Holy Cross Mathematics and Computer Science

MATH 352 -- Abstract Algebra II, Spring 2008

Syllabus and Schedule

Course syllabus
Course revised schedule (as of 4/8/08)

Information and Announcements

The final exam will be given at 8:30am on Saturday, May 3. Final exam review sheet.
Review sheets for the midterms:
1. Exam 1 review sheet
2. Exam 2 review sheet
Review session for final exam: Thursday, May 1 at 10:00am in SW 302.

Examples, Solutions, Class Notes, Etc.

Assignments

Problem Set 1: Section 8.2/1,2,3dh,5b,8,9,11,12,14,15,16. Due: Friday, January 25.
Problem Set 2: Section 8.2/22. Section 8.3/2,3,4,5,6b. Section 8.4/1ac. Due: Friday, February 1.
Problem Set 3: Section 8.4/6,7,12; Section 8.5/1,6,8,10,11. Due: Friday, February 8.
Discussion 1, writeups due: Wednesday, February 13.
Problem Set 4:
- Section 8.5/17. Here's a possible outline to follow:
  1. Show that there is a unique Sylow 7-subgroup H and either 1 or 7 Sylow 3-subgroups.
  2. Determine the structure if Sylow 3-subgroup is unique.
  3. If there are 7 Sylow 3-subgroups, let H = < a > and say one of the Sylow 3-subgroups is K = < b >. What are the possibilities for b^-1ab?
  4. Analyze each case from 3. Some are not possible (why not?) Some yield isomorphic groups (why?).
- Section 10.2/17, 19, 20, 23, 25.
Due: Friday, February 15.
Problem Set 5: Section 10.3/3c,5,7,8,11,12; Section 10.4/2,6,7,8,18. Due: Friday, February 22.
Problem Set 6: Section 10.5/13, 14; Section 10.6/5, 10, 12, 15 (a) (give the addition and multiplication tables -- the multiplicative group will be cyclic; look for a generator), 18, 19, 20. Due: Friday, March 14.
Problem Set 7: Chapter 15/7,8,9,11,17,19; Section 11.1/2,3,8,9. Due: Friday, March 28.
Discussion 2 -- writeups due: Monday, April 7.
Problem Set 8: Section 11.1/11,12,15,16; Section 11.2/7b. Due: Friday, April 4.
Problem Set 9: Section 11.2/8,9,11,12,13. Due: Friday, April 11.
Discussion 3 -- writeups due: Wednesday, April 30.

Downloading Information

The links for assignments and other handouts shown above with the notation (.pdf file) lead to documents in PDF format. To read and print these, you will need to have Adobe Acrobat Reader installed on your computer. This is available at no cost from Adobe.

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Last modified: May 8, 2008