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This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linear equations, bases,...
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This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linear equations, bases, linear independence, matrices, determinants, eigenvalues, inner products, quadratic forms, and canonical forms of matrices. Compared with Linear Algebra (18.06), more emphasis is placed on theory and proofs.
Material Type:
Online Course
Author:
Dr. Dan Ciubotaru
Date Added:
Jun 09, 2011
Date Modified:
Jun 09, 2011
Peer Review for material titled "18.700 Linear Algebra"
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In this undergraduate level seminar series, topics vary from year to year. Students present and discuss the subject matter,...
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In this undergraduate level seminar series, topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required. The topic for fall 2008: Computational algebra and algebraic geometry.
Material Type:
Online Course
Author:
Prof. Steven Kleiman
Date Added:
Jun 09, 2011
Date Modified:
Jun 09, 2011
Peer Review for material titled "18.704 Seminar in Algebra and Number Theory: Computational Commutative Algebra and Algebraic Geometry"
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This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie...
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This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.
Material Type:
Online Course
Author:
Prof. Pavel Etingof
Date Added:
Jun 09, 2011
Date Modified:
Aug 31, 2011
Peer Review for material titled "18.712 Introduction to Representation Theory"
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This course covers the fundamental notions and results about algebraic varieties over an algebraically closed field. It also...
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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 varieties and complex analytic varieties.
Material Type:
Online Course
Author:
Prof. Martin Olsson
Date Added:
Jun 09, 2011
Date Modified:
Jun 09, 2011
Peer Review for material titled "18.725 Algebraic Geometry"
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This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with...
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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 understanding of the basic notions and techniques of modern algebraic geometry.
Material Type:
Online Course
Author:
Prof. Kiran Kedlaya
Date Added:
Jun 09, 2011
Date Modified:
Jun 09, 2011
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The topics for this course vary each semester. This semester, the course aims to introduce techniques for studying...
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The topics for this course vary each semester. This semester, the course aims to introduce techniques for studying intersection theory on moduli spaces. In particular, it covers the geometry of homogeneous varieties, the Deligne-Mumford moduli spaces of stable curves and the Kontsevich moduli spaces of stable maps using intersection theory.
Material Type:
Online Course
Author:
Dr. Izzet Coskun
Date Added:
Jun 09, 2011
Date Modified:
Jun 09, 2011
Peer Review for material titled "18.727 Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces"
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This course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for...
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This course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001). Much of the course material is based on Chapter I (first half) and Chapter II of the text. The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces.
Material Type:
Online Course
Author:
Prof. Sigurdur Helgason
Date Added:
Jun 09, 2011
Date Modified:
Jun 09, 2011
Peer Review for material titled "18.755 Introduction to Lie Groups"
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This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers,...
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This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers, Dirichlet's units theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, basic analytic methods, and basic class field theory. An additional theme running throughout the course will be the use of computer algebra to investigate number-theoretic questions; this theme will appear primarily in the problem sets.
Material Type:
Online Course
Author:
Prof. Kiran Kedlaya
Date Added:
Jun 09, 2011
Date Modified:
Jun 09, 2011
Peer Review for material titled "18.786 Topics in Algebraic Number Theory"
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This course introduces topology, covering topics fundamental to modern analysis and geometry. It also deals with subjects...
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This course introduces topology, covering topics fundamental to modern analysis and geometry. It also deals with subjects like topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such as function spaces, metrization theorems, embedding theorems and the fundamental group.
Material Type:
Online Course
Author:
Prof. James Munkres
Date Added:
Jun 09, 2011
Date Modified:
Jun 09, 2011
Peer Review for material titled "18.901 Introduction to Topology"
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In this course, students present and discuss the subject matter with faculty guidance. Topics presented by the students...
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In this course, students present and discuss the subject matter with faculty guidance. Topics presented by the students include the fundamental group and covering spaces. Instruction and practice in written and oral communication are provided to the students.
Material Type:
Online Course
Author:
Prof. Mark Behrens
Date Added:
Jun 09, 2011
Date Modified:
Jun 09, 2011
Peer Review for material titled "18.904 Seminar in Topology"
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