Stephen Abbott

Calculus I
Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc.

Calculus II
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. 4 hrs. lect.

Linear Algebra
Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc.

Real Analysis
An axiomatic treatment of the topology of the real line, real analysis, and calculus. Topics include neighborhoods, compactness, limits, continuity, differentiation, Riemann integration, and uniform convergence. (MATH 0223) 3 hrs. lect./disc.

Advanced Probability Seminar
An introduction to the mathematical foundations of Probability for students who have completed work in Probability and Real Analysis. The central ideas correspond to the Lebesgue theory of measure and integration. Probability provides additional perspective and motivates intriguing applications of the theory, which students will explore in their final projects. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights through expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 310 and MATH 323)

Topics in Analysis Seminar
The foundation in analysis covered in MATH 0323 provides the tools necessary to engage a range of important and fascinating topics of both a pure and applied nature. In the first part of this seminar we will collectively work our way through the theory of Lebesgue measure and integration, studying the classical Banach spaces of integrable functions. After this common introduction, students will each choose a project from a range of options that includes topics in functional analysis (e.g., the open mapping theorem, the Hahn-Banach theorem) or more classical real analysis (e.g., Fourier series, orthogonal polynomials, the gamma function). Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0323 or by approval). 3 hrs. sem.