Mathematics Course Descriptions

MATH - 100. Great Ideas in Mathematics (4)

Math 100 is an overview of some of the seminal achievements in mathematics from ancient to modern times. Topics include Problem Solving, Number Theory, Geometry, Fractals, Topology, Probability and Statistics, and applications to other fields.

MATH - 101. Elementary Statistics (4)

This course will introduce students to the processes by which valid statistical inferences may be drawn from quantitative data. Topics include design of experiments; sample surveys; measurement; summary and presentation of data; regression and correlation; elementary probability; the law of averages; the central limit theorem; the normal, t and chi-square distributions; confidence intervals; and hypothesis testing. A computer laboratory component will introduce the student to spreadsheets and statistical applications. Offered every semester.

MATH - 102. Biostatistics (4)

Prerequisite: MATH - 104 or sufficiently high score on the Mathematics placement exam (consult with the Mathematics Department for the exact score needed).. This course, required of biology majors, is a survey of statistical concepts and methods, with an emphasis on concepts critical to the life sciences. Topics include design of experiments; measurement; summary and presentation of data; regression and correlation; elementary probability; the normal, binomial, t-, and chi-square distributions; confidence intervals and standard error; and hypothesis testing. Offered every Spring.

MATH - 104. Algebra for Business and Science (2)

This course covers mathematical theory and techniques fundamental to university level scholarship. Topics include: the real number system with number theory concepts (algorithms for computation); percentage; simple and compound interest; linear and exponential functions; systems of linear equations; descriptive statistics. Two hours lecture. Offered every semester.

MATH - 105. Mathematics for Educators (4)

Prerequisite: MATH - 104 or sufficiently high score on the Mathematics placement exam (consult with the Mathematics Department for the exact score needed). This course provides the requisite mathematics preparation for Multiple Subject Teaching Credential Candidates. The curriculum satisfies the California Subject Examination for Teachers (CSET) content domain categories: number sense; algebra and functions, measurement and geometry; statistics; data analysis and probability.

MATH - 106. Quantitative Methods in Business (4)

Prerequisites: Sufficiently high score on the Mathematics placement exam (consult with the Mathematics Department for the exact level needed), or MATH - 104. Topics include introduction to linear systems, linear programming, mathematics of finance, probability and statistics. Topics to be treated in the context of business applications. A computer laboratory component will use spreadsheet and graphing software. Offered every semester.

MATH - 107. Calculus for the Liberal Arts (4)

Prerequisite: MATH - 104 or sufficiently high score on the Mathematics placement exam (consult with the Mathematics Department for the exact score needed). This course provides a one semester introduction to the theory of differential and integral calculus with an emphasis on technical fundamentals. The curriculum is designed for non-science majors for whom advanced coursework in mathematics is not required

MATH - 108. Precalculus (4)

Prerequisites: Two years of high school algebra and sufficiently high score on the Mathematics placement exam (contact the Mathematics Department for the exact level needed), or MATH - 104. Topics include polynomial functions; factor and remainder theorems; complex roots; exponential, logarithmic, and trigonometric functions; and coordinate geometry. May not be taken for credit after completion of 0206-109. Offered every semester.

MATH - 109. Calculus and Analytic Geometry I (4)

Prerequisites: Sufficiently high score on the Mathematics placement exam (contact the Mathematics Department for the exact level needed), or MATH - 108. Differentiation of algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions, and hyperbolic and inverse hyperbolic functions; implicit differentiation; curve sketching; indeterminate forms; velocity and acceleration; optimization; other applications of differentiation; Fundamental Theorem of Calculus, with applications to area and volume. Four hours lecture. Offered every semester.

MATH - 110. Calculus and Analytic Geometry II (4)

Prerequisite: MATH - 109. Topics include: Techniques of integration, including numerical integration and use of tables both printed and electronic; selected applications of integration; introduction to differential equations; parametric equations and polar coordinates; infinite sequences and series. Four hours lecture. Offered every semester.

MATH - 130. Elementary Linear Algebra (4)

Prerequisites: Sufficiently high score on the Mathematics placement exam (contact the Mathematics Department for the exact level needed), or MATH - 108. Topics include systems of linear equations, matrices and determinants; the geometry of vectors in Euclidean space; general properties of vector spaces, bases and dimension; linear transformations in two and three dimensions, eigenvalues and eigenvectors. Offered every Fall.

MATH - 195. Freshman Seminar (4)

An interesting introduction to the field of mathematics for incoming Freshmen in the Fall.

MATH - 201. Discrete Mathematics (4)

Prerequisite: CS - 110 or permission of instructor. Topics include algebraic structures, graph theory, combinatorics, and symbolic logic. Offered every Fall.

MATH - 202. Linear Algebra and Probability (4)

Matrix arithmetric and matrix algebra (determinants, adding and multiplying matrices, matrix inverse, using matrices to solve systems of equations), geometric applications of linear algebra (matrices as transformations, vectors in 2- and 3-dimensions, equations of planes, etc.); discrete probability, random variables, discrete and continuous probability distributions (including binomial and normal), expected value and variance. Offered every Spring.

