Emily Proctor
Associate Professor of Mathematics
eproctor@middlebury.edu
work(802) 443-5954
Spring 2020: Monday, Tuesday, Thursday 2:15-3:30, and by appointment
Warner Hall 312
Degrees, Specializations & Interests:
A.M. , Bowdoin College; A.M., Ph.D. Dartmouth College;
(Riemannian Geometry)
Courses
Courses offered in the past four years.
▲ indicates offered in the current term
▹ indicates offered in the upcoming term[s]
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
Fall 2018
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 2016, Fall 2019
MATH 0223 - Multivariable Calculus ▲ ▹
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 and MATH 0200 or by waiver) 3 hrs. lect./disc. DED
Spring 2017, Spring 2019, Spring 2020, Fall 2020
MATH 0230 - Euc and Non-Euc Geometries
Euclidean and Non-Euclidean Geometries
In roughly 300 BCE, Euclid set down his axioms of geometry which subsequently became the standard by which people understood the mathematics of the world around them. In the first half of the 19th century, mathematicians realized, however, that they could remove one of Euclid’s axioms, the one known as the “parallel postulate,” and still produce logically consistent examples of geometries. These new geometries displayed behaviors that were wildly different from Euclidean geometry. In this course we will study examples of these revolutionary non-Euclidean geometries, with a focus on Klein's Erlangen Program, which is a modern way of understanding them. (MATH 0200 or by waiver) 3 hrs. lect. DED
Spring 2019
MATH 0302 - Abstract Algebra I
Abstract Algebra
Groups, subgroups, Lagrange's theorem, homomorphisms, normal subgroups and quotient groups, rings and ideals, integral domains and fields, the field of quotients of a domain, the ring of polynomials over a domain, Euclidean domains, principal ideal domains, unique factorization, factorization in a polynomial ring. (MATH 0200 or by waiver) 3 hrs. lect./disc. DED
Fall 2016, Fall 2018, Fall 2019
MATH 0335 - Differential Geometry ▹
Differential Geometry
This course will be an introduction to the concepts of differential geometry. For curves in space, we will discuss arclength parameterizations, Frenet formulas, curvature, and torsion. On surfaces, we will explore the Gauss map, the shape operator, and various types of curvature. We will apply our knowledge to understand geodesics, metrics, and isometries of general geometric spaces. If time permits, we will consider topics such as minimal surfaces, constant curvature spaces, and the Gauss-Bonnet theorem. (MATH 0200 and MATH 0223) 3 hr. lect./disc. DED
Fall 2020
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 2016, Winter 2017, Spring 2017, Fall 2017, Winter 2018, Fall 2018, Winter 2019, Spring 2019, Fall 2019, Winter 2020, Spring 2020, Fall 2020, Spring 2021
MATH 0701 - Galois Theory ▲
Galois Theory
This course is a tutorial in Galois theory for students who have completed Abstract Algebra. Starting from the concept of a ring, we will develop the theory of polynomial rings over fields, and use this to carry out an in-depth investigation of field extensions. Our work together will culminate in proving the fundamental theorem of Galois theory. Working independently and in small groups, students will explore related areas of algebra and communicate their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0302) 3 hrs. sem. DED
Spring 2020