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.
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.
Groups. Examples of groups. Basic properties and constructions.
Cosets, Z/nZ.
Abstract fields, abstract vectorspaces. Construction and invariants of vectorspaces.
Properties and construction of operators.
Cyclic and dihedral groups. Finite and discrete subgroups of symmetry groups.
Basic properties and constructions. Groups acting on themselves by left multiplication. Groups acting on themselves by conjugation.
Sylow theorems. Study of permutation groups.
Examples of rings. Basic properties and constructions.
Quotient rings. Integral domains, fields of fractions.
Gauss’ lemma. Eisenstein’s criterion. Algebraic integers.
Dedekind domains. Ideal class groups.
If you enjoyed this free class, the Harvard Extension School offers a wide variety of courses in numerous fields. Search for classes and enroll for credit during the fall and spring registration periods.
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