MATH - 211. Calculus and Analytic Geometry III (4)

Prerequisite: MATH - 110. Topics include analytic geometry in three dimensions; vector functions; arc length and curvature; motion in space; partial differentiation and chain rule; directional derivative and gradient; optimization and Lagrange multipliers; multiple integrals, line integrals, and surface integrals; divergence and curl; theorems of Green, Gauss, and Stokes. Offered every Fall.

MATH - 235. Introduction to Formal Methods (4)

Topics include logic and mathematical proof; set theory, equivalence relations, and mappings; mathematical induction; modular arithmetic; isomorphism; groups; structures of real numbers; convergence and continuity. Emphasis on concepts of proof and mathematical formalism. Offered every Spring.

MATH - 301. Problem-Solving Seminar (4)

Prerequisite: MATH - 110 or permission of instructor. An informal, discussion-oriented class to develop skills for investigating and solving mathematical problems. Topics include elementary mathematics, combinatorics, geometry, number theory and calculus, as well as problems from contests such as the International Mathematical Olympiad and the Putnam Examination. Strongly recommended for students interested in teaching mathematics.

MATH - 310. History of Mathematics (4)

Prerequisite: MATH - 110 or permission of instructor. A history of the development of arithmetic, algebra, geometry, and calculus. Selected topics from recent mathematical history.

MATH - 314. Mathematical Circles (4)

Prerequisites: MATH - 110 and MATH - 130 , or permission of instructor. An introduction to the Eastern European Mathematical Circles culture. Students will learn mathematical folklore and problem-solving methods drawn from geometry and discrete mathematics, and will both observe and teach students in several mathematical circles in the Bay Area. In addition to the mathematics and pedagogy, students will explore issues of equity in educational opportunity. This is a service earning course designed for math, physics, or computer science majors who are interested in teaching.

MATH - 340. Differential Equations (4)

Prerequisites: MATH - 130 or PHYS - 110 , and MATH - 211 , or permission of instructor. Topics include a review of first-and second-order equations, series solutions, systems of linear and non-linear differential equations, numerical methods, qualitative methods, introduction to partial differential equations.

MATH - 345. Mathematical Modeling (4)

Prerequisites: MATH - 110 and MATH - 130. The methodology of mathematical modeling will be explored in several case studies from fields as diverse as political science, biology, and operations research. Problems of data collection, model fitting, and model analysis will be explored. Case studies incorporate topics from: analysis of conflict (business, military, social), population dynamics, and production management.

MATH - 355. Complex Analysis (4)

Prerequisites: MATH - 130 MATH - 211 and MATH - 235 , or permission of instructor. Topics include integration and differentiation of functions of a complex variable, Laurent series, conformal mapping, residues, and Cauchy's theorems.

MATH - 367. Number Theory (4)

Prerequisite: MATH - 235 or permission of instructor. Topics include prime numbers, congruences, quadratic reciprocity, number-theoretic functions, and diophantine equations.

MATH - 370. Probability and Statistics (4)

Prerequisite: MATH - 211 or permission of instructor. Topics include descriptive statistics and data analysis; probability, random variables, and probability distributions; mathematical expectation; confidence intervals and hypothesis tests.

MATH - 380. Foundations of Geometry (4)

Prerequisite: MATH - 110 or permission of instructor. Topics chosen from axiomatics, Euclidean and non-Euclidean geometries, vector spaces and inner products, and symmetry groups.

MATH - 394. Applied Mathematics Research Laboratory (4)

Prerequisite: Permission of instructor. This course offers selected upper division students an opportunity to work on a sponsored research project under the direction of a faculty member. May be repeated for credit. Offered as often as suitable projects can be found.

MATH - 395. Selected Topics in Mathematics (2-4)

Prerequisite: Permission of instructor. This course treats topics not covered in other Mathematics courses, but of interest to faculty and students. May be repeated for credit. Offered intermittently.

MATH - 398. Directed Reading and Research (1-4)

Prerequisite: Written consent of instructor and dean. May be repeated for credit. Offered every semester.

MATH - 422. Combinatorics (4)

Prerequisite: MATH - 235 or permission of instructor.. An in-depth study of combinations and permutations, inclusion-exclusion, the binomial theorem, recurrence relations, and graph theory, with additional topics depending on student and instructor interest (for example, generating functions, combinatorial number theory, finite-state machines). Offered every other Fall.

MATH - 435. Modern Algebra (4)

Prerequisite: MATH - 235 or permission of instructor. Topics include an introduction to the theory of groups, rings, fields, vector spaces, and other algebraic structures.

MATH - 453. Real Analysis (4)

Prerequisites: MATH - 211 and MATH - 235 or permission of instructor. Topics include sequences and series, topology of the real line, limits and continuity, the real number system, the derivative and Riemann integral.

MATH - 482. Differential Geometry (4)

Prerequisites: MATH - 211 and MATH - 235 or permission of instructor. Topics include classical differential geometry of curves and surfaces, curvature, the bending of surfaces, shortest paths in a surface, and tensors in geometry and physics.

MATH - 485. Topology (4)

Prerequisite: MATH - 235 or permission of instructor. Topics selected from point-set topology, algebraic topology, geometric topology, and differential topology.