Textbook
Sections
|
Problems
|
due
|
| Chapter 3, Rings: homomorphisms, ideals and quotients
|
3.4/ 2, 3, 6, 7, 10, 11
|
I'll collect homework on Friday, January 11. |
| Chapter 3, Maximal ideals, Rings of quotients
|
3.5/ 1, 2; 3.6/ 1, 2, 3, 4
|
We will have a quiz on Friday, January 18. |
| Chapter 3, Euclidean rings
|
3.7/ 1, 2, 3, 4, 7, 8
|
I will collect homework on Friday, January 25. |
| Chapter 3, Polynomial rings
|
3.9/ 1-5
|
We will have a quiz on Friday, February 1. |
| Chapter 3, Irreducible polynomials in Q[x]
|
3.10/ 1-5
|
I will collect homework on Friday, February 8. |
| Chapter 4.5, Modules
|
4.5/ 3-7. Let V be the solution space for the linear
homogeneous differential equation y^(4)-y^(3)=0. (a) Show
that V is a k[T]-module if T acts via differentiation.
(b) Show that V is a cyclic k[T]-module.
|
We will have a quiz on Friday, February 15. |
| Chapter 5.1/ Algebraic Elements
|
5.1/ 1-5, 7
|
I will collect homework on Friday, March 1. |
| Chapter 5.1/ Algebraic integers, transcendental elements
|
5.1/ 10, 11, 12, 15; 5.2/ 1, 4
|
We will have a quiz on Friday, March 15. |
| Chapter 5.3/ Roots of polynomials
|
5.3/ 2, 5, some parts of 6, 7.
|
I will collect homework on Friday, March 22.
Note that there are, imho, beautiful
presentation problems in
Section 5.4! |
| Chapter 5.5/ Multiple roots
|
5.5/ 2, 3, 4, 5, 6, 7
|
We will have a quiz Friday, March 29. |
| Chapter 5.6/ Automorphisms
|
5.6/ 1-6
|
I'll collect homework on Friday, April 5. |
| Chapter 5.6/ Symmetric polynomials, first Galois group
|
5.6/ 8, 9 (c), 11, 17. Please review Examples 5.6.1-3.
|
We will have a quiz on Friday, April 12. |
| Chapter 7.1
|
5.6/ 17, examples 5.6.1-3, 7.1/ 1, 2, 3, 4
|
no more quizzes... The final exam is on May 1. |