David Dorman
Office
Warner 207
Tel
(802) 443-5554
Email
dorman@middlebury.edu
Office Hours
Fall 2022: Monday 3:30 PM - 5:00 PM, Tuesday 10:30 AM - Noon, and by appointment
Additional Programs
Mathematics

Courses Taught

Course Description

The Magic of Numbers
Number theory—the study of patterns, symmetries, properties, and the power of numbers—has caught the popular imagination. Youngsters and adults have toyed with numbers, looked for patterns, and played games with numbers throughout millennia. A characteristic of number theory is that many of its problems are very easy to state. In fact, many of these problems can be understood by high school mathematics students. The beauty of these problems is that modern mathematics flows from their study. Students will experiment with numbers to discover patterns, make conjectures and prove (or disprove) these conjectures. 3 hrs. sem.

Terms Taught

Fall 2019

Requirements

CW, DED

View in Course Catalog

Course Description

Independent Study
Approval Required

Terms Taught

Winter 2019, Winter 2020, Winter 2021, Winter 2022, Winter 2023

View in Course Catalog

Course Description

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. 4 hrs. lect.

Terms Taught

Fall 2018, Spring 2020, Spring 2021, Spring 2022

Requirements

DED

View in Course Catalog

Course Description

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.

Terms Taught

Spring 2019, Fall 2019, Fall 2021

Requirements

DED

View in Course Catalog

Course Description

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.

Terms Taught

Spring 2019, Fall 2022, Spring 2023

Requirements

DED

View in Course Catalog

Course Description

Elementary Number Theory
Divisibility and prime factorization. Congruences; the theorems of Lagrange, Fermat, Wilson, and Euler; residue theory; quadratic reciprocity. Diophantine equations. Arithmetic functions and Mobius inversion. Representation as a sum of squares. (MATH 0122 or by waiver)

Terms Taught

Fall 2018, Spring 2022

Requirements

DED

View in Course Catalog

Course Description

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.

Terms Taught

Fall 2021, Fall 2022

Requirements

DED

View in Course Catalog

Course Description

Complex Analysis
An introduction to functions of a complex variable. Mappings of the complex plane, analytic functions, Cauchy Integral Theorem and related topics. (MATH 0223 or by waiver) 3 hrs. lect./disc.

Terms Taught

Spring 2023

Requirements

DED

View in Course Catalog

Course Description

Fundamentals of Algebraic Geometry
Algebraic geometry is one of the oldest areas of mathematics, yet it is thoroughly modern and active. It is the study of geometric spaces locally defined by polynomial equations. The aim of this course is to introduce students to some basic notions and ideas in algebraic geometry. We will study affine and projective spaces, affine and projective curves, singularities, intersection theory, Hilbert’s Nullstellensatz, Bezout’s Theorem, and the arithmetic of elliptic curves. There will be an emphasis on examples and problem solving. (MATH 302) 3 hrs. lect.

Terms Taught

Spring 2020

Requirements

DED

View in Course Catalog

Course Description

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.

Terms Taught

Fall 2018, Winter 2019, Spring 2019, Fall 2019, Winter 2020, Spring 2020, Fall 2020, Winter 2021, Spring 2021, Fall 2021, Winter 2022, Spring 2022, Fall 2022, Winter 2023, Spring 2023

View in Course Catalog

Course Description

Advanced Topics in Algebra: The Arithmetic of Elliptic Curves
The study of elliptic curves has fascinated mathematicians for the last 120 years.
It is the meeting place of algebra, number theory, and analysis. There's something for everyone. It combines hands-on computational with deep theoretical implications. Elliptic curves played a central role in Wiles' proof of Fermat's Last Theorem. They are used in factoring algorithms and elliptic curve cryptosystems have become the backbone of credit card and internet transactions. If you want to become rich and famous The Clay Institute has put a $1 million bounty on the Birch and Swinnerton-Dyer Conjecture which connects the algebraic and analytic theory of elliptic curves. (MATH 0302; Approval required) 3 hrs. sem.

Terms Taught

Fall 2018, Spring 2021

View in Course Catalog

Areas of Interest

Number Theory, Algebraic Geometry

Academic Degrees

B.S., Hobart College; Sc.M., Ph.D., Brown University