algebra, geometry, and intermediate algebra (or MATH 10), or the equivalent.

Combinatorial techniques and introduction to probability. Equations of lines and systems of linear equations, matrices, introduction to linear programming.

Not open for credit to students with credit in MATH 233 or 380. (Lecture 3 hrs.) (CAN MATH 12)

**115. Calculus for Business (3)
**Prerequisites: Three years of high school mathematics including algebra, geometry, and intermediate algebra (or MATH 10), or the equivalent.

Functions, derivatives, optimization problems, graphs, partial derivatives. Lagrange multipliers, integration of functions of one variable. Applications to business and economics. Emphasis on problem-solving techniques.

Not open for credit to students with credit in MATH 119A, 120 or 122. (CAN MATH 34) (Lecture 3 hrs.)

**117. Precalculus Mathematics (4)
**Prerequisites: Three and one half years of high school mathematics including algebra, geometry, and intermediate algebra (or MATH 10) and one half year of trigonometry (or MATH 101), or the equivalent.

Polynomial, rational, exponential, logarithmic, and trigonometric functions. Complex numbers, conic sections, graphing techniques.

Not open for credit to students with credit in MATH 122. (CAN MATH 16)(Lecture 3 hrs., problem session 2 hrs.)

**119A. Survey of Calculus I (3)
**Prerequisties: A grade of “C” or better in MATH 112 or MATH 117, or appropriate MDPT placement.

Functions, limits and continuity, differentiation and integration of functions of one variable including exponential, logarithmic, and trigonometric functions. Graphing, optimization, parametric equations, integration by substitution and by parts, numerical integration. Applications to the life sciences. Emphasis on problem solving.

Not open for credit to students with credit in MATH 115, 120 or 122. (CAN MATH 30) (Lecture 3 hrs.)

**119B. Survey of Calculus II (3)
**Prerequisites: MATH 119A or 122.

Functions of several variable, partial derivatives, optimization. First order differential equations, second order linear homogeneous differential equations, systems of differential equations. Probability, random variables, difference equations. Introduces matrices, Gaussian elimination, determinants. Life science applications. Emphasis on problem solving.

Not open for credit to students with credit in MATH 123 or 224. (CAN MATH 32) (Lecture 3 hrs.)

**120. Calculus for Technology (4)
**Prerequisites: Three and one-half years of high school mathematics including one year of geometry, two years of algebra, and one semester of trigonometry, or the equivalent.

Real and complex numbers and functions; limits and continuity; differentiation and integration of functions of one variable. Introduces calculus of several variables. Science and technology applications.

Not open for credit to students with credit in MATH 122. (Lecture 3 hrs., problem session 2 hrs.)

**122. Calculus I (4)
**Prerequisties: A grade of “C” or better in MATH 117 or High School Trigonometry, or appropriate MDPT placement.

Continuous functions. Derivatives and applications including graphing, related rates, and optimization. Transcendental functions. L’Hospital’s Rule. Antiderivatives. Definite integrals. Area under a curve.

(Lecture 3 hrs., problem session 2 hrs.) (CAN MATH 18)

**123. Calculus II (4)
**Prerequisite: A grade of “C” or better in MATH 122.

Applications of the integral. Techniques of integration. Infinite series including convergence tests and Taylor series. Parametric equations. Polar coordinates. Introduces differential equations.

Not open for credit to students with credit in MATH 222. (CAN MATH 20) (Lecture 3 hrs., problem session 2 hrs.)

**180. Statistics for Everyday Life (3)
**Prerequisites: Three years of high school mathematics including algebra, geometry, and intermediate algebra (or MATH 10), or the equivalent.

Exploratory data analysis, methods of visualizing data, descriptive statistics, misuse and manipulation of data in statistical analysis, probability, binomial and normal distributions, hypothesis testing, correlation and regression, contingency tables.

(Lecture 3 hrs.) (CAN STAT 2)

**222. Intermediate Calculus (4)
**Prerequisite: A grade of “C” or better in MATH 122.

Integration by parts and by partial fractions. Numerical integration. Improper integrals. Infinite series including series convergence tests and Taylor series. Vectors. Partial derivatives and directional derivatives. Double integrals. Introduces differential equations.

Enrollment restricted to CECS majors. Not open for credit to students with credit in MATH 123. Letter grade only (A-F). (Lecture 3 hrs., activity 2 hrs.)

**224. Calculus III (4)
**Prerequisite: A grade of “C” or better in MATH 123 or 222.

Vectors and three-dimensional analytic geometry. Partial derivatives and Lagrange multipliers. Multiple integrals. Vector calculus, line and surface integrals. Green’s Theorem, Stokes’ Theorem and the Divergence Theorem.

