Mathematics Course Descriptions

Mathematics 110 -- Topics in Mathematics - Fall, Spring

Consideration of diverse subjects in mathematics. Course content varies from semester to semester with specific subject matter for each course announced at preregistration. Designed for non-majors who wish to study mathematics other than calculus. One unit. Common Area Satisfied: Mathematical Sciences.

Mathematics 125, 126 -- Calculus for the Social Sciences 1, 2 - Annually

A two-semester introduction to the calculus of one and several variables primarily intended for students majoring in Economics. Topics discussed include elementary linear and matrix algebra, differentiation and integration of real valued functions of one real variable, techniques of integration and differentiation, max-min problems and improper integrals. A brief introduction is given to functions of several variables including applications to constrained optimization problems. This is a terminal sequence. One unit each semester. Common Area Satisfied: Mathematical Sciences.

Mathematics 131, 132 -- Calculus for the Physical and Life Sciences 1, 2 - Annually

Considers the calculus of real-valued functions of one variable for students who are planning further coursework in mathematics or a major in the sciences. Emphasis is placed on a conceptual understanding of the calculus, presenting material from symbolic, numerical, and graphical points of view. The course will make regular use of calculators or computers and will consider a variety of applications to the sciences and social sciences. In the first semester, the concepts of limit, continuity, derivative and integral are developed and applied to algebraic, logarithmic, exponential and trigonometric functions. The second term focuses on the theory and applications of integration, Taylor polynomials and Taylor series, and ordinary differential equations. This course is the prerequisite for Mathematics 241, 242. This course meets four hours per week. One and one-quarter units each semester. Common Area Satisfied: Mathematical Sciences.

Mathematics 133, 134 -- Intensive Calculus for the Physical and Life Sciences 1, 2 - Annually

This sequence is an intensive version of Mathematics 131, 132 that is designed for students with an interest in pursuing a major in mathematics or the sciences, or the premedical program, who require more class time to make the transition to college-level mathematics. See the description of Mathematics 131, 132 for the course content. This course meets five hours per week. One and one-quarter units each semester. Common Area Satisfied: Mathematical Sciences.

Mathematics 136 -- Advanced Placement Calculus - Fall

This course is a one semester version of Mathematics 131,132 for those students who have either received one unit of advanced placement credit in calculus or who have taken a year of calculus in high school. See the description of Mathematics 131, 132 for the course content. This course meets four hours per week. One and one-quarter units. Common Area Satisfied: Mathematical Sciences.
Note: Mathematics 136 fulfills the pre-medical program year long mathematics requirement.

Mathematics 241 -- Multivariable Calculus - Fall, Spring

A study of the calculus of functions of several variables. The course concerns the theory and applications of differentiation and integration of functions of several variables, vector fields, line integrals, Green's theorem. Prerequisite: Mathematics 132, 134, 136 or equivalent. This course meets four hours per week. One and one-quarter units. Common Area Satisfied: Mathematical Sciences.

Mathematics 242 -- Principles of Analysis - Fall, Spring

An in-depth study of the theory of the calculus of functions of one variable. Topics include sequences, series, continuity, differentiability, the extreme value theorem, the mean value theorem, Riemann integration, and the fundamental theorem of calculus. Prerequisite: Mathematics 241. One unit. Common Area Satisfied: Mathematical Sciences.

Mathematics 243 -- Algebraic Structures - Annually in Fall

An introduction to the primary structures in abstract algebra: groups, rings and fields, and the corresponding concept of homomorphism for each of these structures. Emphasis will be placed on using the language of sets, relations, equivalence relations and functions, and developing techniques of proof, including elementary logic and mathematical induction. Prerequisite: Mathematics 132, 134, 136, or equivalent. One unit. Common Area Satisfied: Mathematical Sciences.

Mathematics 244 -- Linear Algebra - Annually in Spring

Designed to acquaint students with the basic techniques of linear algebra. Topics include matrices, vector spaces, subspaces, linear transformations, bilinear forms, determinants, eigenvalue theory, and the finite dimensional spectral theorem. Applications and additional topics are included as time permits. Prerequisite: Mathematics 243. One Unit. Common Area Satisfied: Mathematical Sciences.

Mathematics 301 -- Topics in Geometry - Alternate years in Fall

Centers on some area of geometry other than differential geometry. Possible topics include Euclidean and non-Euclidean geometry, projective geometry, the geometry of transformation groups, and the elementary geometry of algebraic curves. Prerequisite: Mathematics 241 and 244. Breadth area: Geometry and Topology. One unit.

Mathematics 302 -- Differential Geometry - Alternate years in Fall

A first course in the differential geometry of curves and surfaces for students who have completed Multivariable Calculus (Mathematics 241) and Linear Algebra (Mathematics 244). Topics include the Frenet-Serret formulas, smooth surfaces in 3-space, fundamental forms, differentiable manifolds, vector fields, connections and a brief introduction to Riemannian geometry. Prerequisite: Mathematics 241 and 244. Breadth area: Geometry and Topology. One unit.

Mathematics 303 -- Mathematical Models - Alternate years in Spring

Introduction to the role of mathematics as a modeling tool, including the construction, interpretation and application of mathematical models. Applications will be chosen to illustrate various modeling paradigms such as deterministic, probabilistic, discrete and continuous modeling and may include population dynamics, bio-medical applications, stock market analysis, and network and traffic flows. Prerequisite: Mathematics 242 and 244. Breadth area: Applied Mathematics. One unit.

