Math 2231 - Ring Theory (2010)
This course has two goals. The first goal is to introduce students to one aspect of abstract algebra, namely rings. The second goal is get students used to writing formal proofs and thinking logically. This course has a sequel (Math 2233 - Group Theory) which is held in the winter term. Prerequisites: Math 1281.
News (Last Updated Dec. 2, 2010)
Below is a summary of what we did in class, plus any relevant
news and/or information.
Dec. 1 On our last day, we did some more additional
review; in particular, we looked at a number of true/false questions.
- Nov 29 We did some review today.
- Nov 28 Review sheet added.
- Nov 26 We finished our discussion of Chapter 16 by
showing that the F[x] is a PID when F is a field.
- Nov 24 Our section lecture on Chapter 16 was devoted to a proof
of the Division Algorithm for polynomials.
- Nov 22 Today was our first lecture on Chapter 16, the
ring of polynomials.
- Nov 19 We finished our discussion of Chapter 15
and ring homomorphsisms.
- Nov 17 We continued our discussion of homomorphism.
Today we concentrated on the kernel and the proof of the first
isomorphism theorem. HWA 6 was due.
- Nov 15 I was back in town today. I went over Chapter 15
and the concept of a ring homomorphism. I did a number of examples.
I also handed back all the rewritten assignments.
- Nov 12 Dr. Lee gave another lecture discussing
some examples of Chapter 14.
- Nov 10 We finished looking at Chapter 14 by looking
at prime and maximal ideals. I also handed back HWA 5.
- Nov 8 We looked at Chapter 14 on factor rings.
- Nov 5 Dr. Lee gave today's lecture. He did a number
of examples of rings, domains, and fields.
- Nov 3 We continued our discussion of rings by looking
at special types of rings: integral domains and fields. See Chapter 13.
- Nov 1 I handed back the midterm. We also started
Chapter 12 on rings.
- Oct 29 Midterm 1 was today. It will be handed back on Monday.
- Oct 27 More review on groups for the midterm
on Friday.
- Oct 25 Today was a review of material on the permutation
and symmetric groups.
- Oct 22 We did examples of the 1st Isomorphism Theorem.
- Oct 20 Today, we did the First Isomorphism Theorem.
- Oct 18 We proved Cauchy's Theorem for finite abelian groups.
HWA 3 was also handed back.
- Oct 15 Today's class we explored some more properties
of normal groups. In particular, we showed how to make factor groups.
HWA 3 was handed in, and HWA 4 was given out.
- Oct 13 We explored some consequences of Lagrange's Theorem,
and then we looked at normal subgroups. We will continue to
look at Chapter 9 during the next class.
- Oct 8 We spent some time on the idea of a coset,
and we went over the proof of Lagrange's Theorem.
- Oct 6 We finished Chapter 6 by going over Cayley's Theorem
for groups. I also handed back HWA 2 (rewrites are due on the 20th)
- Oct 4 We had our first class on Chapter 6 which covers isomorphisms.
- Oct. 1 Today we showed every permutation can be written
as the product of disjoint cycles, and then showed how each permutation
is the product of transpositions. This material comes from Chapter 5.
- Sept. 29 We started Chapter 5 on permutations. The symmetric
group was also introduced.
- Sept. 27 I wrapped up Chapter 3, and discussed some
of Chapter 4 on cyclic groups. I also handed back HWA 1 (rewrites
dues Oct. 11).
- Sept. 24 We looked at Chapter 3 on subgroups. HWA 1 was
due, and HWA 2 was assigned.
- Sept. 22 Finished up Chapter 2 on elementary properties.
- Sept. 20 We went over the definition of a groups
and saw lots of examples.
- Sept. 17 A gentle introduction to the dihedral groups!
Next class: a formal definition of groups.
- Sept. 15 We reviewed the matrial of Chapter 0.
- Sept. 13 First day! We went over the division
algorithm.
- Sept. 9, 2010 Almost ready to start!
- August 9, 2010 Info sheets now added to the web.
- July 8, 2009 I put the class web page up. There isn't much
here now, but check back in a month.
Instructor:
Adam Van Tuyl
Office: RB 2015
Office Hours: TBD
Email: avantuyl AT lakeheadu.ca
Place and Time:
Class: MWF 1:30-2:30 in RB 1023
Textbook
Contemporary Abstract Algebra (seventh edition)
Joseph Gallian
Homework will be given out about once every week
and half. See course handout for
more details on the acceptable form
for your homework.
Assignment 1 (Due: Sep. 24)
Chap. 0 -- 4, 8, 10, 14, 44, 52
Rewrites due Oct 13
Assignment 2 (Due: Oct. 4)
Chap. 1 -- 1, 2, 3
Chap. 2 -- 4, 10, 14, 24, 36
Chap. 3 -- 6, 10, 18, 26, 42
Rewrites due Oct. 20
Assignment 3 (Due: Oct. 15)
Chap. 4 -- 4, 8, 14, 22, 54
Chap. 5 -- 2, 6, 12, 22, 30, 34
Rewrites due Nov. 1
Assignment 4 (Due: Oct. 25)
Chap. 6 -- 4, 10, 18, 24, 38
Chap. 7 -- 2, 6, 14, 18, 28
Rewrites due Nov. 10
Assignment 5 (Due: Nov. 5)
Chap. 9 -- 2, 10, 12, 14, 18, 54
Chap. 10 -- 2, 8, 10, 14, 22
Rewrites due Nov. 24
Assignment 6 (Due: Nov. 17)
Chap. 12 -- 4, 8, 18, 22, 42
Chap. 13 -- 2, 10, 14, 18, 34, 46 (Hint: use 45)
Rewrites due Dec 6
Assignment 7 (Due: Nov. 29)
Chap. 14 -- 3, 6b, 8, 10, 26, 28 (Hint: use Example 15)
Chap. 15 -- 6, 8, 10a, 14, 44, 50
Rewrites due Dec. 13
All class handouts are available as
PDF files.
Course Information
Handout for first day
Guide to Writing Proofs
Handout on writing proofs
Midterm Information
Handout describing the midterm
Final Exam Information
Handout describing the final exam
Your final mark is broken down as:
40% -- Homework
5% -- Readings
20% -- Midterm
35% -- Final Exam
Sept. 13, 2010
First semester classes begin
Oct. 11, 2010
Thanksgiving (no class)
Oct. 29, 2010
MIDTERM
Nov. 5, 2010
Last day to drop class without academic penalty
Dec. 6, 2010
First semester classes end
Dec. 15, 2010
Final Exam (ATAC 2019)
Lakehead University
LU Math Department
Adam's Home Page
Student Code of Conduct