Math 171: Abstract Algebra, Fall 2014

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

Office: Shanahan 2418
Office hours: Mon 4:00-5:00, TLB 2418, or by appointment.

Class meetings: Mon/Wed 2:45 pm - 4:00 am, Shanahan 2440


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.

The course prerequisites are Math 40 and Math 55. The course will heavily rely on these as prerequisites.

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 Wednesday in class; links to the individual assignments are below. The first two midterms cover the first and second third of the course material, respectively.

Exam Dates:
Oct 8, Midterm 1: (75 minute, in-class)
Nov, 19, Midterm 2: (75 minute, in-class)
Final: Date TBA. 5-hour take home exam.

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

Supplementary notes will be written here.

Dihedral Handout

Class Notes

Class notes will be added here.

Date Topic Class Lecture Additional Notes (Hannah Rose)
Sept 3 Intro To Groups Intro to Groups Notes Additional Notes
Sept 8 More Intro To Groups, Dihedral Groups More Intro / Dihedral Groups Notes Additional Notes
Sept 10 Subgroups Subgroups Notes Additional Notes
Sept 15 Symmetric Groups Symmetric Groups Notes Additional Notes
Sept 17 Homomorphisms/Isomorphisms Homomorphisms/Isomorphisms Additional Notes
Sept 22 Hom/Isomorphisms, Cyclic Groups Hom/Isomorphisms, Cyclic Groups Additional Notes
Sept 24 Cyclic Groups, Cosets & Lagrange Cyclic Groups/Cosets/Lagrange Additional Notes
Sept 29 Lagrange/Normal Subgroups Lagrange/Normal Subgroups Additional Notes
Oct 1 Quotient Groups Quotient Groups Additional Notes
Oct 6 Isomorphism Thms Isomorphism Thms Additional Notes
Oct 13 Isomorphism Thm Proofs Isomorphism Thms Class Handout
Oct 15/24 Group Actions Group Actions Additional Notes
Oct 27 Class Equation Class Equation Additional Notes
Oct 29 Cauchy, Sylow Thms Cauchy, Sylow Thms Additional Notes
Nov 3 Finite Abelian Groups Finite Abelian Groups Additional Notes
Nov 5 Intro to Rings Intro to Rings Additional Notes
Nov 10 Integral Domains, Division Rings, Fields Integral Domains, etc. Additional Notes
Nov 12 Homomorphisms/Quotients Homomorphisms/Quotients Additional Notes
Nov 17 Ring Quotients Quotients Additional Notes
Nov 24 Ring Iso Thms/ Principal Ideals Iso Thms/Principal Ideals Additional Notes
Nov 26 Principal and Maximal Ideals Principal/Maximal Ideals Additional Notes
Dec 2 Euclidean Domains Euclidean Domains Additional Notes
Dec 4 Euclidean Domains and PIDs Euclidean Domains and PIDs Additional Notes
Dec 9 Unique Factorization Unique Factorization Additional Notes


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)
puzzle file (for prob 2)

Assignment 4
Assignment 4 (.tex)

Assignment 5
Assignment 5 (.tex)

Assignment 6
Assignment 6 (.tex)
IDCheckDigit.pdf
colorings.png
hexagon.png

Assignment 7
Assignment 7 (.tex)
engima.pdf

Assignment 8
Assignment 8 (.tex)

Sample Midterm
Sample Midterm Solutions
Sample Midterm Solutions Errata

Assignment 9
Assignment 9 (.tex)

Assignment 10
Assignment 10 (.tex)

Assignment 11
Assignment 11 (.tex) Problem 6 Article Link