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.

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).

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 equivalent, or by placement)

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.

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.

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.

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.

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.

Steve Abbott

Reviews and ratings for Steve Abbott at Middlebury College.Steve Abbott teaches Real Analysis, Topics in Analysis Seminar, Calculus II and more.  Explore top rated instructors and find the best for you.Is Steve Abbott good ? Find out on MiddCourses.

This class is hard. Steve is a great guy and super enthusiastic but his exams are very difficult. Expect to spend a lot of time on this class. He is great in office hours and really want you to succeed, but I wouldn't count on an A

Even though this course was difficult, I would take it a hundred more times with Professor Abbott. He always takes the time during office hours to help you understand the material. He is very accommodating and really want to know you as student.  

Such a great class. Professor abbot actually care about the students a lot! He is always present at office hour and he is willing to stay overtime to help us. The course content is hard but the homework is helpful in understanding the content. 