David Dorman
Office
Warner 207
Tel
(802) 443-5554
Email
dorman@middlebury.edu
Office Hours
Mon 3:00-4:30 PM, Tue 10:30 AM-12:00 PM, and by appointment

Courses Taught

Course Description

Independent Study
Approval Required

Terms Taught

Winter 2021, Winter 2022, Winter 2023, Winter 2024, Winter 2025

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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/disc.

Terms Taught

Spring 2021, Spring 2022

Requirements

DED

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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 equivalent) 3 hrs. lect./disc.

Terms Taught

Fall 2021, Fall 2023, Spring 2024, Spring 2025

Requirements

DED

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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

Fall 2022, Spring 2023

Requirements

DED

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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

Spring 2022, Spring 2024

Requirements

DED

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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, Fall 2023, Fall 2024

Requirements

DED

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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

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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 2020, Winter 2021, Spring 2021, Fall 2021, Winter 2022, Spring 2022, Fall 2022, Winter 2023, Spring 2023, Fall 2023, Winter 2024, Spring 2024, Fall 2024, Winter 2025, Spring 2025

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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

Spring 2021

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Course Description

Quadratic Number Fields
In this senior seminar we will explore the algebra and arithmetic of quadratic extensions of the rational numbers. We will study the rings of integers in these extensions, the structure of the unit group in these rings and unique factorization of ideals in Dedekind domains. We will investigate fractional ideals, splitting of primes, the class group and the finiteness of the class number. Some of the ideas and topics introduced are methods, p-adic methods, cyclotomic theory, Dirichlet’s Units Theorem, Quadratic and Biquadratic Reciprocity and quadratic forms. Using these ideas as a springboard students will investigate a topic of their choosing and write their thesis.

Terms Taught

Spring 2025

Requirements

DED

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Areas of Interest

Number Theory, Algebraic Geometry

Academic Degrees

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