SYLLABUS
Math 31 Homepage General Information Homework Assignments Exam related and Announcements
This
is a tentative course syllabus and it will be updated irregularly. The Homework
Assignments page will be updated every lecture..
Lectures 
Sections in Text 
Brief Description 
Day 1: 1/5 
Chapter 0 
Properties of integers; Euclidean
algorithm, Modular arithmetic 
Day 2: 1/7 
Chapters 0 and 1 
Mathematical Induction,
Equivalence Relations, Properties of Functions, First Examples of groups 
Day 3: 1/8 xhour instead of Saturday 1/10 
Chapter 2 
Binary operations,
Definition and further examples of groups. 
Day 4: 1/9 
Chapter 2, and 3 
Elementary properties of
groups, Finite groups, Subgroups. 
Day 5: 1/12 
Chapter 3 
Subgroups, Subgroup tests. 
Day 6: 1/14 
Chapter 3 and start Chapter
4 
Center of a group,
Centralizer of an element. Cyclic groups: definitions and examples 
1/15 optional xhour problem solving session and
preparation for the quiz 


Day 7: 1/16 
Chapter 4 
Properties of cyclic groups
and start classification of subgroups of cyclic groups. 
1/19 Martin Luther King Jr. Day No class 


Day 8: 1/21 1^{st} 30
minute quiz 
Chapter 4 
Classification of subgroups
of cyclic groups. 
Day 9: 1/22 xhour instead of the class
on 1/19 
Chapter 5 
Permutations; Cycle
notation and Properties 
Day 10: 1/23 
Chapter 5 
Properties of permutations 
Day 11: 1/26 
Chapter 6 
Group isomorphism; Examples 
Day 12: 1/28 
Chapter 6 
Properties of an
isomorphism; Automorphisms 
1/29 optional xhour problem solving session and
preparation for the Midterm exam 


Day 13: 1/30 
Chapter 7 
Cosets; Lagrange's theorem; Arithmetical corollaries 
Day 14: 2/2 Midterm exam 
Chapter 7 
Fermat's little theorem;
Orbits and stabilizers; 
Day 15: 2/4 
Chapter 8 
External Direct Product of
Groups 
Day 16: 2/6 
Chapter 9 
Normal subgroups, Factor
Groups, Hölder's theorem 
Day 17: 2/9 
Chapter 9 
More comments on normal
subgroups, Application of Factor Groups, Internal Direct Product 
Day 18: 2/11 
Chapter 10 
Group Homomorphisms,
properties of subgroups under homormorphisms 
Day 19: 2/12 xhour instead of the class
on 2/13 
Chapter 10 
Normal subgroups and
kernels, First Isomorphism Theorem 
2/13 Winter
Carnival No class J 


Day 20: 2/16 The
date of 2^{nd} 30 minute quiz is changed to 2/18 following students
wishes 
Chapters 10 
Applications and Examples 
Day 21: 2/18 2^{nd} 30
minute quiz 
Chapters 12 
Rings and examples of rings 
Day 22: 2/20 
Chapters 12 and 13 
Subrings, and Integral Domains 
Day 23: 2/23 
Chapter 13 
Fields, Characteristic of a
Ring with Unity 
Day 24: 2/25 
Chapter 14 
Ideals and Factor Rings,
prime and maximal ideals 
2/26 optional xhour problem solving and
preparation for the quiz 


Day 25: 2/27 
Chapter 15 
Ring Homomorphisms,
properties, ideals are kernels 
Day 26: 3/1 3^{rd} 30
minute quiz 
Chapter 15 
Finish Ring Homomorphisms 
Day 27: 3/3 
Chapter 16 
Polynomial rings, division
of polynomials 
Day 28: 3/5 
Chapter 17 
Factorization of
Polynomials, Irreducible polynomials 
Day 29: 3/8 
Chapter 19, 20, 21 
Vector spaces and their
dimensions (briefly). Extensions and algebraic extensions of fields. 