# David Dorman

## Professor of Mathematics

dorman@middlebury.edu

work802.443.5554

Mon 4:00-5:30; Tue 9:30-11:30; Wed 3:30-4:30 and by appointment

Warner Hall 308

**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 2016

##### INTD 0500 - Independent Study ▹

##### 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 2017

##### 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./disc. **DED**

Fall 2014, Spring 2015, Spring 2016, Spring 2017

##### 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**

Fall 2013, Spring 2016, Spring 2018

##### MATH 0217 - Elements of Math Bio & Ecol

**Elements of Mathematical Biology and Ecology**

Mathematical modeling has become an essential tool in biology and ecology. In this course we will investigate several fundamental biological and ecological models. We will learn how to analyze existing models and how to construct new models. We will develop ecological and evolutionary models that describe how biological systems change over time. Models for population growth, predator-prey interactions, competing species, the spread of infectious disease, and molecular evolution will be studied. Students will be introduced to differential and difference equations, multivariable calculus, and linear and non-linear dynamical systems. (MATH 0121 or by waiver) **DED**

Fall 2013

##### 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**

Fall 2016, Fall 2017

##### 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) **CW DED**

Spring 2015

##### 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**

Spring 2017

##### 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

##### 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.

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

##### MATH 0702 - Senior Seminar

**Advanced Algebra and Number Theory Seminar**

This course is a tutorial in Advanced Abstract Algebra and Number Theory for students who have completed work in either subject. Starting from elementary results in linear algebra, we will explore the fundamental mathematical ideas underlying field extensions, constructability, unique factorization, Euclidean fields, and Galois theory. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0241 or MATH 0302; Approval required) 3 hrs. sem.

Fall 2015