(Lecture 3 hrs., problem session 2 hrs. ) (CAN MATH 22)

**233. Fundamental Concepts for Advanced Mathematics (3)
**Prerequisite: A grade of “C” or better in MATH 123 or 222.

Fundamentals of logic and set theory, counting principles, functions and relations, induction and recursion, introduction to probability, elementary number theory, congruences. Introduces writing proofs.

(Lecture 3 hrs.)

**247. Introduction to Linear Algebra (3)
**Prerequisite: MATH 222 or prerequisite or corequisite: MATH 224.

Matrix algebra, solution of systems of equations, determinants, vector spaces including function spaces, inner product spaces, linear transformations, eigenvalues, eigenvectors, quadratic forms, and applications. Emphasis on computational methods.

(Lecture 3 hrs.) (CAN MATH 26)

**297. Directed Study (1-3)
**Prerequisite: Consent of instructor.

For students who wish to undertake special study, at the lower division level, which is not a part of any regular course, under the direction of a faculty member. Individual investigation, studies or surveys of selected problems.

**UPPER DIVISION**

**310. History of Early Mathematics (3)
**Prerequisite/Corequisite: completion of, or concurrent enrollment in a 200-level mathematics course.

History of mathematics through seventeenth century, including arithmetic, geometry, algebra, and beginnings of calculus. Interconnections with other branches of mathematics. Writing component; strongly recommended students enrolling have completed the G.E. A.1 requirement.

(Lecture 3 hrs.)

**323. Introduction to Numerical Analysis (4)
**Prerequisites: MATH 222 or 224, and a course in computer programming.

Numerical solution of nonlinear equations, systems of linear equations, and ordinary differential equations. Interpolating polynomials, numerical differentiation, and numerical integration. Computer implementation of these methods.

(Lecture-discussion 3 hrs., problem session 2 hrs.)

**341. Number Theory (3)
**Prerequisites: MATH 123 or 222, and at least one of MATH 233, 247, 310; recommended, MATH233 or 247.

Divisibility, congruences, number theoretic functions, Diophantine, equations, primitive roots, continued fractions. Writing proofs.

(Lecture 3 hrs.)

**347. Linear Algebra (3)
**Prerequisites: MATH 233 and 247.

In-depth study of linear transformations, vector spaces, inner product spaces, quadratic forms, similarity and the rational and Jordan canonical forms. Writing proofs.

(Lecture 3 hrs.)

**355. College Geometry (3)**

Prerequisite: MATH 247.

Transformations, motions, similarities, geometric objects, congruent figures, axioms of geometry and additional topics in Euclidean and non-Euclidean geometry. Writing proofs.

(Lecture 3 hrs.)

**361A. Introduction to Mathematical Analysis I (3)
**Prerequisites: MATH 222 or 224, and MATH 233 or 247.

Rigorous study of calculus and its foundations. Structure of the real number system. Sequences and series of numbers. Limits, continuity and differentiability of functions of one real variable. Writing proofs.

(Lecture 3 hrs.)

**361B. Introduction to Mathematical Analysis II (3)**

Prerequisite: MATH 361A.

Riemann integration. Topological properties of the real number line. Sequences of functions. Metric spaces. Introduction to calculus of several variables. Writing proofs.

(Lecture 3 hrs.)

**364A. Ordinary Differential Equations I (3)
**Prerequisites: MATH 222 or 224, and prerequisite or corequisite MATH 247.

First order differential equations; undetermined coefficients and variation of parameters for second and higher order differential equations, series solution of second order linear differential equations; systems of linear differential equations; applications to science and engineering.

(Lecture 3 hrs.)

***364B. Ordinary Differential Equations II (3)**

Prerequisite: MATH 364A or 370A.

Existence-uniqueness theorems; Laplace transforms; difference equations; nonlinear differential equations; stability, Sturm-Liouville theory; applications to science and engineering.

(Lecture 3 hrs.)

**370A. Applied Mathematics I (3)
**Prerequisite: MATH 222 or 224.

First order ordinary differential equations, linear second order ordinary differential equations, numerical solution of initial value problems, Laplace transforms, matrix algebra, eigenvalues, eigenvectors, applications.

Not open for credit to mathematics majors. (Lecture 3 hrs.)

**370B. Applied Mathematics II (3)**

Prerequisite: MATH 370A.

Arithmetic of complex numbers, functions of a complex variable, contour integration, residues, conformal mapping; Fourier series, Fourier transforms; separation of variables for partial differential equations. Applications.

Not open for credit to mathematics majors. (Lecture 3 hrs.)

**380. Probability and Statistics (3)**

Prerequisite: MATH 222 or 224.

Frequency interpretation of probability. Axioms of probability theory. Discrete probability and combinatorics. Random variables. Distribution and density functions. Moment generating functions and moments. Sampling theory and limit theorems.

(Lecture 3 hrs.)

