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.