# Steve Abbott

## Professor of Mathematics

abbott@middlebury.edu

work(802) 443-2256

By appointment

Warner Hall 503

**Degrees, Specializations & Interests:**

A.B., Colgate University; M.S., Ph.D., University of Virginia; (Functional Analysis, Operator Theory)

Awarded the 2010 Perkins Award for Excellence in Teaching, see story here.

## Courses

Courses offered in the past four years.

▲ *indicates offered in the current term*

▹ *indicates offered in the upcoming term[s]*

##### FYSE 1211 - Godel, Escher, Bach

**Gödel, Escher, Bach**

At the turn of the 20th century, mathematics took an introspective turn when its practitioners attempted to organize reasoning itself into an axiomatic system of theorems and definitions. The results were provocative and ended in a kind of paradox when logician Kurt Gödel proved that all formalized logical systems would necessarily contain some unprovable truths. Reading Douglas Hofstadter's *Gödel, Escher, Bach*, we will discover the connections among seemingly disparate fields of mathematics, visual arts, and music. Our journey will pass through the philosophical worlds of Lewis Carroll, Artificial Intelligence, non-Euclidean geometry, Zen Buddhism, and crash head-on into questions about the nature of human consciousness and creativity. 3 hrs. sem. **CW DED**

Spring 2014

##### FYSE 1504 - Theater and Mathematics

**Stages of Uncertainty: An Exploration of the Intersections of Theater and Mathematics**

During the previous century, a handful of avant-garde playwrights took inspiration from the various revolutions in geometry, logic, and theories of the infinite to challenge the artistic norms of their respective eras. This unexpected synthesis of mathematics and theater eventually found its way to the mainstage with critical successes such as *Arcadia* (1993), *Proof* (2000), and *A Disappearing Number* (2007). Adopting a bold interdisciplinary spirit, we will fearlessly engage the mathematical ideas with the goal of understanding how they contribute to the mission of the artists. Likewise, we will engage the theater in an authentic way, regularly performing scenes in class and, at the semester’s conclusion, mounting a small production. 3 Hrs. Sem. **ART CW**

Fall 2017

##### INTD 0206 - Math/Science Contemp. Theatre

**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)/* **DED LIT**

Spring 2016

##### MATH 0122 - Calculus II

**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. (MATH 0121 or by waiver) 4 hrs. lect./disc. **DED**

Fall 2014, Fall 2015

##### MATH 0323 - Real Analysis ▲

**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. **DED**

Spring 2014, Fall 2014, Spring 2016, Fall 2017, Spring 2018

##### MATH 0423 - Topics in Analysis

**Topics in Analysis**

In this course we will study advanced topics in real analysis, starting from the fundamentals established in MA401. Topics may include: basic measure theory; Lebesgue measure on Euclidean space; the Lebesgue integral; total variation and absolute continuity; basic functional analysis; fractal measures. (MATH 0323 or by waiver) 3 hrs. lect./disc. **DED**

Spring 2015

##### MATH 0500 - Advanced Study ▲ ▹

**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.

Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Winter 2016, Spring 2016, Winter 2017, Fall 2017, Winter 2018, Spring 2018, Fall 2018, Spring 2019

##### MATH 0704 - Senior Seminar

**Senior Seminar**

Each student will explore in depth a topic in pure or applied mathematics, under one-on-one supervision by a faculty advisor. The course culminates with a major written paper and presentation. This experience emphasizes independent study, library research, expository writing, and oral presentation. The goal is to demonstrate the ability to internalize and organize a substantial piece of mathematics. Class meetings include attendance at a series of lectures designed to introduce and integrate ideas of mathematics not covered in the previous three years. Registration is by permission: Each student must have identified a topic, an advisor, and at least one principal reference source. 3 hrs. lect./disc.

Spring 2014

##### MATH 1015 / PHIL 1015 - Philosophy of Mathematics

**Philosophy of Mathematics**

Mathematics is one of humankind’s greatest cognitive endeavors, yet it raises many puzzling questions. Unlike much of our other knowledge, most mathematical knowledge is not established by gathering empirical evidence. So how is mathematical knowledge possible? Unlike most other things we consider to be real, mathematical objects are not physical objects. So in what sense do mathematical objects, such as numbers, exist? What are the foundations of mathematics? Do some mathematical proofs provide greater understanding than others? No prior knowledge of mathematics or philosophy is required. **DED PHL WTR**

Winter 2015

#### Co-Editor *Math Horizons*

Of all of the publications we know *Math Horizons* is the broadest, most creative forum that exists for communicating the culture, characters and folklore of mathematics today's students. Whether helping our students to know and care about the "who" and the "why" of their chosen subject, giving voice to its current practitioners, or shedding light on the interface between mathematics and the larger academic or popular culture, *Math Horizons *always explores its subjects with an inviting tone and trademark accessibility.

For going on fifteen years, *Math Horizons* has exposed undergraduates-and instructors-to the mathematical world beyond the classroom with authentic detail and good humor that make it easy to pick up and irresistible to read.

**Bruce Torrence and Steve Abbott; Co-Editors, Math Horizons**