Math 31, Winter 2005

Topics in Algebra

General Information Syllabus Homework Assignments Exam Related Class Material


Syllabus

The following is a tentative syllabus for the course. It is based on the 5th edition of Contemporary Abstract Algebra by Joseph A. Gallian.
This page will be updated irregularly. On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.



Lectures Chapter in the Textbook Brief Description
Day 1: January 5, Wednesday Chapter 0 Properties of Integers
Day 2: January 7, Friday Chapter 0 Modular Arithmetic; Mathematical Induction
January 8, Saturday   Classes moved to the X-hour
Day 3: January 10, Monday Chapters 0 and 1 Equivalence Relations; The Dihedral Groups
Day 4: January 12, Wednesday Chapter 2 Definitions and Examples of Groups
Day 5: January 13, Thursday
X-hour instead of January 8
Chapters 2 and 3 Properties of Groups; Finite Groups; Subgroups
Day 6: January 14, Friday Chapter 3 Subgroup tests
January 17, Monday   Martin Luther King Jr. Day. Classes moved to the X-hour
January 18, Tuesday   Last day to add a course
Day 7: January 19, Wednesday Chapter 4 Cyclic groups
January 20, Thursday   First 50-minute quiz (during the X-hour)
Day 8: January 21, Friday Chapter 4 Classification of Subgroups of Cyclic groups
Day 9: January 24, Monday Chapter 5 Permutation Groups
Day 10: January 26, Wednesday Chapters 5 and 6 Properties of Permutations; Isomorphisms
Day 11: January 27, Thursday
X-hour instead of January 17
Chapter 6 Properties of Isomorphisms; Automorphisms
Day 12: January 28, Friday Chapter 7 Cosets and Lagrange's Theorem
Day 13: January 31, Monday Chapter 7 Fermat's Little Theorem; Orbits and stabilizers
Day 14: February 2, Wednesday Chapter 8 External Direct Products
February 2, Wednesday   Take home midterm exam (due Monday, February 7)
Day 15: February 4, Friday Chapter 8 Applications of Group Theory: RSA Algorithm
Day 16: February 7, Monday Chapter 9 Normal Subgroups and Factor Groups
Day 17: February 9, Wednesday Chapter 9 Applications of Factor Groups
February 11, Friday   Winter Carnival holiday. Classes moved to the X-hour
Day 18: February 14, Monday Chapter 10 Group Homomorphisms
Day 19: February 16, Wednesday Chapter 10 The First Isomorphism Theorem
Day 20: February 17, Thursday
X-hour instead of February 11
Chapter 12 Rings and Their Properties; Examples of Rings
Day 21: February 18, Friday Chapter 13 Integral Domains
Day 22: February 21, Monday Chapter 13 Fields; Characteristic of a Ring
Day 23: February 23, Wednesday Chapter 14 Ideals and Factor Rings
February 23, Wednesday   Last day to drop a course
February 24, Thursday   Second 50-minute quiz (during the X-hour)
Day 24: February 25, Friday Chapters 14 and 15 Prime Ideals and Maximal Ideals; Ring Homomorphisms
Day 25: February 28, Monday Chapter 15 Properties of Ring Homomorphisms
Day 26: March 2, Wednesday Chapter 16 Polynomial Rings
Day 27: March 4, Friday Chapter 17 Factorization of Polynomials
Day 28: March 7, Monday Chapter 20 Extension Fields
Day 29: March 9, Wednesday Review etc.