5F
Math 516: Abstract Algebra I
# Math 516: Abstract Algebra I

## Fall Semester, 2003

** Instructor:** Anatoly Libgober

Office: SEO 413

** Phone: ** 312-413-2138

** Office Hours: ** MW 10 a.m. or by appointment.

** Text: ** D.Dummit and R.Foote, Abstract Algebra,
Second Edition, John Wiley and Sons, Inc.

** Hours: ** The course meets MWF at 9 a.m. in Taft Hall 304.
### Topics

This course is an introduction to abstract algebra. It includes
material in group theory, rings and modules. It will cover
Chapters 1-5, section 6.3

and Chapters 7-12 of the text

### Grading and Homework

Grades will be based on three midterms and homework problems assigned at
regular intervals. Problems may be assigned during classes or will
be posted on this site. Most, but not
all problems, will be

coming from the book.

### Other References

Will be given during the lectures.

### Homework

** Homework 1:**(due Friday Aug.29)
Section 1.1 #4,5,7,8,12,16,24,31. Write multiplication table for
(Z/12)^*
Section 1.2 #1,3,4,5,9,10,11.

** Homework 2:**(due Monday Sept.8) Section 1.3: #11,12,15,17,18.
Section 1.4: #10,11. Section 1.5 #1. Section 1.6 #6,8,9,19,24,26.
Section 1.7: #14,15,16,17.

** Homework 3:**(due Monday Sept.15)
Section 2.1: #8,13,14.
Section 2.2: #6,7,14.
Section 2.3: #3,9,14,26
Section 2.4: #8,9,11,14.

** Homework 4:**(due Wedn. Sept.24) Section 2.5 #9a.
Section 3.1 #14,34,35,36,40,41. Section 3.2 #4,12,16. Section 3.3 #8,9
Section 3.5: #9,10,12

** Homework 5:**(due Wedn. Oct 1) Section 4.1: #1,6,8a,10.
Section 4.2: #2,6. Section 4.3: 2a,9,13.25

** Homework 6:**(due Friday. Oct 10) Section 4.4, #5,13,16.
Section 4.5: 5,6,9,12,17,40. Show that a group of order 132 isn't simple

** Homework 7:**(due Monday Oct 20) Section 5.1 #9,10.
Section 5.2: #6,7,9. Section 5.4 #1,2,3,4,5. Section 5.5. #4,6,16
Find subgroups of the Heisenberg group H(Z/pZ) such that H(Z/pZ) is their
semidirect product

** Homework 8: ** Section 6.3 #3,4,5,11. Section 7.1 #5,7,11,13,24,25,26,28. Section 7.2 #1,3,5,10,12.

** Homework 9: ** Section 7.3 #4,6,10,13,21,22,26,29,33.
Section 7.4 #2,4,7,9,16,17,27,22a,30,31.37. Section 7.5 #2,4,5,
Section 7.6 #4,6,7,8,10,11. Appendix II #1,2,4.

** Homework 10: ** Section 8.1 #1a,1b, 2a.8. Section 8.2 #1,3,5.

** Homework 11: ** Section 8.3: #4,6,7. Section 9.1: #4,6,7,11,13,15,17.
Section 9.2: #4,6,8. Section 9.3 #2,3.

** Homework 12:** Section 9.4: #1,2.5,6,7. Section 9.5: #1,3.
Section 10.1 #2,4,5,7,8,9,10,11,15,19,20,21.

** Homework 13:** Section 10.2: #5,6,8,9,10,13.
Section 10.3: #1,2,3,4,6,7,9,11,13,19,20.
Section 10.4: #2,6,7,10,11,13,24.

** Final Exam.
**