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

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

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:

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 finalSolutions