Harvard Math e222 - Abstract Algebra

Algebra is the language of modern mathematics. This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields. The recorded lectures are from the Harvard Faculty of Arts and Sciences course Mathematics 122, which was offered as an online course at the Extension School.

P/S: The lecture videos are in Quicktime (.mov) format, except for Lecture 29 which I was only able to get as an mp3 audio lecture. There are 36 lectures, 36 lecture notes, and two review sessions.

Week 1 (Lectures 01-03)

Review of linear algebra. Groups. Examples of groups. Basic properties and constructions.

Week 2 (Lecture 04-06)

Permutations. Cosets, Z/nZ.

Week 3 (Lecture 07-09)

Quotient groups, first isomorphism theorem. Abstract fields, abstract vectorspaces. Construction and invariants of vectorspaces.

Week 4 (Lecture 10-13)

Abstract linear operators and how to calculate with them. Properties and construction of operators.

Week 5 (Lecture 14-16)

Orthogonal groups.

Week 6 (Lecture 17-19)

Isometries of plane figures. Cyclic and dihedral groups. Finite and discrete subgroups of symmetry groups.

Week 7 (Lecture 20-22)

Group actions. Basic properties and constructions. Groups acting on themselves by left multiplication. Groups acting on themselves by conjugation.

Week 8 (Lecture 23-25)

A5 and the symmetries of an icosahedron. Sylow theorems. Study of permutation groups.

Week 9 (Lecture 26-28)

Rings. Examples of rings. Basic properties and constructions.

Week 10 (Lecture 29) [Audio Only]

Quotient rings, extensions of rings. Integral domains, fields of fractions.

Week 11 (Lecture 30-32)

Special lecture. (Wow! So descriptive. Umm. I may re-watch these and fill this in later).

Week 12 (Lecture 33-35)

Euclidean domains, PIDs, UFDs. GaussвЂ™ lemma. EisensteinвЂ™s criterion. Algebraic integers.

Week 13 (Lecture 36)

Structure of ring of integers in a quadratic field. Dedekind domains. Ideal class groups.

Week 14 (Final Two Review Lectures)

Wrap-up.

Ebook/Video Tutorial

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tulip_flower from 16-08-2013, 06:26