***381. Mathematical Statistics (3)
**Prerequisites: MATH 247 and 380.

Estimation and hypothesis testing. Maximum likelihood and method of moments estimation. Efficiency, unbiasedness, and asymptotic distribution of estimators. Neyman-Pearson Lemma. Goodness-of-fit tests. Correlation and regression. Experimental design and analysis of variance. Nonparametric methods.

(Lecture 3 hrs.)

***382. Random Processes (3)
**Prerequisites: MATH 247 and 380.

Further topics in probability. Markov processes. Renewal theory. Random walks. Queueing theory. Poisson processes. Brownian motion.

(Lecture 3 hrs.)

**410. History of Modern Mathematics (3)
**Prerequisites: MATH 247, 310 and at least three of the following: MATH 233, 341, 355, 361A, 380.

History of mathematics from seventeenth century onward. Development of calculus, analysis, and geometry during this time period. Other topics discussed may include history of probability and statistics, algebra and number theory, logic, and foundations.

(Lecture 3 hrs.)

***423. Intermediate Numerical Analysis (3)**

Prerequisites: MATH 247 and 323.

Numerical solutions of systems of equations, calculation of eigenvalues and eigenvectors, approximation of functions, solution of partial differential equations. Computer implementation of these methods.

(Lecture 3 hrs.)

**444. Introduction to Abstract Algebra (3)
**Prerequisites: MATH 233 and 247 and at least one of MATH 341 or 347.

Groups, subgroups, cyclic groups, symmetric groups, Lagrange’s theorem, quotient groups. Homomorphisms and isomorphisms of groups. Rings, integral domains, ideals, quotient rings, homomorphisms of rings. Fields. Writing proofs.

Not open for credit to students with credit in MATH 444A. (Lecture 3 hrs.)

***451. Differential Geometry (3)
**Prerequisite: MATH 364A or 370A.

Structure of curves and surfaces in space, including Frenet formulas of space curves; frame fields and connection forms; geometry of surfaces in Euclidean three space; Geodesics and connections with general theory of relativity.

(Lecture 3 hrs.)

***461. Introduction to Complex Analysis (3)**

Prerequisite: MATH 361A.

Theory and applications of complex variables. Analytic functions, integrals, power series and applications.

Not open for credit to students with credit in MATH 562A. (Lecture 3 hrs.)

***463. Multivariable Calculus (3)
**Prerequisites: MATH 224, 247, and 361B.

Topology of Euclidean spaces. Partial derivatives. Derivatives as linear transformations. Inverse and implicit function theorems. Jacobians, vector calculus, Green’s and Stokes’ theorems. Variational problems.

(Lecture 3 hrs.)

***470. Introduction to Partial Differential Equations (3)**

Prerequisite: MATH 370A or 364A.

First and second order equations, characteristics, Cauchy problems, elliptic, hyperbolic, and parabolic equations. Introduction to boundary and initial value problems and their applications.

(Lecture 3 hrs.)

***472. Fourier Analysis (3)
**Prerequisite: MATH 364A or 370A.

Theory of Fourier series and Fourier transforms. Physics and Engineering applications. Parseval’s and Plancherel’s identifies. Convolution. Multi-dimensional transforms and partial differential equations. Introduction to distributions. Discrete and fast Fourier transforms.

(Lecture 3 hrs.)

***479. Mathematical Modeling (3)
**Prerequisite: MATH 247; 364A or 370A; 323; and one additional upper-division mathematics course or consent of instructor.

Application of mathematics to develop models of phenomena in science, engineering, business, and other disciplines. Evaluation of benefits and limitations of mathematical modeling.

(Lecture 3 hrs.)

**480./590. Regression Analysis (3)
**Prerequisites: MATH 247, 380; prerequisite or corequisite MATH 381. (Undergraduates enroll in MATH 480; graduates enroll in MATH 590.)

Simple linear regression: estimation and inference, prediction, analysis of residuals, detection of outlier, use of transformations. Multiple linear regression: influence diagnostics, mult-colinearity, selection of variables, simultaneous estimation and inference, validation techniques. Statistical software for data analysis used.

Letter grade only (A-F). (Lecture 3 hrs.)

**483./593. Multivariate Statistical Analysis (3)
**Prerequisites: MATH 381; prerequisite/corequisite MATH 480. (Undergraduates enroll in MATH 483; graduates enroll in MATH 593.)

Discriminate analysis, principal components, factor analysis, cluster analysis, logistic regression, canonical correlation, multidimensional scaling, and some nonlinear techniques. Statistical software used.

Letter grade only (A-F). (Lecture 3 hrs.)

***484. Actuarial Science (3)
**Prerequisites: MATH 381 or consent of instructor.

Statistical techniques applied to risk management. Expected utility theory, individual risk models, compound Poisson distributions and processes, ruin probability and first surplus, stop-loss and proportional reinsurance, statistical survival distributions and life tables, life annuity, actuarial present values, and premiums determination.

