Description:This course was designed for students with a strong interest in advanced mathematics problem solving and contains problem sets covering a broad range of topics, including the pigeonhole principle, probability theory, and the greatest integer function. Students who take the course at MIT are expected to participate in the William Lowell Putnam Mathematical Competition, a nationwide competition for undergraduate students, and the course contains links to this and other national and international mathematics competitions.

Description:This course provides an introduction to discrete mathematics, with a focus on topics that are relevant for computer science and engineering. Material is presented through a complete set of course notes and lecture slides, as well as in-class problems, problem sets, and exams, all with solutions. Topics covered in the course include sets, proofs, relations, modular arithmetic, graphs, state machines, counting, and discrete probability theory.

Description:This course provides an introduction to calculus of functions of a single variable, including differentiation and integration with applications. Material is presented through a complete set of lecture notes, a supplementary course reader, and links to java applets which demonstrate topics throughout calculus. Also included are exams and practice exams with solutions.

Description:This course introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. Included is a complete set of lecture notes, recitations, assignments with solutions, exams with solutions, video and java demonstrations, and a wealth of related resources for probability and statistics.

Description:A course in vector and multivariable calculus, with material presented through a course reader, problem sets, and exams with solutions. Topics covered include vectors, matrices, partial derivatives, double integrals, triple integrals, and vector calculus in two and three dimensions.

Description:This course provides an introduction to matrix theory and linear algebra, using a complete set of video lectures, java applets, problem sets, and exams. Emphasis is on topics that are useful in a broad range of disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.