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 P-130 of the Physics building.

My office hours are Thursday 2:00–4:00pm and Tuesday 5:00pm–6:00pm, in room 4-110 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 x2 + y2 = 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 phi-function
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.