Day & Time: Tuesday and Friday 12:10 — 1:25pm Location: Goldsmith 226 Instructor: Joel Bellaiche Office Hours: Tuesday 2:30pm-4:30pm and by appointment Teaching assistant: John Bergdall Textbook: John B. Fraleigh First Course in Abstract Algebra seventh edition, Adison-Wesley , 2003. ISBN 0201763907. Prerequisites: Introduction to Algebra I or the equivalent. Examinations: There will be one in class midterm and one final exam. |
Tests and Exams: There are no makeups for missed tests. You must take the final examination at the time scheduled by the university; no final exams will be given earlier.
Homework: There will be two kinds of homework:
Help: Help is available if you have trouble with homework or lecture material. My office hours are a good place to start. Discussions with your classmates can also be very helpful and are strongly encouraged.
Class | Topic | Read | Suggested Exercises | Due |
Jan 15 | Introduction. Group acting on a set. | §16 | ||
Jan 18 | Group acting on a set. | §16 | 16:4,5,6,7,8,11,13,16 | |
Jan 22 | Group acting on a set | §16 | ||
Jan 25 | Isomorphism Theorems | §34 | 34:1,2,7,8,9 | |
Jan 29 | Series of groups | §35 | 35: 1,5,7 | |
Feb 1 | Series of groups | §35 | 35:15,16,17,23 | Problems set 1 |
Feb 5 | Series of Groups. Solvable and nilpotent groups. | §35,36 | ||
Feb 8 | No class because of Snow storm | |||
Feb 12 | Sylow's theorems | §36 | 36:1,2,7,8,9,10,11,17,20 | |
Feb 15 | Applications of Sylow's theorems | §37 | 37:3,4,5,6,7 | Problems set 2 |
Feb 26 | Free abelian groups and finitely generated abelian group | §38 | 38:2,3,11,16 | |
Match 1 | Free Group | §39 | 39:1,2,3,4,5,6 | |
March 5 | Group Presentations. Review of rings. | § 40. § 18,19,26,27 | ||
Match 8 | The field of quotients of an integral domain | § 21 | Problems set 3 Solutions to exercise 4 | |
March 12 | Ring of Polynomials | § 22 | ||
March 15 | Factorization of Polynomials | § 22 | ||
March 19 | Factorization of Polynomials, Fraction ringd/td> | § 22,23 | ||
March 22 | Midterm | |||
April 5 | Geometric Construction | § 32 | Problems set 4 | |
April 9 | Finite fields | § 33 | ||
April 12 | Automorphisms of fields | § 48 | ||
April 16 | The isomorphism extension theorem | § 49 | ||
April 19 | Splitting fields | § 50 | ||
April 23 | Separable extensions | § 51 | Problems set 5 | |
April 26 | Galois Theory | § 53 | ||
April 30 | Galois Theory | § 54,55,56 | ||
May 3 | Galois Theory | § 54,55,56 | Problems set 6 |