Abstract Algebra – A Free Course

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 lectures videos

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.

The Quicktime and MP3 formats are available for download, or you can play the Flash version directly. Each week has 3 lectures that are 50 minutes each.

1. Review of linear algebra
2. Permutations
3. Quotient groups, first isomorphism theorem
4. Abstract linear operators and how to calculate with them
5. Orthogonal groups
6. Isometrics of plane figures
7. Group actions
8. A5 and the symmetries of an icosahedron
9. Rings
10. Extensions of rings
11. Special lecture
12. Euclidean domains, PIDs, UFDs
13. Structure of ring of integers in a quadratic field
14. Wrap-up

Instructor: Benedict Gross

Price: Free