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In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem,...
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In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.
Material Type:
Online Course
Author:
Prof. Steven Kleiman
Date Added:
Oct 20, 2011
Date Modified:
Oct 20, 2011
Peer Review for material titled "18.705 Commutative Algebra"
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The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic...
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The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.
Material Type:
Online Course
Author:
Prof. Abhinav Kumar
Date Added:
Oct 20, 2011
Date Modified:
Oct 20, 2011
Peer Review for material titled "18.727 Topics in Algebraic Geometry: Algebraic Surfaces"
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Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts:...
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Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems.
Material Type:
Online Course
Author:
Prof. Pavel Etingof
Date Added:
Oct 20, 2011
Date Modified:
Oct 20, 2011
Peer Review for material titled "18.735 Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics"
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This course will give a detailed introduction to the theory of tensor categories and review some of its connections to other...
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This course will give a detailed introduction to the theory of tensor categories and review some of its connections to other subjects (with a focus on representation-theoretic applications). In particular, we will discuss categorifications of such notions from ring theory as: module, morphism of modules, Morita equivalence of rings, commutative ring, the center of a ring, the centralizer of a subring, the double centralizer property, graded ring, etc.
Material Type:
Online Course
Author:
Prof. Pavel Etingof
Date Added:
Oct 20, 2011
Date Modified:
Oct 20, 2011
Peer Review for material titled "18.769 Topics in Lie Theory: Tensor Categories"
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This course provides an elementary introduction to number theory with no algebraic prerequisites. Topics include primes,...
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This course provides an elementary introduction to number theory with no algebraic prerequisites. Topics include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions and elliptic curves.
Material Type:
Online Course
Author:
Prof. Martin Olsson
Date Added:
Oct 20, 2011
Date Modified:
Oct 20, 2011
Peer Review for material titled "18.781 Theory of Numbers"
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This course is an introduction to analytic number theory, including the use of zeta functions and L-functions to prove...
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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 prime number theorem in arithmetic progressions).
Material Type:
Online Course
Author:
Prof. Kiran Kedlaya
Date Added:
Oct 20, 2011
Date Modified:
Oct 20, 2011
Peer Review for material titled "18.785 Analytic Number Theory"
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This course is a first course in algebraic topology. The emphasis is on homology and cohomology theory, including cup...
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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 Lefschetz fixed point theorem.
Material Type:
Online Course
Author:
Dr. Tyler Lawson
Date Added:
Oct 20, 2011
Date Modified:
Oct 20, 2011
Peer Review for material titled "18.905 Algebraic Topology"
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In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, the Hurewicz theorem,...
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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 possible further topics at the discretion of the instructor.
Material Type:
Online Course
Author:
Prof. Mark Behrens
Date Added:
Oct 20, 2011
Date Modified:
Oct 20, 2011
Peer Review for material titled "18.906 Algebraic Topology II"
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This course is an introduction to differential geometry. The course itself is mathematically rigorous, but still emphasizes...
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This course is an introduction to differential geometry. The course itself is mathematically rigorous, but still emphasizes concrete aspects of geometry, centered on the notion of curvature.
Material Type:
Online Course
Author:
Prof. Paul Seidel
Date Added:
Oct 20, 2011
Date Modified:
Oct 20, 2011
Peer Review for material titled "18.950 Differential Geometry"
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