Letter grade only (A-F). (Lecture 3 hrs.)

***485. Mathematical Optimization (3)
**Prerequisites: MATH 247 and at least one of MATH 323, 347 or 380.

Linear and nonlinear programming: simplex methods, duality theory, theory of graphs, Kuhn-Tucker theory, gradient methods and dynamic programming.

(Lecture 3 hrs.)

**487./587. Statistical Simulation (3)
**Prerequisite: MATH 381 or consent of instructor. (Undergraduates enroll in MATH 487; graduates enroll in MATH 587.)

Simulation modeling techniques; generation of discrete and continuous random numbers from given distributions; Monte Carlo methods; discrete event simulations, statistical analysis of simulated data; variance reduction; statistical validation; introduces simulation languages; industry applications. Statistical packages used.

Letter grade only (A-F). (Lecture 3 hrs.)

***489. Data Analysis With SAS (3)
**Prerequisite: MATH 381 or consent of instructor.

Topics include: Statistical analysis including extraction, presentation of data in graphical form, creation, modification of datasets, interpretation of output, writing of reports. Provides SAS programming techniques for aforementioned topics as well as prepare for SAS base certification.

(Lecture 3 hrs.)

**491. Honors Seminar in Problem Solving (1)**

Prerequisites: Consent of instructor.

Challenging problems form many fields of mathematics, taken largely from national and worldwide collegiate and secondary school competitions. Students required to participate in at least one national competition.

May be repeated to a maximum of 3 units. (Lecture-discussion 1 hr.)

***495. Topics in Modern Mathematics (3)**

Prerequisite: Consent of instructor.

Topics of current interest from mathematics literature.

**496. Special Problems (1-3)
**Prerequisites: Consent of instructor.

Student investigations in mathematics, applied mathematics, mathematics education, or statistics. May include reports and reviews from the current literature, as well as original investigations.

May be repeated to a maximum of 3 units. Letter grade only (A-F).

**497. Directed Studies (1-3)
**Prerequisites: Junior or senior standing and consent of instructor.

Readings in areas of mutual interest to student and instructor which are not a part of any regular course. A written report or project may be required.

May be repeated to a maximum of 3 units.

**498H. Senior Thesis - Honors (3)
**Prerequisites: Admission to Honors in the Major in Mathematics or to the University Honors Program, and consent of instructor.

Planning, preparation, completion, and oral presentation of a written thesis in mathematics, applied mathematics, mathematics education, or statistics.

Not available to graduate students. Letter grade only (A-F).

**540A. Abstract Algebra I (3) F**

Prerequisite: MATH 444.

Group theory including symmetric groups; group actions on sets; Sylow theorems and finitely generated abelian groups; ring theory including polynomial rings, division rings, Euclidean domains, principal ideal domains and unique factorization domains.

Letter grade only (A-F). (Lecture 3 hrs.)

**540B. Abstract Algebra II (3) S**

Prerequisite: MATH 540A.

Modules; Field extensions; Finite fields; Splitting fields, Galois theory. Commutative ring theory including chain conditions and primary ideals. Topics of current interest.

Letter grade only (A-F). (Lecture 3 hrs.)

**541. Elliptic Curves (3) F
**Prerequisites: MATH 341, 444, and consent of instructor; MATH 540A and 461 are recommended but not required.

Fermat’s method of descent; finite fields; Weierstrass normal form; integers and rational points on elliptic curves; group structures of rational points; Mordell’s Theorem; and computation of examples. May also include congruent numbers, Certicom’s public cryptography challenges, Lenstra’s method of factorization, and the Birch/Swinnerton-Dyer Conjecture

Letter grade only (A-F). (Lecture 3 hrs.)

**550A. Topology I (3) S
**Prerequisite: MATH 361B.

Fundamentals of point-set topology: metric spaces and topological spaces; bases and neighborhoods; continuous functions; subspaces, product spaces and quotient spaces; separation properties, countability properties, compactness, connectedness; convergence of sequences, nets and filters.

Letter grade only (A-F). (Lecture 3 hrs.)

**550B. Topology II (3) F
**Prerequisite: MATH 550A.

Further topics in point-set topology: local compactness, paracompactness, compactifications; metrizability; Baire category theorem; homotopy and the fundamental group. Topics may also include uniform spaces, function spaces, topological groups or topics from algebraic topology.

Letter grade only (A-F). (Lecture 3 hrs.)

**560A. Functional Analysis I (3) F**

Prerequisites: MATH 247, 361B.

Linear spaces, metric and topological spaces, nomed linear spaces; four principles of functional analysis: Hahn-Banach, Open Mapping, Uniform Boundedness, and Closed Graph theorems; adjoint spaces; normed space convergence, conjugate spaces, and operator spaces; Banach Fixed Point theorem; Hilbert spaces.

Letter grade only (A-F). (Lecture 3 hrs.)

