This course will provide an introduction to fundamental algebraic structures, and may include significant applications. The majority of the course will consist of an introduction to the basic algebraic structures of groups and rings. Additional work will consist either of the development of further algebraic structures or applications of the previously developed theory to areas such as coding theory or crystallography. As a result of the variable syllabus, this course may not serve as an adequate prerequisite for MATH 81. Students who contemplate taking MATH 81 should consider taking MATH 71 instead of this course.
Lectures: 
M, W, F,  2:10pm  3:15pm 
Kemeny 006  Th,  1:20pm  2:10pm (Xhour) 
Office Hours: 
Monday,  5:00pm  6:00pm 
Kemeny 320  Tuesday,  4:00pm  5:00pm 
Thursday,  11:00am  12:00pm 
#  Date  Topics  Suggested HW & Announcements 

1  Fri, June 23 
Class Information
Section 0: Sets 
Suggested Homework: # 0.3, 0.4 
2  Sat, June 24  Section 1: Binary Operations 
Suggested Homework: # 1.3(ai), 1.4, 1.6(ai) 
3  Mon, June 26  Section 2: Groups 
Suggested Homework: # 2.1, 2.2a, 2.5, 2.6, 2.10 
4  Wed, June 28 
Section 2: Groups
Section 3: Group Theorems 
Announcements:
# 2.12, 3.1, 3.4, 3.11 
5  Thurs, June 29 (Xhour) 
Proofs and Proof Techniques 
Suggested Reading: Handout #1 Handout #2 
6  Fri, June 30 
Section 3: Group Theorems
Section 4: Cyclic Groups 
Suggested Homework: # 3.9, 3.10, 4.1, 4.4, 4.5 
7  Mon, July 3  Section 4: Cyclic Groups 
Suggested Homework: # 4.12, 4.14, 4.16, 4.17, 4.22 
8  Wed, July 5  Section 5: Subgroups 
Announcements:
# 5.1 (except g), 5.4, 5.7, 5.19 
9  Fri, July 7  Section 6: Direct Products 
Suggested Homework: # 6.1, 6.2, 6.6, 6.8, 6.10, 6.11 
10  Mon, July 10  Section 7: Functions 
Suggested Homework:
#7.1(d,f,i), 7.2(b), 7.4, 7.12 
11  Wed, July 12 
Exam Review Exam 1 (Look below for time and location.) 
Announcements:

12  Fri, July 14  Section 8: Symmetric Groups 
Suggested Homework:
# 8.1, 8.2, 8.4, 8.7, 8.10, 8.11 
13  Mon, July 17  Section 8: Symmetric Groups 
Suggested Homework:
# 8.14, 8.15 
14  Wed, July 19  Section 9: Cosets 
Announcements:
# 9.1, 9.2, 9.3 
15  Fri, July 21  Section 9: Cosets 
Suggested Homework:
# 9.6 (their \(f\) is our \(r\) and their \(g\) is our \(s\)), 9.10, 9.12, 9.18 
16  Mon, July 24  Section 10: Counting Group Elements 
Suggested Homework:
# 10.5, 10.6, 10.7, 10.8, 10.9, 10.14, 10.16, 10.21 
17  Wed, July 26  Section 11: Normal Subgroups 
Announcements:
# 11.1, 11.3, 11.11, 11.13 
18  Fri, July 28 
Section 11: Normal Subgroups Section 12: Homomorphisms 
Suggested Homework:
# 11.17, 11.18, 11.19, 11.20 # 12.1, 12.5, 12.8, 12.11 
19  Mon, July 31  Class canceled today.  
20  Wed, Aug 2  Section 12: Homomorphisms 
Announcements:
# 12.15, 12.27, 12.29, 12.30, 13.2, 13.4 
21  Fri, Aug 4  Section 13: Homomorphisms and Normal Subgroups 
Announcements:
none today 
22  Mon, Aug 7 
Exam Review Exam 2 (Look below for time and location.) 
Suggested Homework:
# 
23  Wed, Aug 9  Section 13: Homomorphisms and Normal Subgroups 
Announcements:
# 13.8, 13.9, 13.14, 13.16 
24  Fri, Aug 11  Section 14: The Fundamental Theorem of Finite Abelian Groups 
Suggested Homework:
# 14.1, 14.2, 14.3, 14.7, 14.8 
25  Mon, Aug 14  Section 16: Rings 
Suggested Homework:
# 16.2, 16.3, 16.4, 16.6, 16.9, 16.11, 16.13, 16.17a, 16.20 
26  Wed, Aug 16 
Section 17: Subrings, Ideals, and Quotient Rings 
Announcements:
# 17.1, 17.2, 17.3, 17.4, 17.6, 17.14, 17.20 (some require material that we'll finish on Friday) 
27  Thurs, Aug 17 (Xhour) 
Applications of Algebra (Canceled) 

28  Fri, Aug 18  Section 18: Ring Homomorphisms 
Suggested Homework:
# 18.1, 18.2, 18.3, 18.15 
29  Mon, Aug 21 
Section 19: Polynomials Eclipse! 
Suggested Homework:
(See Wednesday) 
30  Wed, Aug 23 
Section 19: Polynomials Section 20: Fields 
Announcements:
# 19.1, 19.2, 19.7, 19.10, 19.12 # 20.1, 20.2, 20.3, 20.8 
Sun, Aug 27  Final exam (Look below for time and location.) 
Weekly graded homework assignments, posted above. Daily suggested homework from the textbook, not graded.
Exam 1:  Wednesday, July 12, 5:00pm  7:00pm — Kemeny 006 
Exam 2:  Monday, August 7, 5:00pm  7:00pm — Kemeny 008 
Final Exam:  Sunday, August 27, 11:30am  2:30pm — Kemeny 006 
Homework:  25% 
Exam 1:  20% 
Exam 2:  25% 
Final Exam:  30% 
June 22:  Classes begin 
June 24:  Special Saturday day of classes 
July 4:  Independence Day, no classes 
July 6:  Final day for electing use of the NonRecording Option (NRO) 
August 2:  Final day for dropping a fourth course without a grade notation of "W" 
August 9:  Final day to withdraw from a course 
August 23:  Last day of classes 
August 27:  Math 31 final exam 