MIT OpenCourseWare: New Courses in Mathematics

18.100C Real Analysis (MIT)

Seidel, Paul — 2013-04-11T13:35:39+05:00

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.The three options for 18.100:Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible.Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology.Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication. This fulfills the MIT CI requirement.

18.S997 Introduction To MATLAB Programming (MIT)

Farjoun, Yossi — 2013-01-28T16:12:18+05:00

This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB® in particular.

18.781 Theory of Numbers (MIT)

Kumar, Abhinav — 2013-01-22T16:45:18+05:00

This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.

18.100A Introduction to Analysis (MIT)

Mattuck, Arthur — 2013-01-16T10:12:26+05:00

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.

18.337J Parallel Computing (MIT)

Edelman, Alan — 2012-12-21T14:42:47+05:00

This is an advanced interdisciplinary introduction to applied parallel computing on modern supercomputers. It has a hands-on emphasis on understanding the realities and myths of what is possible on the world's fastest machines. We will make prominent use of the Julia Language software project.

18.330 Introduction to Numerical Analysis (MIT)

Demanet, Laurent — 2012-12-14T16:24:02+05:00

This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra.

18.904 Seminar in Topology (MIT)

Snowden, Andrew — 2012-12-13T09:13:53+05:00

This course is a seminar in topology. The main mathematical goal is to learn about the fundamental group, homology and cohomology. The main non-mathematical goal is to obtain experience giving math talks.

18.152 Introduction to Partial Differential Equations (MIT)

Speck, Jared — 2012-06-28T08:14:02+05:00

This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.

18.03SC Differential Equations (MIT)

Mattuck, Arthur — 2012-02-08T14:08:08+05:00

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.

18.06SC Linear Algebra (MIT)

Strang, Gilbert — 2012-01-24T16:18:50+05:00

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.

18.024 Multivariable Calculus with Theory (MIT)

Breiner, Christine — 2011-12-08T10:51:15+05:00

This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.

18.440 Probability and Random Variables (MIT)

Sheffield, Scott — 2011-12-07T11:34:46+05:00

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

18.702 Algebra II (MIT)

Artin, Michael — 2011-10-28T12:57:09+05:00

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

18.701 Algebra I (MIT)

Artin, Michael — 2011-10-28T12:56:15+05:00

This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.

18.022 Calculus of Several Variables (MIT)

McKernan, James — 2011-06-08T13:16:40+05:00

This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.

18.335J Introduction to Numerical Methods (MIT)

Johnson, Steven G. — 2011-06-08T13:15:01+05:00

This course offers an advanced introduction to numerical linear algebra. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra software. Problem sets require some knowledge of MATLAB®.

18.303 Linear Partial Differential Equations: Analysis and Numerics (MIT)

Johnson, Steven G. — 2011-06-08T13:13:19+05:00

This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems.

18.100B Analysis I (MIT)

Wehrheim, Katrin — 2011-06-02T12:47:08+05:00

Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

18.014 Calculus with Theory (MIT)

Breiner, Christine — 2011-05-18T13:00:27+05:00

18.014, Calculus with Theory, covers the same material as 18.01 (Single Variable Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus.

18.03 Differential Equations (MIT)

Miller, Haynes — 2011-03-16T14:26:50+05:00

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.