CIEB | Abstract Algebra – Benedict Gross Harvard Extension School training

Genre: eLearning

Contents:
1. Introduction.Linear Algebra,Definition of groups
2. Generalities on groups, symmetric groups on n letters, subgroups of Z, cyclic subgroups
3. Isomorphisms, homomorphisms, images
4. Kernels, normality, centers and inner autos
5. Equivalence relations, cosets

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6. Congruences mod n
7. Quotients
8. More on quotients, vectorspaces
9. Quotients and vector spaces part 2
10. Bases and vectorspaces, matrice and linear transformations
11. Bases, matrices
12. Eigenvalues and eigenvectors

13. Review, orthogonal group
14. Orthogonal groups and geometry
15. Finite groups of motions
16. Discrete groups of motions
17. Discrete groups of motions, abstract group actions
18. Group actions
19. Group actions part 2
20. Group actions, basic properties and constructions part1
21. Group actions, basic properties and constructions part2
22. Group actions, basic properties and constructions part3
23. Alternating group structure
24. Rings part 1
25. Rings part 2
26. Rings, examples, properties and constructions part1
27. Rings, examples, properties and constructions part2
28. Rings, examples, properties and constructions part3
29. Quotient groups, extensions of rings, integral domains, fields of fractions
30. Special lecture part1
31. Special lecture part2
32. Special lecture part3.mov
33. Euclidian domains,PIDs,UFDs,Eisenstein’s criterion, algebraic integers part1
34. Euclidian domains,PIDs,UFDs,Eisenstein’s criterion, algebraic integers part2
35. Euclidian domains,PIDs,UFDs,Eisenstein’s criterion, algebraic integers part3
36. Structure of ring of integers in a quadratic field,Dedekind domains,ideal class groups
Review part 1
Review part 2
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