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Advanced Analytic Methods in Science and Engineering

from MIT OpenCourseware (Free)

Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical...

Advanced Calculus for Engineers

from MIT OpenCourseware (Free)

This course analyzes the functions of a complex variable and the calculus of residues. It also covers subjects such as ordinary differential equations, partial differential...

Advanced Complexity Theory

from MIT OpenCourseware (Free)

The topics for this course cover various aspects of complexity theory, such as  the basic time and space classes, the polynomial-time hierarchy and the randomized classes...

Advanced Partial Differential Equations with Applications

from MIT OpenCourseware (Free)

The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on...

Algebra I

from MIT OpenCourseware (Free)

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

Algebra II

from MIT OpenCourseware (Free)

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic...

Algebraic Combinatorics

from MIT OpenCourseware (Free)

This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics...

Algebraic Geometry

from MIT OpenCourseware (Free)

This course covers the fundamental notions and results about algebraic varieties over an algebraically closed field. It also analyzes the relations between complex algebraic...

Algebraic Geometry

from MIT OpenCourseware (Free)

This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an...

Algebraic Geometry

from MIT OpenCourseware (Free)

Algebraic Topology

from MIT OpenCourseware (Free)

This course is a first course in algebraic topology. The emphasis is on homology and cohomology theory, including cup products, Kunneth formulas, intersection pairings, and the...

Algebraic Topology II

from MIT OpenCourseware (Free)

In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and...

Algorithmic Aspects of Machine Learning

from MIT OpenCourseware (Free)

This course is organized around algorithmic issues that arise in machine learning. Modern machine learning systems are often built on top of algorithms that do not have provable...

Analysis I

from MIT OpenCourseware (Free)

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

Analysis II

from MIT OpenCourseware (Free)

This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis. The first half of the course covers multivariable calculus. The rest of the...

Analytic Number Theory

from MIT OpenCourseware (Free)

This course is an introduction to analytic number theory, including the use of zeta functions and L-functions to prove distribution results concerning prime numbers (e.g., the...

Behavior of Algorithms

from MIT OpenCourseware (Free)

This course is a study of Behavior of Algorithms and covers an area of current interest in theoretical computer science. The topics vary from term to term. During this term, we...

Calculus of Several Variables

from MIT OpenCourseware (Free)

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.

Calculus with Applications

from MIT OpenCourseware (Free)

This course features a collection of learning tools, including a set of interactive Java Applets , a glossary of calculus terminology,...

Calculus with Theory

from MIT OpenCourseware (Free)

This is the first course in a two-part sequence on Calculus with Theory, 18.014 and 18.024 . The course is taught using the textbook by...