**560B. Functional Analysis II (3) S
**Prerequisite: MATH 560A or consent of instructor.

Spectral theory of operators on normed spaces; special operators; elementary theory of Banach algebras; selected topics from applied functional analysis.

(Lecture 3 hrs.)

**561A. Real Analysis I (3) S**

Prerequisite: MATH 361B.

Theory of measure and integration, focusing on the Lebesgue integral on Euclidean space, particular the real line. Modes of convergence. Fatou’s Lemma, the monotone convergence theorem and the dominated convergence theorem. Fubini’s theorem.

Letter grade only (A-F). (Lecture 3 hrs.)

**561B. Real Analysis II (3) F
**Prerequisite: MATH 561A or consent of instructor.

Lp spaces of functions. Holder’s inequality. Minkowski’s inequality. Norm convergence, weak convergence and duality in Lp. Further topics from convergence of Fourier series, measure-theoretic probability, the Radon-Nikodym theorem; other topics depending on time and interest.

Letter grade only (A-F). (Lecture 3 hrs.)

**562A. Complex Analysis I (3) F
**Prerequisite: MATH 361B. (MATH 461 is recommended.)

Axiomatic development of real and complex numbers; elements of point set theory; differentiation and analytic functions, classical integral theorems; Taylor’s series, singularities, Laurent series, calculus of residues.

Letter grade only (A-F). (Lecture 3 hrs.)

**562B. Complex Analysis II (3) S**

Prerequisite: MATH 562A.

Multiple-valued functions, Riemann surfaces; analytic continuation; maximum modulus theorem; conformal mapping with applications, integral functions; gamma function, zeta function, special functions.

Letter grade only (A-F). (Lecture 3 hrs.)

**563 Applied Analysis (3) F
**Prerequisites: MATH 361B.

Hilbert Spaces, Lp spaces, Distributions, Fourier Transforms, and applications to differential and integral equations from physics and engineering.

(Lecture 3 hrs.)

**564. Applied Nonlinear Ordinary Differential Equations (3) F**

Prerequisites: MATH 361B; 364A or 370A.

Stability and asymptotic analysis, Perturbation methods, Phase plane analysis, Bifurcation, Chaos, Applications to science and engineering.

(Lecture 3 hrs.)

**570. Partial Differential Equations (3) S**

Prerequisites: MATH 364A, 463, 563.

Cauchy’s problem; classification of second order equations; methods of solution of hyperbolic, parabolic, and elliptic equations.

Letter grade only (A-F). (Lecture 3 hrs.)

**574. Stochastic Calculus and Applications (3) S**

Prerequisites: MATH 361B, 364A or 370A, 380.

Review of probability theory. Markov processes. Wiener processes. Stochastic integrals. Stochastic differential equations. Applications to Finance and Engineering.

(Lecture 3 hrs.)

**575. Calculus of Variations (3) S
**Prerequisites: MATH 563 and one of MATH 364A, 370A.

Classical theory. Necessary and sufficient conditions for extrema of multiple integrals. Hamilton-Jacobi theory. Applications to eigenvalue problems. Direct methods. Pontryagin maximum principle. Principle of optimality.

Letter grade only (A-F). (Lecture 3 hrs.)

**576. Numerical Analysis (3) F
**Prerequisites: MATH 323, 361B, 364A.

Advanced numerical methods. Introduction to error analysis, convergence, and stability of numerical algorithms. Topics may include solution of ordinary differential equations, partial differential equations, systems of linear and nonlinear equations, and optimization theory.

Letter grade only (A-F). (Lecture 3 hrs.)

**577. Numerical Solution of Partial Differential Equations (3) S**

Prerequisite: MATH 423 or MATH 576 or consent of instructor.

Survey of finite difference methods for solving hyperbolic, parabolic, and elliptic PDE’S, analysis of their accuracy, convergence, and stability properties. Includes selected initial-value and boundary-value problems, characteristics, domain of dependence, von Neumann’s method of stability analysis, matrix method of stability analysis, and solution of large scale sparse linear systems by direct and iterative methods. Finite element method introduced.

(Lecture 3 hrs.)

**580. Statistical Inference (3) F
**Prerequisites: MATH 381 or consent of instructor.

Properties of a random sample, convergence in probability, law of large numbers, sampling form normal distribution, central limit theorem, principles of data reduction, likelihood principle, point estimation, Bayesian estimation, methods of evaluating estimators, hypothesis testing, decision theory, confidence intervals.

Letter grade only (A-F). (Lecture 3 hrs.)

**581. Experimental Design and Analysis (3) F
**Prerequisite: MATH 381 or consent of instructor.

Design of experiments to permit efficient analysis of sources of variation with application to quality assurance. Factorial and fractional factorial designs; block designs; confounding. Fixed and random effect models. Effects of departure from assumptions; transformations. Response surface techniques. Taguchi methods.

