# Jay Pantone

## Math 31

Summer 2017, Dartmouth College

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 (X-hour)
•  Office Hours: Monday, 5:00pm - 6:00pm Kemeny 320 Tuesday, 4:00pm - 5:00pm Thursday, 11:00am - 12:00pm

#### Course Information

The official syllabus is here.

##### Announcements
• June 19: Because of the shortened term, the college has scheduled an extra day of classes on Saturday, June 24. We will meet from 11:45am to 12:50pm.
• June 27: When suggested homework is assigned, that does not imply that you have to read the corresponding sections in the book. We will cover all the necessary material in class. If you have trouble with a problem, then you can read the book, but be aware that we are not covering every topic that the book does.
• July 26: Exam 2 has been rescheduled for Monday, August 7, 5pm - 7pm, in Kemeny 008. The deadline to alert me of any scheduling conflicts is Sunday, July 30.
• August 11: We are using next week's X-hour, on Thursday August 17, for an extra lecture day.
• August 23: Office Hours before the exam:
• Thursday, 3pm - 5pm
• Friday, 2pm - 4pm

##### Daily Calendar
# 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(a-i), 1.4, 1.6(a-i)
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:
• Homework 1 has been posted.
Suggested Homework:
# 2.12, 3.1, 3.4, 3.11
5 Thurs, June 29
(X-hour)
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:
• Homework 1 due today.
• Homework 2 assigned today.
Suggested Homework:
# 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:
• Homework 2 due today.
• Homework 3 assigned today.
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:
• Homework 3 due today.
• Homework 4 assigned today.
Suggested Homework:
# 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:
• Homework 4 due today.
• Homework 5 assigned today.
Suggested Homework:
# 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:
• Homework 6 assigned today.
Suggested Homework:
# 12.15, 12.27, 12.29, 12.30, 13.2, 13.4
21 Fri, Aug 4 Section 13: Homomorphisms and Normal Subgroups Announcements:
• Homework 5 due today.
Suggested Homework:
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:
• Homework 6 due today.
• Homework 7 assigned today.
Suggested Homework:
# 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:
• Homework 7 due today.
• Homework 8 assigned today.
Suggested Homework:
# 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
(X-hour)
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:
• Homework 8 due today.
• Office Hours before the exam:
• Thursday, 3pm - 5pm
• Friday, 2pm - 4pm
Suggested Homework:
# 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.)

#### Syllabus

The official syllabus is here.

##### Homework Assignments

Weekly graded homework assignments, posted above. Daily suggested homework from the textbook, not graded.

##### Exam Dates
 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

##### Textbooks
• Abstract Algebra, 2nd edition, by Saracino. (ISBN: 978-1577665366)