Abstract Algebra: Theory of Groups and Vector Spaces

Course Description

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 (E-222).

Copyright Information

All rights reserved to Prof. Gross and Harvard University. If you enjoyed this free class, the Harvard Extension School offers a wide variety of courses in numerous fields. Check out: http://www.extension.harvard.edu/
Abstract Algebra: Theory of Groups and Vector Spaces
Benedict Gross received his undergraduate and doctorate degrees from Harvard, and taught at Princeton and Brown before joining the Harvard faculty in 1985. He served as dean of Harvard College, chair of the department of mathematics, and as a member of several Harvard curriculum and faculty committees. Among his honors are the Cole Prize from the American Mathematical Society, and a MacArthur Fellowship. He is the co-author of the book The Magic of Numbers.
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Video Lectures & Study Materials

Visit the official course website for more study materials: http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

# Lecture Play Lecture Notes & Slides
1 Review: Linear algebra & Definition of groups (49:55) Play Video Lecture Notes
2 Symmetric groups, Subgroups of ℤ & Cyclic subgroups (50:12) Play Video Lecture Notes
3 Isomorphisms & Homomorphisms (48:58) Play Video Lecture Notes
4 Kernels, Normality, Centers and Inner Autos (53:08) Play Video Lecture Notes
5 Equivalence Relations & Cosets (47:13) Play Video Lecture Notes
6 Congruence mod n (52:02) Play Video Lecture Notes
7 Quotients (54:23) Play Video Lecture Notes
8 More on Quotients & Vectorspaces (51:45) Play Video Lecture Notes
9 More on Vectorspaces (51:30) Play Video Lecture Notes
10 Bases and vectorspaces; Matrices and linear transfer (56:54) Play Video Lecture Notes
11 Bases & Matrices (50:31) Play Video Lecture Notes
12 Eigenvalues and Eigenvectors (50:37) Play Video Lecture Notes
13 Review for midterm & Orthogonal groups (52:50) Play Video Lecture Notes
14 Orthogonal Groups & Geometry (52:09) Play Video Lecture Notes
15 Finite groups of motions (53:53) Play Video Lecture Notes
16 Discrete groups of motions (53:34) Play Video Lecture Notes
17 Abstract group actions (46:01) Play Video Lecture Notes
18 Group actions (51:25) Play Video Lecture Notes
19 Group actions II (53:24) Play Video Lecture Notes
20 Basic properties and constructions of group actions (54:39) Play Video Lecture Notes
21 Groups acting on themselves by left multiplication (51:43) Play Video Lecture Notes
22 Groups acting on themselves by conjugation (51:15) Play Video Lecture Notes
23 Alternating group structure (57:30) Play Video Lecture Notes
24 Ring Theory (50:55) Play Video Lecture Notes
25 Ring Theory II (49:13) Play Video Lecture Notes
26 Examples of Rings (53:42) Play Video Lecture Notes
27 Examples of Rings II (47:56) Play Video Lecture Notes
28 Basic properties and constructions of Rings (50:16) Play Video Lecture Notes
29 More on Rings (49:48) Play Video Lecture Notes
30 Extensions of Rings: Quotient rings (54:28) Play Video Lecture Notes
31 Extensions of Rings: Integral domains (42:27) Play Video Lecture Notes
32 Extensions of Rings: Fields of fractions (53:08) Play Video Lecture Notes
33 Gauss’ lemma (52:01) Play Video Lecture Notes
34 Eisenstein’s criterion (51:29) Play Video Lecture Notes
35 Algebraic integers (58:01) Play Video Lecture Notes
36 Dedekind domains & Ideal class groups (52:35) Play Video Lecture Notes
37 Review 1 (50:41) Play Video
38 Review 2 (1:00:24) Play Video

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