Math 351, Fall 1999

Course handouts

• First part of syllabus. September 01 to October 11
  

Since lecture of September 15 was devoted to a discussion of homework problems, later lectures are delayed one class. Similar use of the September 27 class now leaves us two classes behind schedule, although the slides for September 27 include material on factor groups not shown during that class.

• Second part of syllabus.

Exam schedule:

• Wednesday, October 13 (chapters 1 and 2) By popular demand, the exam has been postponed until Monday, October 18. It will be a closed book exam. There will be no workshop class on October 18, and the time can be used for finishing the exam, although the exam will be planned to be finished in 80 minutes.
  
• Wednesday, November 17 (everything else) Again, popular demand has caused this exam to be postponed until November 22, and the workshop period will be available for finishing the exam.
  
• (Final) Tuesday, December 21, 8 -- 11 AM in SEC-217 (regular leture room).

Copies of slides shown in lecture.

I also include a four-per-page format. This will be better if you want to print the slides, but seems less useful for viewing. Links will be added when that format is ready for use.

• September 01.Sections 1.1 thru 1.3, and alternate form for printing.
  
• September 08.Sections 1.4, and alternate form for printing.
  
• September 13.Sections 1.7, 2.1 and 2.2, and alternate form for printing.
  
• September 20.Section 2.3 and 2.4, originally prepared for September 15, and alternate form for printing.
  
• September 22.Section 2.5, and alternate form for printing.
  
• September 27.Troublesome exercises from chapter 1 and Section 2.6, with alternate form for printing.
  
• October 04.The homomorphism theorems, Section 2.7, with alternate form for printing.
  

Workshops

• #1 Chapter 1, problems 1 thru 4. Sep. 13. (corrected version). Only first problem is to be written up. An analysis and solution of problem 2 has been prepared (see section labeled "essays".
  
• #2 End Chapter 1, and begin chapter 2. Sep. 20. Note that only one indexing of workshops problems is used, so this contains a reworking of problem 4 and new problems 5 and 6. Only problem 5 is to be written up.
  
• #3 Chapter 2 -- groups. Sep. 27. A new slant on problem 6 and new problems 7 and 8. This problem 6 is to be written up.
  
• #4 Sections 2.4 thru 2.7 -- inner automorphisms and group actions. Oct. 04. A new slant on problem 3 and new problems 9 and 10. Either problem 3 or problem 9 is to be written up.
  
• #5 Workshop 5 contains an extension of problem 8, together with new problems 11 and 12. None of these need be handed in. The style of the problems was designed to call attention to the details that appear as certain statements are analyzed. Since the exam will look at these details, these questions should aid in preparing for the exam. After the exam, you were asked to take an exam problem that you did not do well and work out the details as a replacement for this workshop.
  
• #6 Chapter 3 -- the symmetric group. Oct. 25. Revisiting problem 9 and new problems 13 and 14. You may choose any of these problems to be written up.
  
• #7 Introduction to rings. Nov. 01. You may choose any of these problems to be written up.
  
• #8 Ideals and quotient rings. Nov. 08. You may choose any of these problems to be written up.
  
• #9 Fields. Nov. 15. You may choose any of these problems to be written up.
  
• Workshop 10, Nov. 29, asked to correct a weakness on the second hour exam from Nov. 22.
  
• #11 Using the isomorphism theorem. Dec. 06. Only one problem.
  
• #12 General review. Dec. 13. Just a few hints about what to expect on the final exam.
  

Essays

This section contains discussions of individual problems that may go into some of the painful details. They were not distributed in printed form although there is nothing to prevent these files from being printed. Rather that print them without looking at them, you should skim them to find what they contain and look at parts more closely when you need to model your solution of a workshop problem on one of these discussions.

• Associativity of symmetric difference. Starting from exercise 1.2#13e, the proof attempted in the September 15 class is completed and analyzed.
  
• Workshop problem 2. The sketch given in the workshop class on September 13 is expanded into a proof. The comments on organizing proofs in first order logic mentioned in the lecture of September 20 were based on what I had written here.