Sam Evens, Math 60220, Basic Graduate Algebra, Spring 2024
MW 2-3:15, HH 229
Office hours: TBA, or after class, or by appointment. You can arrange a meeting either by talking to me or by emailing me at sevens (at sign) nd (dot) edu to arrange a meeting.
Some References:
Robert Ash, Abstract Algebra: The Basic Graduate Year. This is available from Dover, but there are copies available on the web.
Serge Lang, Algebra, Revised 3rd edition, Springer-Verlag.
Michael Artin, Algebra , Prentice Hall.
D. Dummit and R. Foote, Abstract Algebra, Prentice Hall.
Serre, Groupes Finis, course notes used for proofs of Sylow theorems
Notes by A. Myasnikov on free groups provides more detail than Ash, V.5.8
Course Notes:
1-22 Notes: more on finitely generated modules over a PiD
1-29 Notes on Categories and Functors
1-31 notes on exactness of Hom and Tensor Product
2-14 embeddings of injective modules
2-28 Intro to Field Extensions
3-4 Properties of degree; splitting fields
3-6 Splitting Fields and Algebraic Extensions
3-18 Algebraic closures and separable extensions
3-25 Lecture on Normal Extensions
4-22 Lecture on Insolvability of Quintics
4-29 Hilbert basis theorem and integral extensions
Notes on Noether Normalization Lemma, did not cover
Notes on the Nullstellensatz, did not cover
Problem Sets:
Problem Set 1, due Wednesday January 31
Problem Set 2, due Wednesday February 7
Problem Set 3, due Wednesday February 14
Problem Set 4, due Wednesday February 21
Problem Set 5, due Wednesday February 28
Problem Set 6, due Wednesday March 6
Problem Set 7, due Wednesday March 20
Problem Set 8, due Wednesday April 3
Problem Set 9, due Wednesday April 10
Problem Set 10, due Wednesday April 17
Problem Set 11, due Wednesday April 24
Problem Set 12, due Wednesday May 1