Teaching that I have done at ULL and at Wesleyan and Purdue Universities
(ULL) Fall, 2008: Math 537 - Algebraic Topology. Textbook: Homology theory, 2nd edition, by James W. Vick. In this course, we carefully covered the first two chapters, part of chapter three, and, additionally, we outlined Appendix I.
(ULL) Fall, 2008: Math 250 (Section 010) - Survey of Calculus. A description is given five entries below this one.
(ULL) Fall, 2008: Math 250 (Section 008) - Survey of Calculus. A description is given four entries below this one.
(ULL) Spring, 2008: Math 536 - Topology. Textbook: Topology, 2nd edition, by Munkres. This course
is the sequel to 535 (which is described just two entries below this one).
(ULL) Spring, 2008: Math 250 - Survey of Calculus. A description is given two entries below this one.
(ULL) Fall, 2007: Math 535 - Topology. Textbook: Topology, 2nd edition, by Munkres. This is the first semester course of a year-long graduate sequence in topology. The course is primarily for students doing a Ph.D., although some students who are currently pursuing only a Master's degree take this course.
(ULL) Fall, 2007: Math 250 - Survey of Calculus. Textbook: Applied Calculus, 3rd edition, by Hughes-Hallett, Gleason, Lock, Flath, et al. Common majors of students in this course include accounting, business management, finance, and marketing.
(Wesleyan) Spring, 2007: Math 524 - Introductory Algebraic Topology. Textbook: Topology, 2nd edition, by Munkres. This is the second-semester course in topology for first-year graduate students.
(Wesleyan) Spring, 2007: Math 221 - Vectors and Matrices. Please drop down two entries for a description of this course.
(Wesleyan) Fall, 2006: Math 229 - Ordinary Differential Equations. Textbook: Elementary Differential Equations with Boundary Value Problems, 5th edition, by Edwards and Penney. Whenever possible, proofs were given, and, on the two midterms and the final, the students had to do some proofs.
(Wesleyan) Fall, 2006: Math 221 - Vectors and Matrices. Textbook: Elementary Linear
Algebra, 8th edition, by Anton. This class consisted of 29 students, including freshmen, sophomores, juniors, and seniors, with freshman being the most common class. Because Wesleyan is a top ten liberal arts college, even students that are not math majors should be exposed to careful proofs and they ought to have some experience with writing proofs on their own. Thus, whenever possible, we proved our theorems, and, on each exam and the final, students were expected to do at least one or two proofs.
(Purdue) Spring, 2006: Math 341 - Introduction to Real Analysis. Textbook: "Understanding Analysis," by Stephen Abbott.
(Purdue) Fall, 2005: Math 510 - Vector Calculus. This course is for
students who are studying for a Master's degree in engineering. The goal of
the course is to study Green's Theorem, Stokes' Theorem, and Gauss' Theorem
carefully. For example, by mid-November, the high point of the course was
that we gave proofs of versions of Green's and Stokes' Theorems that,
hopefully, all students understood.
(Purdue) Spring, 2005: Math 453 - Introduction to Abstract Algebra. Two sections of this course. Textbook: "Abstract Algebra - A Geometric Approach," by Theodore Shifrin. We studied modular arithmetic, rings, ideals, polynomial rings, the concrete construction of splitting fields for polynomials in F[x], groups, cyclic groups.
(Purdue) Fall, 2004: Math 271 - Several Variable Calculus. See below for a description of this course.
(Purdue) Spring, 2004: Math 453 - Elements of Algebra, I. Two sections of this course; three lectures per week. Textbook: "Introductory Modern Algebra, A Historical Approach," by Saul Stahl. Audience: primarily juniors and seniors majoring in math, math education, and computer science. We studied roots of unity, solvability by radicals for equations of low degree, modular arithmetic, finite fields, polynomials, groups, and other topics.
(Purdue) Fall, 2003: Math 271 - Several Variable Calculus. Four lectures per week, with one discussion section (led by a T.A.). This course is for freshmen who have already had one year of calculus. Many of the students are engineering majors, and many of the best engineering students take this course.