Math 2231 - Ring Theory
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, 2009)
Below is a summary of what we did in class, plus any relevant
news and/or information.
- Dec. 2, 2009 I did review for the final.
- Nov. 30, 2009 I went over maximal and prime ideals
(Section 6.3)
- Nov. 27, 2009 We went over the proof of the First
Isomorphism Theorem (Section 6.2).
- Nov. 25, 2009 We discussed the kernel of an
homomorphism, and showed how it is an ideal.
- Nov. 23, 2009 We continued our discussion of Section 6.2.
Read 6.2 again for next class.
- Nov. 20, 2009 Today, we looked at old homework assignments,
and I gave pointers on how to do your rewrites.
- Nov. 18, 2009 We finished up Section 6.1 today, and started
looking at Section 6.2.
- Nov. 16, 2009 Today, we started Chapter 6. I introduced
the idea of an ideal from Section 6.1.
- Nov. 13, 2009 We finished Section 5.2. I also covered
the first part of Section 5.3. You will not be responsible
for the material on roots and extension fields in that section.
- Nov. 11, 2009 We started looking at Section 5.2 on Congruence
Class Arithmetic in F[x]/(p(x)). I also handed back HWA 5.
- Nov. 9, 2009 Today we looked at Section 5.1 on
congruence in F[x]. Please read 5.2 before the next class.
- Nov. 6, 2009 Class cancelled because I was sick.
- Nov. 4, 2009 The midterms will be handed back today.
As well, we will finish Chapter 4 today when we look at
factorization of polynomials over R[x] and C[x].
- Nov. 2, 2009 We looked at Section 4.5 on irreducibilty
in Q[x]. Read 4.6 for the next class.
- Oct. 30, 2009 The midterm was today.
- Oct. 28, 2009 We reviewed Chapters 1-3 for the midterm.
- Oct. 26, 2009 We started by finishing Section 4.3. We then
looked at Section 4.4 and the connection between roots
and irreducibility. In the next class, we will do some review
for the midterm on Friday.
- Oct. 23, 2009 Today's topic was on irreducibilty (Section 4.3).
The homework assignment was also due today.
- Oct. 21, 2009 We talked about the greatest common
divisor of two polynomials in F[x]. This was Section 4.2.
- Oct. 19, 2009 I went over the proof of the Division Algorithm
for polynomials. Please note: you can have a break on your reading
assignment. I'm behind a class.
- Oct. 16, 2009 We finished Section 3.3 on isomorphism by describing
some ways to determine if two rings are not isomorphic. We also started
Section 4.1 on polynomial rings. I handed back HWA 3, and I made some changes
to HWA 4 (see the email I sent you).
- Oct. 14, 2009 I went over the formal definition of a ring
isomorphism. I also handed out a review sheet for the midterm. HWA 3 was due
in class today.
- Oct. 9, 2009 We discussed more properties of rings (Section 3.2),
and I gave an informal definition of an isomorphism.
- Oct. 7, 2009 We went over the properties of rings (Sections 3.1
and 3.2).
- Oct. 5, 2009 I introduced the definition of a ring, and we went
over many examples (see Section 3.1).
- Oct. 2, 2009 We reviewed the material of Chapter 2. I emphasized
the questions raised in your emails.
- Sept. 30, 2009 Today we talked about the structure
of Z_p when p is a prime number (Section 2.3).
- Sept. 28, 2009 We went over Section 2.2 on the properties
of Z_n, the set of congruence classes modulo n.
- Sept. 25, 2009 We began Section 2.1 on congruences.
We will finish this section up on Monday. I also
gave out the new HWA; the first HWA was due in class.
- Sept. 23, 2009 Today we finished all the material
in Chapter 1. Next class -- Chapter 2.
- Sept. 21, 2009 We finished Section 1.2 on the Euclidean
Algorithm, and then started Section 1.3 on prime numbers and
factorization.
- Sept. 18, 2009 Today we discussed section 1.2 on divisiblity
and the greatest common divisor. We will save our discussion of
the Euclidean algorithm for the next class.
- Sept. 16, 2009 We went over the division algorithm and its
proof (Section 1.1).
- Sept. 14, 2009 On Friday (Sept. 11), we went over the course
handout. Today, we did some review of the material from Math 1281. In
particular, we covered Appendices A-C.
- Aug. 19, 2009 I added the course handout to the webpage,
and updated some other information on the page (e.g., marking scheme).
- July 17, 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: MWF 11:30-12:30
Email: avantuyl AT lakeheadu.ca
Place and Time:
Class: MWF 10:30-11:30 in RB 1044
Textbook
Abstract Algebra: an introduction (2nd Edition) by T. Hungerford
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: Sept. 25)
Appendix B -- 6ab, 21, 22
Section 1.1 -- 1cd, 4, 6, 8
Assignment 2 (Due: Oct. 5)
Section 1.2 -- 4, 7, 19, 22, 27
Section 1.3 -- 6, 11a, 17, 21
Assignment 3 (Due: Oct. 14)
Section 2.1 -- 4, 9, 14, 22, 31
Section 2.2 -- 1c, 2c, 7, 9, 10ab
Section 2.3 -- 4, 6, 9
Assignment 4 (Due: Oct. 23)
Section 3.1 -- 9, 13b, 24, 29
Section 3.2 -- 5, 7, 14, 23, 24, 28
Section 3.3 -- 10b, 13, 28, 32ac, 33ce
(Note: 3.1 - #29, 3.2 - #28, and 3.3 #28 will
be done in groups)
Assignment 5 (Due: Nov. 6)
Section 4.1 -- 5a, 7, 11, 16
Section 4.2 -- 4, 8, 14, 15
Section 4.3 -- 1a, 7, 10b, 16, 20
Assignment 6 (Due: Nov. 16)
Section 4.4 -- 5, 10, 13, 19
Section 4.5 -- 1c, 5b, 12, 13
Section 4.6 -- 3b, 5, 6, 7
Assignment 7 (Due: Nov. 25)
Section 5.1 -- 4, 9, 11
Section 5.2 -- 2, 5, 14a
Section 5.3 -- 1a, 3, 6
Assignment 8 (Due: Dec. 3)
Section 6.1 -- 13, 15a, 18
Section 6.2 -- 5, 8a, 12
Section 6.3 -- 1, 6, 8
All class handouts are available as
PDF files.
Course Information
Handout for first day
Guide to Writing Proofs
Handout on writing proofs
Midterm Info Sheet
Handout describing the midterm
Final Exam Info Sheet
Handout describing the final exam
Your final mark is broken down as:
40% -- Homework
5% -- Readings
20% -- Midterm
35% -- Final Exam
Sept. 10, 2009
First semester classes begin
Oct. 12, 2009
Thanksgiving (no class)
Oct. 30, 2009
MIDTERM
Nov. 6, 2009
Last day to drop class without academic penalty
Dec. 3, 2009
First semester classes end
Dec. 7-19, 2009
First semester exams
Lakehead University
LU Math Department
Adam's Home Page
Student Code of Conduct