(Lecture 3 hrs.)

**582. Time Series (3)
**Prerequisites: MATH 381.

Includes moving averages, smoothing, Box-Jenkins (ARIMA) models, testing for nonstationarity, model fitting and checking, prediction and model selection, seasonal adjustment, ARCH, GARCH, cointegration, state-space models. Statistical packages used throughout course.

(Lecture 3 hrs.)

**583. Survey Sampling (3)
**Prerequisites: MATH 381 or consent of instructor.

Theory and practice of sampling from finite populations. Simple random sampling, stratified random sampling, systematic sampling, cluster sampling. Properties of various estimators including ratio, regression, and difference estimators. Error estimation for complex samples.

Letter grade only (A-F). (Lecture 3 hrs.)

**584. Statistical Quality Control (3) F
**Prerequisite: MATH 381 or consent of instructor.

Introduction to methods of statistical quality control. Includes control charts, acceptance sampling, process capability analysis, and aspects of experimental design.

(Lecture 3 hrs.)

**585. Nonparametric Statistics (3)
**Prerequisites: MATH 480 or consent of instructor.

Alternatives to normal-theory statistical methods, analysis of categorical and ordinal data, methods based on ranks, measures of association, goodness of fit tests, order statistics.

Letter grade only (A-F). (Lecture 3 hrs.)

**586. Data Mining (3) S
**Prerequisites: MATH 480 or consent of instructor.

Basics of data mining algorithms with emphasis on industrial applications. Prediction and classification techniques such as Multivariate Adaptive Regression Splines, decision trees, neural networks, and other methods. Several software packages utilized.

Letter grade only (A-F). (Lecture 3 hrs.)

**587./487. Statistical Simulation (3)
**Prerequisites: MATH 381 or consent of instructor. (Undergraduates enroll in MATH 487; graduates enroll in MATH 587.)

Simulation modeling techniques; generation of discrete and continuous random numbers from given distributions; Monte Carlo methods; discrete event simulations, statistical analysis of simulated data; variance reduction; statistical validation; introduction to simulation languages; industry applications. Statistical packages used throughout the course.

Letter grade only (A-F). (Lecture 3 hrs.)

**590./480. Regression Analysis (3)
**Prerequisites: MATH 247 and 380, prerequisite or corequisite MATH 381. (Undergraduates enroll in MATH 480; graduates enroll in MATH 590.)

Simple linear regression: estimation and inference, prediction, analysis of residuals, detection of outliers, use of transformations. Multiple linear regression: influence diagnostics, multicollinearity, selection of variables, simultaneous estimation and inference, validation techniques. Statistical software for data analysis used.

Letter grade only (A-F). (Lecture 3 hrs.)

**593./483. Multivariate Statistical Analysis (3)
**Prerequisites: MATH 381, prerequisite or corequisite MATH 480. (Undergraduates enroll in MATH 483; graduates enroll in MATH 593.)

Discriminate analysis, principal components, factor analysis, cluster analysis, logistic regression, canonical correlation, multidimensional scaling, and some nonlinear techniques. Statistical software used.

Letter grade only (A-F). (Lecture 3 hrs.)

**695. Seminar in Mathematics (3) F,S
**Prerequisite: Consent of instructor.

Presentation and discussion of advanced work, including original research by faculty and students. Topics announced in the

May be repeated to a maximum of 6 units. Letter grade only (A-F).

**697. Directed Studies (1-3) F,S
**Prerequisite: Consent of instructor.

Research on a specific area in mathematics. Topics for study to be approved and directed by faculty advisor in the Mathematics and Statistics Department.

Letter grade only (A-F).

**698. Thesis (2-4) F,S
**Prerequisite: Advancement to candidacy for M.S. in Mathematics and completion of at least one 500 and/or 600 level mathematics course.

Formal report of research or project in mathematics.

**Mathematics Education Courses (MTED)**

Satisfying the Entry-Level Math (ELM) requirement (see “Undergraduate Programs” section of this Catalog) is a prerequisite for all mathematics education courses.

**LOWER DIVISION**

**105. Activity-Based Probability and Statistics for Elementary and Middle School Teachers (3)
**Prerequisites: Three years of high school mathematics including algebra, geometry, and intermediate algebra (or MATH 10), or the equivalent.

Activity-based exploration of randomization, data representation, measures of central tendency and dispersion. Analysis of experiments requiring hypothesizing, experimental design and data gathering. Basic laws of probability and set theory, combinations, permutations, and simulations.

Not open for credit to Mathematics majors. Letter grade only (A-F). (Lecture 2 hrs., activity 2 hrs.)

**110. The Real Number System for Elementary and Middle School Teachers (3)
**Prerequisites: Three years of high school mathematics including algebra, geometry, and intermediate algebra (or MATH 10), or the equivalent.

