Day & Time: Tuesday and Friday 10:40 — 11:55am Location: Goldsmith 0116 Instructor: Joel Bellaiche Office Hours: Monday : 2:30 — 4:30pm Teaching assistant: Keith Merril Textbook: John B. Fraleigh First Course in Abstract Algebra seventh edition, Adison-Wesley, 2003. ISBN 0201763907. Prerequisites:Linear Algebra Examinations: There will be two in class tests. The first will be on Friday, October 3rd and the second on Tuesday, November 11th . The final exam will be on Monday, December 11th from 9:15am to 12:15pm |
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 (even about graded homework). You may also ask the TA.
Program: We will define and study the three most important algebraic structures: groups, rings, and fields. This corresponds to the first four sections of the textbook.
Class | Topic | Read | Suggested Exercises | Due |
Aug 29 | Introduction. Reminder of set theory | §0 | ||
Sep 2 | Reminder of set theory. | §0 | 0: 11,16,17,19,29,30,36 | |
Sep 5 | Binary Laws. Isomorphic Binary Structure. | §2,3 | 2:14,15,16,23,24,26,27,28,29,30,34 | |
Sep 9 | Isomorphic binary strucures. Groups | §3,44 | 3:2,34,5,6,7,8,10,11,12,33,34. 4 :1 to 6,24 | |
Sep 12 | Groups. Subgroups | §4,5 | 4:10,11,12,20,25,29,33,34 | Problem set 1 |
Sep 16 | Subgroups. Cyclic subroups. | §5 | 5:.5:1,2,8,11,12,13,37,38,43,44,52,55,57 | |
Sep 19 | Cyclic groups. Generating sets | §6,7 | 6:5,8,12,17,32,45,51. | Problem set 2 |
Sep 23 | Cyclic groups. Generating sets | §7 | 7:1,2 | |
Sep 26 | Cayley digraphs. Group of permutations. | §7,8 | 7:11,16. 8:1,2,3,4,5,6,7,11,12,35,46,47 | Problem set 3 |
Sep 29 (Monday) | Orbits, Cycles. Transpositions, the alternate subgroup. | §9 | 9:1,2,10,11,15,16,23,27,34 | |
Oct 3 | Midterm | §1 to 9 | Training Midterm 1 Solutions Solutions to the midterm | |
Oct 7 | Cosets and the theorem of Lagrange | §9,10 | 10:1,4,6,12,19,30,31,32,41,43 | |
Oct 10 | No class | |||
Oct 13 | No class | |||
Oct 17 | Direct Products and Finitely generated abelian groups | §11 | 11:3,4,15,26,29,54 | Problem set 4 |
Oct 21 | No classs | |||
Oct 24 | Homomorphisms | § 13; | 13:1,2,3,4,5,6,7,8,14 | |
Oct 28 | Homomorphisms and Factor groups | § 13,14 | 13:25,26,27,44,45,53 | |
Oct 31 | Factor groups | § 14,15 | 14:1 to 6, 23,30,36. | Problem set 5 |
Nov 4 | Simple groups, center, commutator groups | § 15 | 15:1 to 12,20,21,23,31,34,35,39 | |
Nov 7 | Groups action on a set. Review | § 16 | Problem set 6 | |
Nov 11 | Midterm 2 | § 0 to 15, excepted 12 | Training exercises Solutions | |
Nov 14 | Groups action on a set, applications | §16 | 16:1,23,5,7,8,12,14,19 | |
Nov 18 | Rings and field | §18 | 18:7,8,9,11,12,33,38,46,47,55 | |
Nov 21 | Integral Domain/td> | §19 | 19:1,14,17,24,26,30 | |
Nov 24 | Fermat and Euler's Theorem | §20 | 20:1,10,23,27,28,29 | Problem set 7 |
Nov 27 | No class | |||
Dec 2 | Solving congruences. The field of quotient of an integral domain | §20,21 | 20:11,12,13,14,15,16,17 | Problem set 8 |
Dec 5 | The field of quotient. Rings of polynomials | §21,22 | 21:1,2,4. 22:1,2,3,4,5,6,18 | |
Dec 9 | Polynomials. Review | §22 | 22:12,13,14,15,17,23 | Problem set 9 |
Dec 11 | Final exam (9h15am to 12:15pm) | Cumulative (section 0 to 22 excepted 12) | training finalSolutions |