Math 5a
Introduction to Abstract Algebra
Fall 2014-15
MWF 9:00 AM // 151 Sloan
Course Description | Policies | Textbooks | Lecture Notes | Handouts | Homework | Sections

Instructor:  Pei Yu Tsai, 282 Sloan, 626-395-4350, pytsai at
Office Hours: 
Wednesday 2-3pm or by appointment
TA: Maria Nastasescu, 158 Sloan, mnastase at
Office Hours: Mondays 4-5:30pm



Exams are available on December 15 at 3 pm in Math 5 return box. I will be available in my office 12/15 3-5 pm, 12/16 4-5 pm. (Solution has been uploaded.)
The final will be take-home and open-book (only textbook, class note, homework and homework solutions are allowed). It covers Chapter 3-5 of Dummit&Foote (Section 4.4 not included). You will have 6 hours to complete your solution in a standard bluebook.
Final Exam Due 3 pm on Thursday, December 11
You are allowed to have one break up to an hour after the first three hours. Other short breaks for water and restroom are allowed but are counted toward the six hours exam time.
Maria Review Session on Sunday 1pm. Location: Sloan 151.
Office Hour in groups (of any order) by appointment are welcome.

Course Description

In Ma5a we will discuss groups. This material comes from Chapters 1-5 of the text. We will spend the first half of the term on basics, such as the introductory material in Chapter 0 of the text, the definition of a "group", examples of groups, basic properties of groups, subgroups, homomorphisms, and factor groups. In the second half of the term we will talk about permutation groups, semidirect products, and Sylow's Theorem.


Grading: 50% Homework, 25% Midterm, and  25% 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.

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.

Homework should be handed in into the Ma5a mailbox next to the Math department office on the second floor of Sloan.


Abstract Algebra by D. S. Dummit and R.M. Foote, third edition, John Wiley 2004.
ISBN: 0-471-43334-9

Lecture Notes

Date Description
Chapter 0 Lecture Note
Chapter 1 Lecture Note
Chapter 2 Lecture Note
Chapter 3
Lecture Note
Remark Some of the numberings may differ from actual lecture.


Date Description
09/29 Course information sheet
10/01 Well-Ordering Principle and Principle of Mathematical Induction
  Perfect numbers
10/22 Remark on how to do Hw3 Problem 5
10/24 Class notes for October 24th
10/26 Practice problem set
11/17 Possible numbers of Sylow subgroups of groups of order 12


Due Date Homework  Solutions
Oct. 7
Homework 1 (Have been returned to Ma5 return box)

Oct. 14
Homework 2

Oct. 21
Homework 3 (updated on 10/15)

Oct. 28
Homework 4 (updated on 10/22 #6,#7 are switched.)


Nov. 11
Homework 5 (updated on 11/07, #5 typo fixed)

Nov. 18
Homework 6 (choose 7 to turn in)(updated on 11/12)(hint is up.)

Nov. 25
Homework 7 (updated on 11/24)

Dec. 5
Homework 8 (updated on 12/04, changes made to #3)



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