# Emily Proctor

## Associate Professor of Mathematics

eproctor@middlebury.edu

work802.443.5954

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]*

##### FYSE1423 - The Story of Geometry

**The Story of Geometry**

The field of geometry is thousands of years old and over time has undergone a number of revolutionary changes. In this seminar we will study geometry through a historical lens. Beginning with the axiomatic geometry of Euclid, we will trace the development of the subject, learning how the realization in the mid-19th century that one of Euclid’s axioms could be dropped led to the exciting discovery of hyperbolic and spherical geometries. We will learn how these geometries relate to the modern notions of manifolds and curvature, concluding with a discussion of Perelman’s breakthrough proof of the century-old Poincaré Conjecture. 3 hrs. sem. **CW DED**

Fall 2014

##### MATH0121 - 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 2013

##### MATH0200 - 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

##### MATH0223 - 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 2014, Spring 2015, Spring 2017

##### MATH0302 - 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**

Spring 2013, Fall 2016

##### MATH0323 - 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 2013

##### MATH0335 - 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**

Spring 2013, Fall 2014

##### MATH0402 - Topics In Algebra

**Topics in Algebra**

A further study of topics from MATH 0302. These may include field theory, algebraic extension fields, Galois theory, solvability of polynomial equations by radicals, finite fields, elementary algebraic number theory, solution of the classic geometric construction problems, or the classical groups. (MATH 0302 or by waiver) 3 hrs. lect./disc. **DED**

Spring 2014

##### MATH0500 - 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.

Winter 2013, Spring 2013, Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Winter 2016, Fall 2016, Winter 2017, Spring 2017, Fall 2017, Spring 2018

##### MATH0704 - 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 2013