Advanced Algebra I

Midterm 11/22(Sat.) 2pm- 4+ pm.

Final Examination 1/9, 2004 (Sat.) 2pm-4+pm.

Please find the example of non-radical extension in the new version of Homework 14.

NB: most documents are in pdf format. You might need Acrobat Reader (which is free to download) to view it. Some version of Ghostview also works.

lecture 1: Set theory: Zorn's Lemma, Cardinality.

lecture 2: Group actions.

lecture 3: Sylow theorems and application to classification of fintie groups.

lecture 4: Solvable groups and nilpotent groups, Jordan-Holder theorem.

You might find this interesting:

Ronald Solomon
Bull. Amer. Math. Soc. 38 (2001), 315-352.
　

lecture 5: Free groups and presentation of groups, Todd-Coxeter algorithm

lecture 6: Representation of finite groups and characters

lecture 7: Characters

lecture 8: Group algebra

lecture 9: Burnside's theorem

lecture 10: Permutation representations and more examples.

lecture 11: Induced representations

lecture 12: Field extensions ( algebraic and finite extension)

lecture 13: Algebraic closure

lecture 14: Splitting fields and normal extension

lecture 15: Fundamental theorem of finite dimensional Galois extension

lecture 16: Cyclotomic and cyclic extension

lecture 17: Radical extension and solving equations by radicals.

lecture 18: Finite fields

lecture 19: Separable extension