One semester survey of major concepts and computational techniques of calculus including limits, derivatives and integrals. Emphasis on basic examples and applications of calculus such as approximation, differential equations, rates of change and error estimation for students who will take no further calculus. Offered Spring Only. Prerequisite: MAT100 or equivalent. Restrictions: Cannot receive course credit for both MAT102 and MAT103. Note: will not be offered in AY 2014-2015.

# All courses in Spring 2014

Second semester of the 3-semester calculus sequence 103/104/201. Main topics are Integration and Series. Offered Fall and Spring.

This course is geared toward students with no prior university math experience. It aims to provide a view of mathematics as a living, growing, creative human endeavor that classifies as both a science and an art, to give a feeling for, and some mastery of, the mathematical way of thinking (including "doing mathematics") as well as an awareness of some of the many applications of mathematics in today's world. Active class participation is an essential component of the course, required along with participation in Professor Keith Devlin's (free) Stanford MOOC "Introduction to Mathematical Thinking." We expect to offer this again in Fall 2015.

Mathematics has profoundly changed our world, from the way we communicate with each other and
listen to music, to banking and computers. This course is designed for those without college
mathematics who want to understand the mathematical concepts behind important modern applications.
The course consists of individual modules, each focusing on a particular application (e.g., digital
music, sending secure emails, and using statistics to explain, or hide, facts). The emphasis is on
ideas, not on sophisticated mathematical techniques, but there will be substantial problem-set
requirements. Students will learn by doing simple examples.

A continuation of MAT103/104, the third semester in the calculus sequence gives a thorough introduction to multivariable calculus. Topics include limits, continuity and differentiability in several variables, extrema, Lagrange multipliers, Taylor's theorem, multiple integrals, integration on curves and surfaces, Green's theorem, Stokes' theorem, divergence theorem. Emphasizes concrete computations over more theoretical considerations. Offered both Fall and Spring. Prerequisite: MAT104 or equivalent.

Linear Algebra, mostly in real n-space. Companion course to 201. Main topics are matrices, linear transformations, linear independence and dimension, bases and coordinates, determinants, orthogonal projection, least squares, eigenvalues, eigenvectors and their applications to quadratic forms and dynamical systems. Offered Fall and Spring.

Advanced linear algebra.. More theoretical treatment of vector spaces and matrices than that found in MAT202, but more concrete than that of MAT217. A course for those with a strong mathematical background and interest. Recommended for physics majors. Offered Spring only.

Continues the rigorous theoretical introduction to analysis in several variables, including basic linear algebra, begun in MAT216. Offered Spring Only. New in Spring 2014.

Introduction to numerical methods with emphasis on algorithms, applications and computer implementation issues. Topics covered include solution of nonlinear equations; numerical differentiation, integration and interpolation; direct and iterative methods for solving linear systems; numerical solutions of differential equations; two-point boundary value problems; and approximation theory. Lectures are supplemented with numerical examples using MATLAB. Prerequisites: MAT201 and MAT202; or MAT203 and MAT204; or equivalent.

An introduction to differential equations, covering both applications and fundamental theory.

Draws problems from the sciences & engineering for which mathematical models have been developed and analyzed to describe, understand and predict natural and man-made phenomena. Emphasizes model building strategies, analytical and computational methods, and how scientific problems motivate new mathematics.
This interdisciplinary course in collaboration with Molecular Biology, Psychology and the Program in Neuroscience is directed toward upperclass undergraduate students and first-year graduate students with knowledge of linear algebra and differential equations.

Fourier series, Fourier transforms, and applications to the classical partial differential equations.
Prerequisites: MAT215 or MAT218 or consent of instructor.
(Replaces MAT330 beginning AY 2012-13)

Calculus of functions of one complex variable, power series expansions, residues, and conformal mapping. Prerequisites: MAT201 and MAT202 or equivalent.
(Replaces MAT317 beginning AY 2012-13)

Continuation of Algebra I.

This course will cover the fundamental theorems and algorithms of graph theory. Topics include: connectivity, mathchings, graph coloring, planarity, the four-color theorem, extremal problems, network flows, and related algorithms. Prerequisite: MAT202 or MAT204 or MAT217, or equivalent.
(Replaces MAT306 beginning AY 2012-13)

The mathematical concept of a game is an abstraction which encompasses conflict-cooperation situations in which strategy (not just chance) plays a role. Games in extensive form, pure and behavioral strategies; normal form, mixed strategies, equilibrium points; coalitions, characteristic-function form, imputations, solution concepts; related topics and applications. Prerequisites: MAT202 or 204 or 217 or equivalent. MAT215 or equivalent is recommended.
(Replaces MAT308 beginning AY 2012-13)

Sequences of independent trials, applications to number theory and analysis, Monte Carlo method. Markov chains, ergodic theorem for Markov chains, Entropy and McMillan theorem. Random walks, recurrence and non-recurrence; connection with linear difference equations. Strong laws of large numbers, random series and products. Weak convergence of probability measures, weak Helly theorems, Fourier transforms of distributions. Limit theorems of probability theory. Prerequisites: MAT203 or MAT218 or equivalent.
(Replaces MAT390 beginning AY 2012-13)

The theory of Lebesgue integration in n-dimensional space. Differentiation theory. Hilbert space theory and applications to Fourier transforms, and partial differential equations. Introduction to fractals. The third semester of a four-semester sequence, but may be taken independently. Prerequisites: MAT215 or MAT218 or equivalent.
(Replaces MAT332 beginning AY 2012-13)

The course will target the following topics: The definition of knots in the 3-sphere, first invariants; algebraic knots and links in the 3-sphere; classification of algebraic knots, Puiseux pairs, iterated torus knots; fibred links, monodromy, the case of algebraic links; higher dimensional algebraic knots, Milnor theory of complex isolated hypersurface singularities.