David Dorman

Professor of Mathematics

 
 work802.443.5554
 Warner Hall 308

Degrees, Specializations & Interests:
B.S., Hobart College; Sc.M., Ph.D., Brown University;
(Number Theory, Algebraic Geometry)

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Courses

Course List: 

Courses offered in the past four years.
indicates offered in the current term
indicates offered in the upcoming term[s]

FYSE1483 - 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

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INTD0500 - Independent Study      

Independent Study
Approval Required

Winter 2016

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MATH0121 - 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

Spring 2013

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MATH0122 - 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

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MATH0200 - 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 2012, Fall 2013, Spring 2016

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MATH0217 - 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

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MATH0223 - 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

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MATH0225 - Topics in Linear Alg & Diff Eq      

Topics in Linear Algebra and Differential Equations
Topics may include diagonalization of matrices, quadratic forms, inner product spaces, canonical forms, the spectral theorem, positive matrices, the Cayley-Hamilton theorem, ordinary differential equations of arbitrary order, systems of first-order differential equations, power series, and eigenvalue methods of solution, applications. (MATH 0200 or by waiver) 3 hrs. lect./disc. DED

Spring 2013

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MATH0241 - 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

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MATH0302 - 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 2012

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MATH0500 - 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 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Winter 2016, Spring 2016, Fall 2016, Spring 2017

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MATH0702 - 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

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MATH0704 - 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

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Department of Mathematics

Warner Hall
303 College Street
Middlebury College
Middlebury, VT 05753