Math 171: Abstract Algebra, Spring 2014

Instructor: Prof. Mohamed Omar
Email: [lastname] at hmc dot edu

Office: TLB 2418
Office hours: TBA, TLB 2418, or by appointment.

Class meetings: Tues/Thurs 9:35 am - 10:50 am
Class webpage: http://www.math.hmc.edu/~omar/math171/

Course Outline

This course is an introduction to the fascinating subject of abstract algebra. This course unifies many of the algebraic structures you have encountered in the past into one unified cohesive theory. The major topics in the course are groups, rings, fields and additional topics. Topics in group theory include groups, subgroups, quotient groups, Lagrange's theorem, symmetry groups, and the isomorphism theorems. Topics in ring theory include Euclidean domains, PIDs, UFDs, fields, polynomial rings, ideal theory, and the isomorphism theorems. In recent years, additional topics have included the Sylow theorems, group actions, modules, representations, and introductory category theory. Prerequisites: Math 40 and Math 55.

The required text for this course is ``Abstract Algebra'' by Dummit and Foote, 3rd Edition. Readings and homework will be regularly assigned from this book.

Course Structure

This course has 4 graded components: Daily Quizzes (10% total), Assignments (20% total), 2 Midterm exams (20% each) and a cumulative final Exam (30%). The daily quizzes are intended to be benchmarks for you to recognize if you are falling behind in the class. Assignments are weekly and due Tuesday in class; links to the individual assignments are below. The first two midterms cover the first and second third of the course material. The final exam is cumulative.

Exam Dates:
Midterm 1: Feb 25 (75 minute, in-class)
Midterm 2: Apr 8 (75 minute, in-class)
Final: Available May 1st. 5-hour take home exam. Due: May 9th, 5:00pm for seniors. May 12th, 2:00pm for everyone else.

Course Policies on Assignments

You are ENCOURAGED to discuss homework problems with other students (unless marked otherwise). Solutions must be written up individually, in your own words. You may use all resources from class. Please note that I know there are easy to find solutions online to almost all of the problems in our textbook. So that you may adequately explore the material in Math 171 on your own, you may not use consult these solutions at any time during the course without my permission. Doing so will be viewed as a violation of the HMC Honor Code.

Disabilities

Students who need disability-related accommodations are encouraged to discuss this with the instructor as soon as possible.

Supplementary Notes

A cool write-up about the Rubik's Cube Group

More about the Enigma Machine

Class Notes

Class notes will be added here.

Date Topic Class Lecture
Jan 21 Intro to Groups Intro to Groups Notes
Jan 23 Group Arithmetic Group Arithmetic Notes
Jan 28 Subgroups, Dihedral Groups Subgroups/Dihedral Groups Notes
Jan 30 Dihedral Groups Dihedral Handout
Feb 4 Symmetric Groups Symmetric Groups
Feb 6 Group Homomorphisms and Isomorphisms Homomorphisms
Feb 11 More on Homomorphisms, Cyclic Groups Homomorphisms and Cyclic Groups
Feb 13 More on Cyclic Groups, Cosets and Lagrange's Theorem Cyclic Groups, Cosets and Lagrange's Theorem
Feb 18 More on Lagrange's Theorem, Normal Subgroups More Lagrange's Theorem, Normal Subgroups
Feb 20 Quotient Groups/First Isomorphism Theorem Quotient Groups/Isomorphism Theorems
Feb 27 Isomorphism Theorems/Intro to Group Actions Isomorphism Theorems/Group Actions
Mar 4 Group Actions Group Actions
Mar 6 Conjugacy and the Class Equation Class Equation
Mar 11 Class Equation (Cauchy's Theorem)/Intro to Sylow Theorem Class Equation/Cauchy's Theorem/Intro to Sylow
Mar 13 Proof of Sylow Theorem Proof of Sylow Theorem
Mar 25 Intro to Rings Intro to Rings
Mar 27 Types of Rings/Special Rings Types of Rings/Special Rings
Apr 1 Ring Homomorphisms Ring Homomorphisms
Apr 3 Quotient Rings Quotient Rings
Apr 10 Ring Isomorphism Theorems Ring Isomorphism Theorems
Apr 15 Types of Ideals Types of Ideals
Apr 17 Euclidean Domains Euclidean Domains
Apr 22 Principal Ideal Domains Principal Ideal Domains
Apr 24 Unique Factorization Domains Unique Factorization Domains
Apr 29 PID => UFD PID/UFD


Assignments

Assignments will be posted here.

Click here for the preamble file needed to compile the .tex files below.

Assignment 1
Assignment 1 (.tex)

Assignment 2
Assignment 2 (.tex)

Assignment 3
Assignment 3 (.tex)

Assignment 4
Assignment 4 (.tex)

Assignment 5
Assignment 5 (.tex)

Assignment 6
Assignment 6 (.tex)
Identification Digit Check
Benzene Ring

Assignment 7
Assignment 7 (.tex)

Assignment 8
Assignment 8 (.tex)

Assignment 9
Assignment 9 (.tex)

Assignment 10
Assignment 10 (.tex)

Assignment 11
Assignment 11 (.tex)