# David Dorman

## Professor of Mathematics

dorman@middlebury.edu

work(802) 443-5554

Fall 2020: Academic Leave

75 Shannon 102K

**Degrees, Specializations & Interests:**

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

(Number Theory, Algebraic Geometry)

## Courses

Courses offered in the past four years.

▲ *indicates offered in the current term*

▹ *indicates offered in the upcoming term[s]*

##### FYSE 1483 - The Magic of Numbers

**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. **CW DED**

Fall 2019

##### INTD 0500 - Independent Study ▹

**Independent Study**

Approval Required

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

##### MATH 0122 - Calculus II ▲

**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. (MATH 0121 or by waiver) 4 hrs. lect. **DED**

Fall 2018, Spring 2020, Spring 2021, Spring 2022

##### 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**

Spring 2018, Spring 2019, Fall 2019, Fall 2021

##### 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 2019, Fall 2022

##### MATH 0241 - Elementary Number Theory ▲

**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) **DED**

Fall 2018, Spring 2022

##### 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 2021, Fall 2022

##### MATH 0338 - Fundamental Algebraic Geometry

**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. **DED**

Spring 2018, Spring 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.

Spring 2018, 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

##### MATH 0702 - Adv Topics Algebra/Ellip Curve

**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.

Fall 2018, Spring 2021