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 equivalent, or by placement)

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.

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.

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.

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.

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.

Complex Analysis An introduction to functions of a complex variable. Mappings of the complex plane, analytic functions, Cauchy Integral Theorem and related topics.

David Dorman

Reviews and ratings for David Dorman at Middlebury College.David Dorman teaches Calculus II, Abstract Algebra I, Linear Algebra and more.  Explore top rated instructors and find the best for you.Is David Dorman good ? Find out on MiddCourses.

Professor Dorman is really passionate about mathematics and hes also a very understanding person outside of class. There is just a lot of homework and the exams are kind of hard. But this class is very easy if you're on top of your homework!

From an AP Calculus perspective, Calc 2 is more like Calc 1.5, since you're sort of going over differentiation, basic integration, and basic differential equations again. Lectures with Dorman are extremely slow-paced, which ironically makes it hard to keep track of what he's teaching. Only exams and quizzes make up your final grade, and their questions are almost always taken from the textbook homework. Most of the Calc 2 concepts can be learned via self-study.

Dorman is such a funny professor. And you can see that he is extremely in love with math. On top of that, he is always ready to have some other conversations outside of math. Calc 2 itself is very manageable if you are actually interested in math