Mathematics 304 -- Ordinary Differential Equations - Alternate years in Fall

Linear differential equations are studied; basic existence theorems are proved; equations with constant coefficients and series methods are treated in detail. Topics in non-linear systems are discussed, including existence and uniqueness theorems, series methods. Beginning in 2000-2001, this this course will be offered in a full year linked sequence continuing with MATH 373 (Applied Mathematics). Prerequisite: Mathematics 242 and 244. Breadth area: Applied Mathematics. One unit.

Mathematics 305 -- Complex Analysis - Alternate years in Spring

The fundamentals of complex analysis. Topics include the complex number system, analytic functions, the Cauchy-Riemann equations, Cauchy's integral theorem, Cauchy's integral formula, Taylor series, Laurent series, the calculus of residues and conformal mapping. Prerequisite: Mathematics 244. Breadth area: Analysis. One unit.

Mathematics 351, 352 -- Abstract Algebra - Alternate years

An in-depth study of the structure of groups, rings and fields. Depending on the instructor, applications to Galois theory, number theory, geometry, topology, physics, etc., are presented. Prerequisite: Mathematics 244. Breadth area: Algebra. One unit each semester.

Mathematics 357 -- Combinatorics - Alternate years

A breadth-first introduction to the subject that discusses a representative sampling of combinatorial problems and techniques for solving them, including a selection of counting techniques, techniques for existence questions, and a variety of examples. Examples may include partitions, graphs and trees, graph traversals, tournaments, graph coloring and chromatic polynomials, magic squares, Latin rectangles and squares, and combinatorial block designs. Prerequisite: Mathematics 244. Breadth area: Algebra. One unit.

Mathematics 361, 362 -- Real and Abstract Analysis - Alternate years

Topological ideas are introduced through a treatment of metric space topology. After the study of open, closed, compact and connected spaces with emphasis on their behavior under continuous mappings, selected topics from functional analysis are considered. These include lim sup and lim inf, relation of uniform convergence to differentiation and integration, and the Stone Weierstrass approximation theorem. The second semester topics include an introduction to Lebesgue-Stieltjes integration, Hilbert space and other material from linear space theory. Breadth area: Analysis. Prerequisite: Mathematics 242 and 244. One unit each semester.

Mathematics 363 -- Topics in Topology - Alternate years in Spring

Considers various aspects of topology of surfaces and solids, including orientability, the Euler number, and the fundamental group. One of the goals of the course is the topological classification of surfaces. Prerequisite: Mathematics 242 and 244. Breadth area: Geometry and Topology. One unit.

Mathematics 371 -- Methods of Numerical Analysis - Alternate years

The numerical solution of problems using computers. Considerable time is devoted to selecting the appropriate algorithm for a given problem and analyzing the resulting numerical errors. Includes such topics as error analysis of computer arithmetic, approximation of functions, solution of linear and nonlinear equations, numerical integration, numerical solution of ordinary differential equations. Beginning in 2000-2001, the combination Mathematics 371, 372 will no longer satisfy the full year linked sequence requirement for the Mathematics major. Prerequisite: Mathematics 242 and 244. Breadth area: Analysis. One unit.

Mathematics 372 -- Numerical Linear Algebra - Alternate years

The numerical solution of problems from linear algebra using computers. Gaussian elimination in floating point arithmetic, iterative techniques for solving linear systems, numerical eigenvalue and diagonalization methods. Applications. Beginning in 2000-2001, the combination Mathematics 371, 372 will no longer satisfy the full year linked sequence requirement for the Mathematics major. Prerequisite: Mathematics 242 and 244. Breadth area: Applied Mathematics. One unit.

Mathematics 373 -- Principles and Techniques of Applied Mathematics - Alternate years in Spring

Provides an understanding of a wide spectrum of phenomena through the use of mathematical ideas, abstractions, and techniques. Topics included are partial differential equations including the heat and wave equations, Fourier analysis, eigenvalue problems, Green's functions. Beginning in 2000-2001, this course will be offered in a full-year linked sequence beginning with Mathematics 304 (Ordinary Differential Equations). Prerequisite: Mathematics 304. Breadth area: Applied Mathematics. One unit.

Mathematics 375, 376 -- Probability and Statistics - Alternate years

Provides an introduction to the theory and applications of probability and statistics. Topics in probability theory include both continuous and discrete distributions, conditional probability, random variables, expectation, and the Central Limit Theorem. Topics in statistics include maximum likelihood estimation, the sampling distributions of estimators, hypothesis testing, regression analysis, and an introduction to the analysis of variance. Prerequisite: Mathematics 242. Breadth area: Applied Mathematics. One unit each semester.

Mathematics 391, 392 -- Seminar - Annually

Provides an opportunity for individual and group investigation of topics not covered in ordinary course work. Active participation on the part of the students is normally required. The subject matter varies to suit individual students and is often related to the research activity of the professor. Examples of areas of study: Lie groups, functional analysis, complex analysis, probability theory, commutative algebra, applied mathematics, the classical groups, mathematical logic, automata and formal languages, topics in discrete modeling, and qualitative theory of differential equations. One unit each semester.

Mathematics 400 -- Directed Reading - Fall, Spring

This is an independent reading project for upper division students. Normally this will be on a topic that is not covered by the regular course offerings. Permission of the instructor and/or Department Chair is required for this course. One unit.

Mathematics 495, 496 -- Mathematics Honors Thesis - Annually

This is a large project extending over the course of the fourth year. It can consist of original research or be of an expository nature and is written under the guidance of one or more members of the Department. Normally, a student will earn one unit in the spring semester of the fourth year for successful completion of an honors thesis, unless the thesis work is done as part of the student's participation in a departmental seminar. In that case, no extra credit is given above the credit for the seminar itself. For a particularly extensive project, and with permission of the Department Chair, a student may earn one unit in each semester of the fourth year for completion of the thesis.