Homework is typically due two class periods after we finish the section. NOTE: Significant bonus points are available for proving any of the conjectures you make as a result of the computer explorations. You may not actually always have the tools in the preceding section for the proof though--sometimes later techniques may be needed. Thus, I will accept proofs of these conjectures at any time in the semester, but they must be written up especially carefully.

I asked Joe Gallian about solutions, and he said he is in the process of preparing them, and he added the following:

"Thanks for your letter. If it is not a bother I ask you to keep track of

the "solutions" you or your students produce and we can compare them to

what I come up with. Although I had a particular conjecture in mind for

each exercise there may be more than one possible."

So proofs would be very cool to send to him!

Chapter 12: 3, 6, 7, 18, 19, 33. Computer # 1, 4, 5 (from the website, not the book, which only has up to #3).

Chapter 13: 2, 13-16, 20, 23, 27, 41, 53, 60. Computer # 1-6 all.

Chapter 14: 25, 33, 39, 40 (take A to be an ideal, not just a set), 41, 43, 47.

Chapter 15: 4, 26, 28, 34, 40, 42, 50, 53, 60, 63

Chapter 16: 7, 11, 13, 21, 22, 33, 40

Chapter 26: 6, 9 , 13, 21 (hint--for 6, use cor to Dyck's theorem after trying to construct a group table to determine the max number of elements--note: if you get closure, you have gotten at least all of the elements, even if there is some duplication),