# Steve Abbott

## Professor of Mathematics

abbott@middlebury.edu

work802.443.2256

**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

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

**Mathematics and Science as Art in Contemporary Theatre**

In Tom Stoppard’s Jumpers, philosopher George Moore employs a list of mathematical arguments to make his case for the existence of a moral God. George’s confused allusions to the paradoxes of Zeno and Bertrand Russell form an interesting backdrop to a host of moral questions that include an astronaut stranded on the moon, the installation of an atheist as Archbishop of Canterbury and the mysterious circumstances surrounding the dead body of George’s debating partner concealed in the next room. This is just one example of how acclaimed playwrights such as Tom Stoppard, Rinne Groff, Michael Frayn, and others have effectively explored mathematical and scientific themes for artistic purposes. Through readings and exercises, and by conducting labs and staging scenes, this class will gain some first-hand insight into the complementary ways in which science and art aim to seek out their respective truths. **DED LIT**

Fall 2011, Fall 2013

##### MATH 0121 - Calculus I

**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. **DED**

Spring 2012, Spring 2013

##### 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 2011, Fall 2013, Fall 2014, Fall 2015

##### MATH 0200 - Linear Algebra

**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. **DED**

Fall 2012, Spring 2013

##### 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**

Fall 2012, Spring 2014, Fall 2014

##### 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.

Fall 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Spring 2016

##### 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 1006 - Heart of Mathematics

**The Heart of Mathematics**

Wrestling with the infinite, tiling a floor, predicting the shape of space, imagining the fourth dimension, untangling knots, making pictures of chaos, conducting an election, cutting a cake fairly; all of these topics are part of the landscape of mathematics, although they are largely excluded from the calculus-centric way that the subject is traditionally presented. Following the acclaimed text, *The Heart of Mathematics*, by Ed Burger and Michael Starbird, we will dive headfirst into ideas that reveal the beauty and diverse character of pure mathematics, employing effective modes of reasoning that are useful far beyond the boundaries of the discipline. **DED WTR**

Winter 2012

##### 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**