Middlebury

 

Emily Proctor

Associate Professor of Mathematics

Email: 
Phone: work802.443.5954
Office Hours: Tu 11-12, W 11-12, Th 2:30-4:00, and by appointment
Download Contact Information

Degrees, Specializations & Interests:
A.M. , Bowdoin College; A.M., Ph.D. Dartmouth College;
(Riemannian Geometry)

Website

 

Courses


indicates offered in the current term
indicates offered in the upcoming term[s]

FYSE 1423 - 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

More Information »

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 2011, Spring 2012, Fall 2013

More Information »

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 2011, Spring 2012, Spring 2014, Spring 2015

More Information »

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 2011, Spring 2013

More Information »

MATH 0323 - 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

More Information »

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

Spring 2011, Spring 2013, Fall 2014

More Information »

MATH 0402 - 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

More Information »

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.

Spring 2011, Fall 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015

More Information »

MATH 0704 - 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

More Information »

MATH 1004 - The Shape of Space      

The Shape of Space
We know that the earth we live on is a sphere, but consider the three-dimensional shape of the universe. Does it go on forever, or could it wrap back on itself in some way? In this course we will consider the shape of space. We will learn how topologists and geometers visualize three-dimensional spaces, with a goal of learning about the eight three-dimensional shapes that form the building blocks of all three-dimensional spaces. In the process, we will learn about the celebrated Poincare Conjecture. The ideas we encounter will be deep, but we will study them in a hands-on way.

DED WTR

Winter 2011

More Information »