MAT 512: Algebra for Teachers
About the course
The textbook for the course is Integers, Polynomials, and Rings by Ronald S. Irving. Have a look at the syllabus for course policies and more information.
Homework assignments
Homework assignments are due at the beginning of class on Monday.
Time and location
We meet on Monday and Wednesday, 6:05–7:25 pm, in room P130
of the Physics building.
My office hours are Thursday 2:00–4:00pm and Tuesday
5:00pm–6:00pm, in room 4110 of the Mathematics Building. For other
times, please contact me by email.
Tentative schedule
Please read the assigned pages in the textbook each week.
Class 
Date 
Topic 
Reading 
1 
Jan 23 
Introduction 
Read pages 1–21 this week. 
2 
Jan 25 
Division theorem 

3 
Jan 30 
Greatest common divisor, Euclidean algorithm 
Read pages 23–40 this week. 
4 
Feb 1 
Bezout's theorem, applications 

5 
Feb 6 
Congruences, equivalence relations 
Read pages 41–55 this week. 
6 
Feb 8 
Solving congruences 

7 
Feb 13 
Unique factorization 
Read pages 57–82 this week. 
8 
Feb 15 
Rings: definition and examples 

9 
Feb 20 
Units 
Read pages 83–101 this week. 
10 
Feb 22 
Irreducible elements, solutions to x^{2} + y^{2} = p. 

11 
Feb 27 
Exam 1 (in class) 
Material from class and Ch.1–5 
12 
Mar 1 
Congruence rings, integral domains 

13 
Mar 6 
Roots of unity, theorems of Euler and Fermat 
Read pages 95–113 this week. 
14 
Mar 8 
Euler's phifunction 

15 
Mar 20 
Polynomial rings, factoring polynomials 
Read pages 127–139 this week. 
16 
Mar 22 
Minimal polynomial, field extensions 

17 
Mar 27 
Quadratic polynomials, cubic polynomials 
Read pages 141–158 this week. 
18 
Mar 29 
Cubic polynomials, quartic polynomials 

19 
Apr 3 
Primitive polynomials, Gauss lemma 
Read pages 177–191 this week. 
20 
Apr 5 
Eisenstein's criterion 

21 
Apr 10 
Exam 2 (take home) Unique factorization for polynomials 
Material from class and Ch.6–10 
22 
Apr 12 
Polynomials over finite fields 

23 
Apr 17 
Quadratic polynomials over finite fields 
Read pages 201–220 this week. 
24 
Apr 19 
Polynomial congruences 

25 
April 24 
Ring homomorphisms and isomorphisms 

26 
April 26 
Finite fields 

27 
May 1 
Finite fields 

28 
May 3 
Final Exam (take home) 
Comprehensive 
Exam 1
Here are solutions to Exam 1.
Exam 2
Here are solutions to Exam 2.
Final Exam
Here are solutions to the Final Exam.