Introduction to problem solving processes and strategies. Development and analysis of structure, properties, and operations of real number system. Concept and process development using appropriate models, manipulative, and activities.

Not open for credit to Mathematics majors. (Lecture 2 hrs., activity 2 hrs.)

**211. Geometry and Measurement for Elementary Teachers (3)
**Prerequisites: “C” or better in MTED 110 and one year of high school geometry.

Problem solving and hands-on modeling of real-world geometry situations focusing on patterning, informal geometry, congruence, similarity, constructions, transformations, tessellations, measurement in 1, 2, and 3 dimensions (English and Metric units). Computer applications are integrated into the course.

Not open for credit to Mathematics majors. (Lecture 2 hrs., activity 2 hrs.)

**UPPER DIVISION**

**301. Computer Applications in Mathematics for Teachers (3)
**Prerequisites: One year of high school geometry and one of MTED 110 or MATH 122.

Designed for pre-service or inservice teachers. Software evaluation; teacher tools (spreadsheets, databases, email, collaborative tools, and applications); mathematics using technology; programming; technology use issues in schools.

Satisfies California Level I teaching credential computer technology standard. Open for credit to pre-service or in-service teaching credential students only. (Lecture 2 hrs., activity 2 hrs.)

**311. Topics of Enrichment in Mathematics for the Elementary Teacher (3)
**Prerequisites: MTED 110 and either MTED 211 or MATH 122 or consent of instructor. Formerly MATH 311.

Enrichment topics in mathematics for elementary teacher, such as theory of arithmetic, numeration systems, elementary logic, mensuration, metric system, topological equivalence, probability and statistics and network theory.

Not open for credit to mathematics majors or to students with credit in MATH 311. (Lecture 3 hrs.)

**312. Geometry and Measurement for Mathematics Specialists in Elementary and Middle Schools (3)**

Prerequisites: MTED 110 and one year of high school geometry.

Exploration, conjecture, justification of geometric relationships, applications relevant to teaching geometry (K-10). Problem solving, informal geometry, proof, non-Euclidean geometry, congruency, similarity, constructions, transformations, tessellations, measurement (English and Metric) in 1, 2 , and 3 dimensions. Computer construction utility used.

Not open for credit to Mathematics majors. Letter grade only (A-F). (Lecture 2 hrs., activity 2 hrs.)

**315. History of Mathematics for Mathematics Specialists in Elementary and Middle Schools (3)**

Prerequisites: MTED 110, 312.

Mathematics ideas throughout history with orientation toward various civilizations and cross-cultural views. Covers origins and interrelationships of areas of K-9 mathematics curriculum, including arithmetic, algebra, geometry, statistics and probability, cryptography, and other mathematics topics.

Not open for credit for mathematics majors. Letter grade only (A-F). (Lecture 2 hrs; activity 2 hrs.)

**320. Number Theory for Middle School Teachers (3)**

Prerequisites: MTED 105, 110.

Concepts and justification involving basic properties of natural numbers, mathematical induction, Euclidean algorithm, and the Fundamental Theorem of Arithmetic. Topics include proofs and problem-solving with divisibility, primes and composites, and prime factorizations; congruences and other examples.

Not open for credit for mathematics majors. Letter grade only (A-F). (Lecture 2 hrs; activity 2 hrs.)

**324. Algebraic Structures for Middle School Teachers (3)**

Prerequisites: MTED 105, 110.

Properties of real and complex numbers, groups, rings, real and complex fields; polynomial equations and inequalities; polynomial, rational, radical, absolute value, exponential, and logarithmic functions; matrices and vectors.

Not open for credit for mathematics majors. Letter grade only (A-F). (Lecture 2 hrs; activity 2 hrs.)

**325. Functions, Models and Concepts of Calculus for Mathematics Specialists in Elementary and Middle Schools (3)**

Prerequisites: MTED 110, 312.

Numeric, symbolic, graphical, verbal representation of functions; sequences and sums. Intuitive development of concepts of limit, continuity, derivative, integral. Applications, including differential equations. Algebraic methods and technology emphasized in context of learning calculus.

Not open for credit for mathematics majors. Letter grade only (A-F). (Lecture 2 hrs; activity 2 hrs.)

**402. Problem Solving Applications in Mathematics for Elementary and Middle School Teachers (3)
**Prerequisites: “C” or better in both MTED 110, and either 211 or 312 or the equivalent and a course in Critical Thinking.

Problem solving processes and strategies; interrelates and applies content from many mathematics areas (real number system, algebra, number theory, geometry, measurement, probability and statistics); develops questioning strategies, fostering understanding of algebra and geometry. Technology integrated throughout.

Not open for credit to Mathematics majors. (Lecture 2 hrs., activity 2 hrs.)

