The course described on this page ended December 16, 2004

## Math 375:

Abstract Algebra I

Department of Mathematics and Computer Science Hobart and William Smith Colleges Fall, 2004. Instructor: David J. Eck (eck@hws.edu) Monday, Wednesday, Friday, 1:55--2:50 PM. Room Napier 101. Course Handout: http://math.hws.edu/eck/courses/math375_f04.html Office Hours for Fall 2004: Monday and Wednesday, 1:00-- 1:50 Tuesday through Friday, 10:30--11:30

Assignments and other information for Math 375

will be posted on this page as the course is taught

during the Fall term of 2004.

## End of Term: December 16

The final exam for this course is scheduled for December 16 at 1:30 PM. For information about the exam, including a list of office hours during exam week, see the

## Fifteenth Week: December 6, 8, and 10

In the last week of classes, we will continue covering material from the handout on Rings and Fields. It is suggested that you do all the exercises from this handout, but they will not be collected or graded. A solution sheet for the exercises will be handed out in class on Friday.

Note: Exercise 4 in Chapter 2 of the handout isnot true. (So don't try to prove it!)

## Fourteenth Week: November 29; December 1 and 3

There is a test on Wednesday of this week. This test marks the end of the main part of the course, which covered the fundamentals of group theory. After the test, we will begin a brief look at some other parts of abstract algebra: rings, fields, and polynomial rings. Our path through this set of topics is just one thread out of many topics covered in Parts 3 and 4 of the textbook. Instead of trying to pick relevant readings out of the book, we will be using the following handout, which includes just the topics that we will cover in class:

We should cover the first four pages of this handout on Friday.

## Thirteenth Week: November 22

There is only one class this week, because of Thanksgiving break. We will be talking about Chapter 11. Remember that there is a test coming up after break, on Wednesday, December 1. An information sheet about the test is available.

## Twelfth Week: November 15, 17, and 19

We will be finishing up Chapter 10 this week. We might start Chapter 11, but we will also spend some time doing problems to review for the test. The following homework for the week is due on Monday, November 22:

- Chapter 10, pages 205--209: # 2, 6, 8, 12, 14, 20, 22, 36, 42, 44, 50
We have rescheduled the upcoming test, originally scheduled for Monday, November 22. The test will instead be given after Thanksgiving break, on Wednesday, December 1.

## Eleventh Week: November 8, 10, and 12

We will wrap up Chapter 9 and begin Chapter 10 this week. The following homework on Chapter 9 is due this Friday, November 12:

Chapter 9, pages 186--190, # 8, 10, 14, 20, 36, 44 46, 48, 54, 62 Some hints: For number 20, you might need the fact that every non-identity element in an infinite cyclic group has infinite order. For number 48, you can use the result of Exercise 47 without proving it. (Exercise 47 will be done in class.) For number 54, we already know that the intersection of subgroups is a subgroup; you only have to prove normality.

## Tenth Week: November 1, 3, and 5

This week, we will covering Chapter 9. The following exercises are due on Friday, November 5, and they cover earlier material:

- Chapter 8, p. 162, # 4, 8, 12, 24, 34, 36
- Supplementary Exercises, p. 169, # 20, 30, 40

## Ninth Week: October 25, 27, and 29

There is a test on Wednesday, October 27. We will be covering Chapter 8 on Monday and Friday, but note that nothing from chapter 8 will be covered on the test.

An information sheet about the test is available.

## Eighth Week: October 18, 20, and 22

The following homework was originally assigned to be due on October 22, but it has been moved. This homework will be due next Monday, October 25:

- Chapter 7, pages 145--146: # 2, 8, 10 16, 18, 20, 24, 26, 34
We will finish Chapter 7 and begin Chapter 8 by Friday. Remember that there is a test coming up on Wednesday, October 27.

## Seventh Week: October 13 and 15

There is no class on Monday of this week, because of Fall Break.

We will finish up Chapter 6 and begin Chapter 7 this week. I will also spend some time on

equivalence relations, which are covered in Chapter 0, pages 17--20.Everyone in the class has agreed to move the next test from Monday, October 25 to Wednesday, October 27.

## Sixth Week: October 4, 6, and 8

We will cover Chapter 6 this week. The homework for the week, from pages 129--132, is Exercises 2, 6, 10, 22, 26, 30, 32, 40, and 42. Because of Fall Break, this homework will not be due until Friday of next week, October 15.

## Fifth Week: September 27 and 29; October 1

We will cover Chapter 5 this week. You are only responsible for pages 93 to 105. We will do nothing at all in the class with the last section of the chapter, which talks about a check-digit scheme using D

_{5}.The following homework exercises are due next Wednesday, October 6:

- Supplementary Exercises, pages 89--91: Exercises 6, 14, 22, 32
- Chapter 5 Exercises, pages 111-113: Exercises 4, 6, 8, 12, 18, 26, 34, 38
- Additional Exercise: Investigate the powers of an n-cycle. What does (a
_{1},a_{2},...,a_{n})^{k}look like, as a product of disjoint cycles?

## Fourth Week: September 20, 22, and 24

There is a test in class on Friday, September 24. It will cover everything we have done up to the middle of Chapter 4. This includes everything in the textbook except for the section in Chapter 0 on equivalence relations.

Because of the test, there is no homework assignment this week.

## Third Week: September 13, 15, and 17

The reading for the week is Chapter 3 (although a few of the things that we discuss in class actually come from Chapter 4). The homework for the week, which is due next Wednesday, is: Chapter 3, page 67, problems number 2, 6, 8, 10, 12, 14, 18, 26, 28, 36, 48, 52.

Remember that there will be a test next week, on Friday, September 24.

There is a Department Picnic this Thursday, September 16. It starts at 5:30 on the north side of Eaton Hall -- rain location Albright lobby.

## Second Week: September 6, 8, and 10

The reading assignment for the week is Chapters 1 and 2, although we might still be finishing up Chapter 2 next Monday. The homework, which is due next Wednesday, September 15, is:

From Chapter 1, p. 37--38: # 2, 12, 14, 16 From Chapter 2, p. 54--56: # 2, 8, 12, 14, 18, 22, 26, 28, 30, 36Note that the due date for last week's homework was moved from Monday, September 6 to Wednesday, September 8. Also, note that we have not yet covered equivalence relations -- we will return to them later in the course when we actually need them (in Chapter 7).

Advance notice:There is a department picnic on Thursday of next week, September 16, at 5:30 near Eaton Hall.

## First Week: August 30 and September 1 and 3

During the first week of the term, we will go over some of the background material in Chapter 0. I expect that you already know about mathematical induction and functions, and we will not spend a great deal of time on those topics. I do not find the stuff about check digits in things like ISBN numbers and bar codes very interesting, and I will not expect you to know it. The section on equivalence relations will be important later in the course. We might skip it for now and cover it later when we need it. In any case, there are no homework exercises about equivalence relations this week. I hope that I will be able to begin the real material of the course, Chapter 1, on Friday.

The homework for the week is: Chapter 0, pages 23 and 24, Problems number 2, 4, 8, 10, 12, 14, 16, 22, 26, and 28.

The homework is due at the beginning of class, next Monday, September 6. I will hand out my own solutions to the homework at that time, so you must turn in the homework on time to get credit. You are permitted and encouraged to work with other people in the course on the homework, but you should write up your own solutions in your own words to turn in.