Ma 005b/105b:  Introduction to Abstract Algebra (Winter 2016-17)

ANNOUNCEMENTS

Registration for Winter term opens Thursday, November 17, 2016.

This page was last updated:  .


COURSE DESCRIPTION

The second term of Math 5 will be devoted to the study of rings and modules; this includes some linear algebra. The material corresponds roughly to Chapters 7 through 12 in the text for the course, Abstract Algebra by Dummit and Foote. High points include the proof of unique factorization in principal ideal domains and the description of finitely generated modules over principal ideal domains.


PREREQUISITES

TBA


SCHEDULE

MWF 09:00 - 09:55, 151 Sloan.


INSTRUCTORS

Elena Mantovan
PROFESSOR OF MATHEMATICS
EXECUTIVE OFFICER FOR MATHEMATICS
Sloan 262
626-395-4342


TA's

Xiao (Luciena) Xiao


OFFICE HOURS

Monday at 1:30pm in 262 Sloan Laboratory (EM)

Wednesday at noon in 382 Sloan Laboratory (XX)


POLICIES

Grading: Roughly 40% Homework, 30% Midterm, and 30% Final.

Homework Policy: Students may work together on homework as long as each student writes up their own homework in their own words.

In solving homework problems you will wish to quote theorems and lemmas from class and the text. Results from the text in sections not yet covered cannot be quoted unless you supply your own proof. The same holds for results from other texts not covered in class.

Many of the problems which will be assigned this year in Math 5, also were assigned in previous years. Do not consult old solution sets in working on this years homework.

At most one late homework set will be accepted, and except in unusual circumstances, only if arrangements have been made with me in advance. Other than in exceptional circumstances, homework will not be accepted more than a week after the deadline.


TOPICS COVERED

Introduction to Rings, Euclidean Domains, Principal Ideal Domains, and Unique Factorization Domains, Polynomial Rings.

Introduction to Modules, Vector spaces, Modules over Principal Ideal Domains.


TEXTBOOKS

D. Dummit and R. Foote, Abstract Algebra


LECTURE NOTES

Date Description
 Syllabus This is a short description of each lectures and shall be updated weekly.
 Midterm Review Notes  
Final Review Notes  
 Modules over PIDs  

 

HOMEWORK

Due on Fridays at noon

Due Date Homework Solutions
01/13 Set 1 Set 1 Solutions
01/20 Set 2 Set 2 Solutions
01/27 Set 3 Set 3 Solutions
02/03 Set 4 Set 4 Solutions
02/10 at 10am Midterm (see below)  
02/17 Set 5 Set 5 Solutions
02/24 Set 6 Set 6 Solutions
03/03 Set 7 Set 7 Solutions
03/10 Set 8 Set 8 Solutions
03/16 at 10am Final (see below)  

EXAMS

Midterm exam was posted on Friday, February 3rd. An email was sent out with a link to the exam.  If you have not received the email please contact PMA Undergraduate Student Affairs Administrator Meagan Heirwegh.

The midterm is due back by 10am on Friday February 10, 2017.

Final exam is posted here. An email was sent out with a password to the exam.  If you do not received the email please contact PMA Undergraduate Student Affairs Administrator Meagan Heirwegh.

The final exam is due back by 10am on Thursday, March 16, 2017.


READING