**403. Connections, Integration, and Reasoning in Mathematics for Teachers of Foundational Mathematics (3)**

Prerequisites: MTED 105, 110, 312, 315, 320, 324, 325, and 402.

Examination, analysis, and integration of mathematics topics appropriate for teachers of Foundational Mathematics. Topics will include problem solving, hypothesis and justification, and mathematics connections and communication.

Not open for credit for mathematics majors. Letter grade only (A-F). (Lecture 2 hrs; activity 2 hrs.)

**411. Topics and Issues in Secondary School Mathematics (3)
**Prerequisites: MATH 310, 341, 355, 380, 410, 444; EDSS 300M or consent of the instructor.

Analysis of topics and issues in secondary school mathematics curriculum. Problem solving, mathematical connections, communication, structures, conjecture, proof, manipulatives, technology, assessment. Observations/interview experiences and portfolio assemblage required. Intended for students preparing to enter Single Subject Credential Program in mathematics.

(Lecture 2 hrs., activity 3 hrs.)

**495. Special Topics in Mathematics Education (1-3)**

Prerequisite: Consent of instructor.

Topics of interest in Mathematics Education.

May be repeated to a maximum of 9 units with different topics in different semesters. Letter grade only (A-F).

**GRADUATE LEV****EL**

**511. Mathematics Teaching and Learning (3)**

Prerequisite: Consent of instructor.

Theories of mathematics teaching and learning. Key issues in mathematics and mathematics education. Historical development and contemporary views of various theoretical perspectives for teaching and learning mathematics, including the roles of standards and various mathematics and education organizations.

Letter grade only (A-F). (Lecture and Discussion, 3 hrs.)

**512. Curriculum and Assessment in Mathematics (3) **

Prerequisite: MTED 511 or consent of instructor.

Theories of mathematics curriculum and forms of assessment. Introduces major philosophies, issues, resources and technologies pertaining to curricula and assessment of mathematics. Relevant histories and contemporary practices of design and implementation of curriculum and assessment of mathematics.

Letter grade only (A-F). (Lecture and Discussion, 3 hrs.)

**540. Algebra in the Secondary School Curriculum (3)
**Prerequisite: MTED 511; prerequisite or corequisite: MTED 512 or consent of instructor.

Issues/topics concerning algebraic learning using curricular standards. Examining texts, curricula, algebraic thinking and teaching research. Common errors and possible remedies, algebra for mathematizing situations. Relationship of K-12 algebra curriculum to modern algebra and its structures. Fundamental theorem of algebra.

Letter grade only (A-F). (Lecture and Discussion, 3 hrs.)

**550. Geometry and Measurement in the School Curriculum (3)
**Prerequisites: MTED 511; prerequisite or corequisite: MTED 512 or consent of instructor.

Content, curriculum, standards, and research in learning and teaching geometry, spatial sense and measurement in K-12. Justification and proof, applications and abstraction, tools and technology in geometry teaching and learning. Current issues in teaching and learning of geometry and measurement.

Letter grade only (A-F). (Lecture and Discussion, 3 hrs.)

**560. Analysis in the Secondary School Curriculum (3)
**Prerequisites: MTED 511 and MATH 361A; prerequisite or corequisite: MTED 512 or consent of instructor.

Fundamental concepts of calculus, functions, mappings, related topics and proofs in real and complex analysis, relating mathematics analysis to secondary curriculum. Issues and techniques in teaching and learning of mathematical analysis. Examination of mathematics education research and mathematics frameworks.

Letter grade only (A-F). (Lecture and Discussion, 3 hrs.)

**580. Probability and Statistics in the School Curriculum (3)
**Prerequisites: MTED 511; prerequisite or corequisite: MTED 512 or consent of instructor.

Content, curriculum, and research in learning and teaching probability and statistics in K-12 schools. Includes role of applications, abstraction, tools and technology in probability and statistics teaching and learning.

Letter grade only (A-F). (Lecture and Discussion, 3 hrs.)

**590. Special Topics in Mathematics Education (1-3)**

Prerequisites: Consent of instructor.

Advanced study of special topics in the field of mathematics education.

May be repeated for a total of six units with different topics. Letter grade only (A-F). (Seminar 1-3 hrs.)

**695. Seminar in Mathematics Education (1-3)**

Prerequisites: Consent of instructor.

Presentation of and discussion of advanced work in mathematics education.

May be repeated for a total of six units. Letter grade only (A-F). (Seminar 1-3 hrs.)

**697. Directed Studies in Mathematics Education (1-3)
**Prerequisites: MTED 511, 512; EDP 520; Advancement to Candidacy; consent of instructor.

Research project in mathematics education.

Letter grade only (A-F).

**698. Thesis in Mathematics Education (1-4)
**Prerequisites: MTED 511, 512; EDP 520; Advancement to Candidacy; consent of instructor.

Research in mathematics education culminating in a formal report.

Letter grade only (A-F).