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 2013

Second semester of the standard 3-semester calculus sequence 103/104/201 for science, engineering and finance. Topics include techniques and applications of integration, convergence of infinite series and improper integrals, Taylor's theorem, introduction to differential equations and complex numbers. Emphasizes concrete computations over more theoretical considerations. Offered both Fall and Spring. Prerequisite: MAT103 or equivalent.

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

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.

A development of logic from the mathematical viewpoint, including propositional and predicate calculus, consequence and deduction, truth and satisfaction, the Godel completeness and incompleteness theorems. Applications to model theory, recursion theory and set theory, as time permits. Some underclass background in logic or in mathematics is recommended.
(Replaces MAT312 beginning AY 2012-13)

Introduction to real analysis, Lebesgue theory of measure and integration on the line and n-dimensional space, introduction to Fourier Series.

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

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)

Algebraic number theory. Topics covered include number fields and their integer rings, class groups, zeta and L-functions. Prerequisites: MAT217 and MAT322 (in the old numbering system) or MAT345 (Algebra I, in the new numbering system). MAT346 (Algebra II) recommended as a corequisite.
(Replaces MAT453 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)

Wiener measure, Stochastic differential equations, Markov diffusion processes, Linear theory of stationary processes, Ergodicity, mixing, central limit theorem for stationary processes, Gibbs random field. If time permits, the theory of products of random matrices and PDE's with random coefficients will be discussed. Prerequisite: MAT390 in the old numbering system or MAT385 in the new system.
(Replaces MAT391 beginning AY 2012-13)