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.

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.

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 Calculus II, Multivariable Calculus, Calculus I and more.  Explore top rated instructors and find the best for you.Is Steve Abbott good ? Find out on MiddCourses.

Professor Abbot makes sure to keep everyone in the class engaged. While he may seem fast paced at times, he does a good job in explaining problems and always has office hours and there is a TA. He understands that a lot of people are taking this class for non math major requirements so he doesn't get too deep in the actual math. More of an overall understanding of calc.

Real analysis is THE infamous course for all math majors. Was it difficult - yes, did a learn a lot - also yes. Definitely if you can take it with Abbott, he is so passionate about the material and his book is just delightful to read. If you have to take it good luck and have fun!

Steve Abbott was the goat. He literally wrote the book we used, and it is genuinely amazing (clear, rigorous, and actually readable). The class was the most fun I have had in a Middlebury math course, but it is also super demanding. To really get everything out of it, plan on 20+ hours a week.