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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...

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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...

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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...

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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...

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

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

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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...

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

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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...

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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...

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

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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...

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

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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...

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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...

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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...

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Discover the derivative---what it is, how to compute it, and when to apply it in solving real world problems. Part 1 of 3.

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Discover the integral---what it is and how to compute it. See how to use calculus to model real world phenomena. Part 2 of 3.

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Master the calculus of curves and coordinate systems; approximate functions with polynomials and infinite series. Part 3 of 3.