Day & Time: Monday and Wednesday 3:40 — 4:55pm Location: Goldsmith 0116 Instructor: Joel Bellaiche Office Hours: Tuesday 2:30pm-4:30pm and by appointment Teaching assistant: Alex Charis 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 two in class tests. The first will be on Wednesday, February 13 and the second on Wednesday, April 2. The final exam is a take-home 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:
Written work: We write to communicate. Please bear this in mind as you complete assignments and take exams. You must explain your work in order to obtain full credit; an assertion is not an answer. student or professor.
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. You may also ask the TA.
Class | Topic | Read | Suggested Exercises | Due |
Jan 16 | Introduction. Rings and Fields | §18 | 18:3,7,8,11,15,19,27,33,38,43,46,52,55 | |
Jan 23 | Rings and Fields. Domains | §18,19 | 19:3,4,14,15,16,17,23,30 | |
Jan 28 | Domains. Little theorem of Fermat | §19,20 | 20:11,12,23,27,28 | |
Jan 30 | Euler's theorem. The field of quotients of a domain | §20,21 | 21:4,15 | |
Feb 4 | Rings of Polynomials | §22 | 22:7,12,18,23 | Problems set 1 Solutions |
Feb 6 | Rings of Polynomials. Division of polynomials; roots | §22,23 | 23:9,14,25,34,35 | |
Feb 11 | Irreducible polynomials. Eisensetein's criterion | §23 | 23:16,17,18,19,20,21,31,36 | |
Feb 13 | Midterm I (Solutions) | Problems set 2 Solutions | ||
Feb 25 | Unique factorization of Polynomials. Kernel of an homormorphism and Ideals | §23,26 | 26:18,30 | |
Mar 3 | Factor Ring. Prime and Maximal Ideals. | §26,27 | 27:10,11,13 | |
Mar 5 | Prime and Maximal Ideals. Princial Ideals. Principal ideal domains | §27 | 27:15,18,19,28,34,35, | Problems set 3 |
Mar 12 | Principal ideal domains. Z, and K[X] (K a field) are principal ideal domains. Application to the minimal polynomial of a matrix. | §27 | ||
Mar 19 | Extensions Field | §29 | 29;1,6,9,19,20,21,25,29,30,31,32 | Problems set 3 |
Mar 24 | Vector Spaces. Algebraic Extensions | §30,31 | 30:1,4,5,6,7. 31:1,2,3,12,14,27 | |
Mar 26 | Geometric Constructions. | §32 | 32:1,2,4 | Problems set 4 |
Mar 31 | Review | Training exercises for midterm II | 32:1,2,4 | |
Apr 2 | Midterm 2 | |||
Apr 7 | Finite fields | 33 | 33:1,2,3,8,9,10,11,12 | |
Apr 9 | Finite Fields. Introduction to Galois Theory | 33,48 | ||
Apr 14 | Automorphisms of fields | 48 | 48:1,2,3,4,9,22,23,25,29 | |
Apr 16 | Automorphisms of fields. The isomorphism extension theorem | 48,49 | 49:1,2,3,7 | Exercises 5 |
Apr 28 | Separable extensions. | 51 | Exercises 6 | |
Apr 30 | Galois extensions. The main results of Galois theory. |