Steve Abbott
Office
Warner 211
Tel
(802) 443-2256
Email
abbott@middlebury.edu
Office Hours
On leave academic year 2022/2023
Additional Programs
Academic Affairs Mathematics

I have been a professor of mathematics at Middlebury since 1993.  I’ve also had visiting appointments at Saint Olaf College, the University of Virginia, CRASSH at Cambridge University, and the University of Otago in Dunedin, New Zealand.  In the past, I’ve served as co-editor of Math Horizons and am currently co-editing the undergraduate series Texts for Quantitative Critical Thinking, published by Springer. I am also a program chair for The Bridges Organization, an interdisciplinary group dedicated to the intersections of mathematics and art.  

Courses Taught

Course Description

Mathematics and Science as Art in Contemporary Theatre
In Tom Stoppard’s Arcadia, the playwright somewhat miraculously manages to use the tension between Euclidean geometry and modern fractal geometry to explore the classical/romantic dichotomy in literature, science, art, and human personality. This is just one example of how acclaimed playwrights such as Stoppard, Rinne Groff, Michael Frayn, Simon McBurney, and others have effectively incorporated mathematical and scientific themes for artistic purposes. Our goal is to explore this relatively recent phenomenon in theater with an eye toward understanding the complementary ways in which science and art aim to seek out their respective truths. The course is intended to be experiential in both theatrical and scientific terms; our explorations will include the staging of scenes and discussions of theatre as performance; we will also undertake labs in the various mathematical sciences related to the material within the plays. (Dramatic Literature)/

Terms Taught

Spring 2020

Requirements

DED, LIT

View in Course Catalog

Course Description

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.

Terms Taught

Fall 2019, Fall 2020, Spring 2021

Requirements

DED

View in Course Catalog

Course Description

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.

Terms Taught

Spring 2019

Requirements

DED

View in Course Catalog

Course Description

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.

Terms Taught

Spring 2020

Requirements

DED

View in Course Catalog

Course Description

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.

Terms Taught

Fall 2019, Fall 2020, Fall 2021, Spring 2022

Requirements

DED

View in Course Catalog

Course Description

Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

Terms Taught

Spring 2019, Fall 2019, Winter 2020, Spring 2020, Fall 2020, Winter 2021, Spring 2021, Fall 2021, Winter 2022, Spring 2022, Fall 2022, Winter 2023, Fall 2023

View in Course Catalog

Course Description

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)

Terms Taught

Spring 2022

View in Course Catalog

Course Description

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.

Terms Taught

Spring 2019

View in Course Catalog

Areas of Interest

Real and functional analysis

Intersections of mathematics and the arts, particularly with theater

Academic Degrees

A.B., Colgate University (1986)

M.S., Ph.D., University of Virginia (1993)

 

Selected Publications

Understanding Analysis, Springer 2015

The Proof Stage, Princeton University Press, 2023