Stephen Abbott
he/him
Nathan Beman Professor of Mathematics
- Office
- Warner 211
- Tel
- (802) 443-2256
- abbott@middlebury.edu
- Office Hours
- Monday and Wednesday 3:00-4:00 PM, Tuesday and Thursday 3:30-4:30 PM
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
MATH 0121
Current
Calculus I
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. (MATH 0105 or (M1DP 20 And M2DP 40) by waiver) 4 hrs. lect./disc.
Terms Taught
Requirements
MATH 0122
Upcoming
Calculus II
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. MATH 0121 Or APAB[4] Or APBC[3] Or (M1DP[30] And M2DP[30]) 4 hrs. lect/disc.
Terms Taught
Requirements
MATH 0200
Linear Algebra
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 MATH 0122 Or APAB[4 Or APBC[3] Or IBAN[6] Or (M1DP[40] And M2DP[20]) 3 hrs. lect./disc.
Terms Taught
Requirements
MATH 0223
Upcoming
Multivariable Calculus
Course Description
Multivariable Calculus
The calculus of functions of more than one variable. Introductory vector analysis, analytic geometry of three dimensions, partial differentiation, multiple integration, line integrals, elementary vector field theory, and applications. MATH 0122 Or APBC[4] Or IBAN[6] Or (M1DP[50] And M2DP[10]) 3 hrs. lect./disc.
Terms Taught
Requirements
MATH 0310
Probability
Course Description
Probability
An introduction to the concepts of probability and their applications, covering both discrete and continuous random variables. Probability spaces, elementary combinatorial analysis, densities and distributions, conditional probabilities, independence, expectation, variance, weak law of large numbers, central limit theorem, and numerous applications. (MATH 0223 Concurr And MATH 0224 Concurr) 3 hrs. lect./disc.
Terms Taught
Requirements
MATH 0323
Current
Real Analysis
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 0200 And MATH 0223) Or MATH 0224) 3 hrs. lect./disc.
Terms Taught
Requirements
MATH 0500
Current
Upcoming
Advanced Study
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
MATH 0710
Advanced Probability Seminar
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
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