Homework Assignments

for Block I

**RINGS AND FIELDS**

Lesson #

Date(s)

Section

Topic

Homework Assignment

1

Jan. 14

18

 Course Overview

Introduction to Rings		 Read Section 18;
Do problems:
pp. 174-177 #6, 10, 11, 18, 24, 25, 33, 35, 38, 44, 48, 50
(Due Mon., Jan. 21)

& Presentations:
pp. 174-177 #40, 41, 51, 52, 53
(Due Fri., Jan. 18) 

2

Jan. 16

18

 Rings and Fields

Problem-solving

3

Jan. 18

18

 Student Presentations

4

Jan. 21

19

 Integral Domains Read Section 19;
Do problems:
pp. 182- 184 #2, 3, 10, 14, 17, 23, 26, 27, 30
(Due Fri., Jan. 25)

5

Jan. 23

19

 Integral Domains/Characteristic of a Ring

6

Jan. 25

20

 Fermat's Little Theorem Read Section 20;
Do problems:
pp. 189-190 #4, 10, 17-19, 23, 24, 27-30
(Due Fri., Feb. 1)

7

Jan. 28

20

 Euler's Theorem

8

Jan. 30

21

 The Field of Quotients Read Section 21;
Do problems:
pp. 196-197 #2, 4
(Due Mon., Feb. 4 but not to be collected)

9

Feb. 1

22

 Rings of Polynomials

Read Section 22;
Do problems:
pp. 207-209 #4, 16, 17, 20, 21, 22, 23, 27, 28, 31 (Note: 31 refers to 29 & 30, so you might have to think a bit about those problems too. I only want your write-up for 31.)
(Due Fri., Feb. 8)

10

Feb. 4

22

 The Evaluation Homomorphisms

11

Feb. 6

23

 Factorization of Polynomials Read Section 23;
Do problems:
pp. 218-220 #3, 7, 11, 14, 15, 19, 21, 25, 27-31
(Due Mon., Feb. 11 but not to be collected)

& Presentations:
pp. 219-220 #34, 35, 36 (if time allows, we'll talk about 27-31 too)
(Due Mon., Feb. 11)

12

Feb. 8

23

 Factorization of Polynomials

13

Feb. 11

23

 Student Presentations

14

Feb. 13

 

 Exam I (covers Sections 18-23) The take-home will be distributed; it is due Mon., Feb. 18
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