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Course

Code:	MATH 122
Subject:	Mathematics
Topic:	Abstract Algebra
Views:	50,938

Educator

Name:	Harvard University (Harvard)
Type:	University

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Instructor

Name

Benedict Gross

Abstract Algebra: Theory of Groups and Vector Spaces

Video Lectures

Displaying all 38 video lectures.

Lecture 1 Play Video	Review: Linear algebra & Definition of groups Week 1: Review of linear algebra. Groups. Examples of groups. Basic properties and constructions.This video: Introduction to the course; Review: Linear algebra; Definition of groups
Lecture 2 Play Video	Symmetric groups, Subgroups of ℤ & Cyclic subgroups Topics: Administrative notes; Generalities on groups; Symmetric groups on n letters; A stabilizer subgroup; The subgroups of ℤ; Cyclic subgroups gen by elementNotes for this lecture:
Lecture 3 Play Video	Isomorphisms & Homomorphisms Topics: The story so far; Isomorphisms; Homomorphisms; Images
Lecture 4 Play Video	Kernels, Normality, Centers and Inner Autos Week 2: Permutations. Cosets, Z/nZ. Topics in this video: Review, kernels, normality; Examples; Centers and inner autos
Lecture 5 Play Video	Equivalence Relations & Cosets Topics: Equivalence relations; Cosets; Examples
Lecture 6 Play Video	Congruence mod n Topics: Congruence mod n; (Z/nZ)*
Lecture 7 Play Video	Quotients Week 3: Quotient groups, first isomorphism theorem. Abstract fields, abstract vectorspaces. Construction and invariants of vectorspaces.
Lecture 8 Play Video	More on Quotients & Vectorspaces
Lecture 9 Play Video	More on Vectorspaces Week 3: Quotient groups, first isomorphism theorem. Abstract fields, abstract vectorspaces. Construction and invariants of vectorspaces.This video: ...ContinuedNotes for this lecture: http://www.extension.harvard.edu/sites/default/files/openlea... lectures are from the Harvard Faculty of Arts and Sciences course Mathematics 122, which was offered as an online course at the Extension School. View Complete course (Syllabus, Notes, Problem Sets, etc) at: http://www.extension.harvard.edu/open-learning-initiative/ab...
Lecture 10 Play Video	Bases and vectorspaces; Matrices and linear transfer Week 4: Abstract linear operators and how to calculate with them. Properties and construction of operators.
Lecture 11 Play Video	Bases & Matrices
Lecture 12 Play Video	Eigenvalues and Eigenvectors
Lecture 13 Play Video	Review for midterm & Orthogonal groups
Lecture 14 Play Video	Orthogonal Groups & Geometry
Lecture 15 Play Video	Finite groups of motions
Lecture 16 Play Video	Discrete groups of motions
Lecture 17 Play Video	Abstract group actions Week 6: Isometries of plane ﬁgures.
Lecture 18 Play Video	Group actions Week 6: Isometries of plane ﬁgures. Cyclic and dihedral groups. Finite and discrete subgroups of symmetry groups.This video: Group actionsNotes for this lecture: http://www.extension.harvard.edu/sites/default/files/openlea... lectures are from the Harvard Faculty of Arts and Sciences course Mathematics 122, which was offered as an online course at the Extension School. View Complete course (Syllabus, Notes, Problem Sets, etc) at: http://www.extension.harvard.edu/open-learning-initiative/ab...
Lecture 19 Play Video	Group actions II
Lecture 20 Play Video	Basic properties and constructions of group actions Week 7: Group actions. Basic properties and constructions. Groups acting on themselves by left multiplication. Groups acting on themselves by conjugation.
Lecture 21 Play Video	Groups acting on themselves by left multiplication
Lecture 22 Play Video	Groups acting on themselves by conjugation
Lecture 23 Play Video	Alternating group structure Week 8: A5 and the symmetries of an icosahedron. Sylow theorems. Study of permutation groups
Lecture 24 Play Video	Ring Theory Week 8: A5 and the symmetries of an icosahedron. Sylow theorems. Study of permutation groups
Lecture 25 Play Video	Ring Theory II Week 8: A5 and the symmetries of an icosahedron. Sylow theorems. Study of permutation groups
Lecture 26 Play Video	Examples of Rings Week 9: Rings. Examples of rings. Basic properties and constructions.
Lecture 27 Play Video	Examples of Rings II
Lecture 28 Play Video	Basic properties and constructions of Rings
Lecture 29 Play Video	More on Rings
Lecture 30 Play Video	Extensions of Rings: Quotient rings
Lecture 31 Play Video	Extensions of Rings: Integral domains
Lecture 32 $Extensions of Rings: Fields of fractions$ Play Video	Extensions of Rings: Fields of fractions
Lecture 33 Play Video	Gauss’ lemma
Lecture 34 Play Video	Eisenstein’s criterion Week 12: Euclidean domains, PIDs, UFDs. Gauss' lemma. Eisenstein's criterion. Algebraic integers.
Lecture 35 Play Video	Algebraic integers Week 12: Euclidean domains, PIDs, UFDs. Gauss' lemma. Eisenstein's criterion. Algebraic integers.
Lecture 36 Play Video	Dedekind domains & Ideal class groups Week 13: Structure of ring of integers in a quadratic ﬁeld. Dedekind domains. Ideal class groups.
Lecture 37 Play Video	Review 1
Lecture 38 Play Video	Review 2