Introduction to Algebra I (MATH 30a, Fall 2008)

[ Policies & Procedures | Schedule of Lectures ]

Day & Time: Tuesday and Friday 10:40 — 11:55am

Location: Goldsmith 0116

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

Assessment: The course grades will be computed as follows:: 30% Homework; 20% First test; 20% Second test; 30% 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:

Exercises (often from the text book) give you a chance to test your understanding of the basic concepts, practice your skill at computing with them, and sometimes at proving theorems about them. They are also necessary to develop a familiarity and an intuition with the abstract concepts algebra. They will not be collected.
Graded homework: There will be eleven graded homework due each Tuesday, The two lowest grades will be dropped.

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.

Schedule of Lectures

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 final Solutions