22m:120 fall 2005

Abstract Algebra I

22m120, Fall 2005

Instructor: Fred Goodman

Announcements:

Review sheet for final.

 

Contact Information:

 

Lectures:

MWF 12:30, 118 MLH

 

Discussions:

Tuesdays, 12:30, 214 EPB

Office:

325G Maclean Hall

Email:

goodman at math dot uiowa dot edu

Phone:

Office: 319-335-0791

Paper Mail:

Fred Goodman
Department of Mathematics MLH
The University of Iowa
Iowa City, IA 52242-1419 USA

Office Hours:

T, Th 11-12

and by appointment

 

Teaching Assistant:

Oscar Vega

Office hours: M 1-2 PM, Th. 9- 10 AM.

 

Syllabus:

Click here for syllabus in PDF format.

Textbooks:

Frederick M. Goodman, Algebra: Abstract and Concrete, 2nd edition, Prentice Hall, 2002.


This text is required.

I. N. Herstein, Topics in Algebra, 2nd edition, John-Wiley 1975.

(You can often find an inexpensive international edition at abebooks.com.)

This text is recommended.

Other recommended reading:

Artin, Algebra .

Vinberg, A Course in Algebra.

Jacobson, Basic Algebra I, 2nd edition.

Assignment lists:

There will be 8 to 12 written assignments. Details willappear here as the assignments are made. Please see the remarks on the syllabus about the standard of explanation expectedon the homework. For homwork solutions, see http://www.math.uiowa.edu/~ovega/algebra/ .

First assignment, Due Wednesday Aug. 31.

Section 1.3, Exercises 1,2,3

Section 1.4 , Exercises 1, 2, 3, 8 (For 1, do not compute all 64 products. Instead, compute sufficiently many products to determine all the rest, and explain why your computations determine all the rest -- compare exercise 1.3.3.)

2nd assignment, Due Friday Sept. 9

Section 1.5: Exercises 1-7, 12, 14

Section 1.6: Exercises 1, 3, 4b, 7, 10, 11

3rd assignment, Due Friday Sept. 16

Section 1.7, Exercises 5, 6, 11-15

Section 1.8, Exercises 5, 6, 8, 9

4th assignment, Due Friday Sept. 23

Section 1.7: 4, 16

Section 1.8: 10 a , 15, 16

Section 1.10: 10

Section 2.1: 11-13

5th assignment, Due Friday Sept. 30

Section 2.2: 11, 16, 17. 19, 25

Section 2.3: 1, 2, 9

Section 2.4: 10-12, 20

6th assignment, Due Friday Oct. 7

Section 2.4: Exercises 14, 15

Section 2.5: Exercises 7, 8, 13, 14

Section 2.6: Exercises 2, 6

Section 2.7: Exercises 5, 6, 7

7th assignment, Due Friday Oct. 21

Section 3.1: Exercises 8-15

Section 3.2: Exercises 1, 4-6

Optional: Do the exercises on greatest common divisor in this handout.

8th assignment, Due Friday Oct. 28

Section 3.3: Exercises 1, 2, 4, 5, 8, 10

Section 5.1: Exercises 3, 6, 8, 12, 16, 20

9th assignment, Due Friday Nov. 4

Section 5.1: Exercises 17, 18, 19. (Exercise 20 was repeated, sorry.)

Section 5.4: Exercises 1, 2, 5, 6, 7, 8, 9

10th assignment, Due Monday Nov. 14

Section 5.3: Exercises 2, 7.

Section 5.4: Exercises 11, 12, 13, 14, 15.

Please note: I have changed the text on page 245 (about groups of order 28) and also the text of Exercise 5.4.14. So please print out pages 245-247 again before doing these exercises.

11th assignment, Due Friday Dec 2

Section 6.1: Exercises 4, 13, 16

Section 6.2: Exercises 1, 2, 3, 11, 15 (The definition of idempotent is in exercise 12.), 22

Section 6.3: Exercises 2, 7, 8, 9

LAST assignment, Due Friday Dec 8

Section 6.4:  Exercises  1, 2, 3, 10, 13

Section 6.5:  Exercises  4, 5, 7,  10, 11, 12

CONGRATULATIONS,  THAT’S THE END.

Exams:

There will be two midterm exams, tentative dates:

There will be a comprehensive final exam (exam period 21 Thursday Dec. 15 at 12:00). The text of the exams will appear here after the exams havebeen done by all students.

Practice tests and reviews:

Review sheet for first exam.

Review sheet for 2nd exam.

Text of the first exam.

Text of the 2nd exam.

Exams from Previous Semesters:

Midterm, 2004.

Midterm, 1998.

Final, 2004.

Final, 1998.