Math 28

Winter Term, 2002


Friday Jan 4: First day of class

Wednesday Jan 9: No Class

Thursday Jan 10: Class meets in X-hour 8:45-9:50. First homework is due. Write up the problems through Problem 15 to turn in. The mandatory problems are 2,4,7,8,9,10,14,15. If you are not familiar with mathematical induction, start reading Appendix B on mathematical induction and do as many problems from that appendix as you can. If you find you are having trouble with functions, you may start working on the appendix on relations but if you are relatively comfortable with functions, just skip that appendix. When we do a problem in several different ways in class, turning in multiple solutions done in class to that problem won't count for extra credit! It is when you or your group finds extra solutions independently that they count for extra credit. After this first assignment you will also start getting homework problems from the supplementary problems for the chapters, problems that have not been discussed in class. However, the majority of the homework will consist of problems from the main text, and we will discuss many, probably most, of the problems from the main text in class. Turn in the problems in a notebook, using the table of contents page you can download from the website to make a table of contents. If you don't have a table of contents, I can't grade the notebook, because I won't have a place to put the grades. Please look over the material in the notes through Problem 27 for our class discussion on Thursday.

Wednesday, Jan 16: Second homework is due. Write up problems 16 through 33 to turn in. Problem 19 is optional, though if we have time later on, we will come back to it. The mandatory problems are 16, 18, 20, or else start working problems in the appendix on mathematical induction, 24, 27, 29, 30, 32, 33. The feedback form has been revised. Print it out and get feedback from other students on your solutions to the non-mandatory problems. There is a three-hole punch available in the math department office; you may use it to punch holes in the feedback forms so you can put them with your problems in your notebooks.

Friday, Jan 18 Please be prepared to discuss the problems through Problems 42-50. Problems 43 and 44, which are based on Problem 42, are intended to give you a bit of a stretch, so you might want to start with Problems 45-50.

Monday, Jan 21:  No class, Martin Luther King Day.  Class moved to X-hour at 8.45 Thursday.

Wednesday, Jan 23:  Please be prepared to discuss problems 51-56.  Please turn in problems 34-50.  The mandatory problems are Problem 36, 37, 38, 40, 41, 43 (the phrase "the y-axis" should be replaced by "the line x=n"), 46, 49, 50.

Friday, Jan 25.  There was a sense in class that some people would like to attack the next set of problems instead of jumping forward into induction.  So please read the section on Ramsey numbers and be prepared to discuss problems 58-62.  Youíll find that they dovetail nicely with the problem we were working on in class on Thursday.

Monday, Jan 28.  Please read Chapter 2 through Problem 71 and be prepared to discuss the problems through Problem 71.  Chapter 2 is available from the web site, as is the current draft of the entire book.  The file containing the whole book does have an index if you are beginning to have trouble finding definitions, etc.

Wednesday, Jan 30.  Please turn in problems 51-71.  The mandatory problems are 54, 56, 57, 59, 65, 66, 68 (which you may have already done as part of Problem 21), 69.  Eventually I would like to see Problems 62 and 71, but it is unreasonable to expect everyone to get them this week.

For Friday Feb. 1, Please look over problems 74-78 and 83-85 and be prepared to discuss them in class.  Also our mid term should probably be sometime next week.  Think about whether it would be better for you to have it in the X-hour or to have it some evening (most likely Wednesday).

For Monday, Feb. 4, Please look over problems 86 to 95 and 97.  My Monday office hours are going to need to be at 3 instead of 4 because the department has a faculty candidate giving a talk at 4:00.

For Wednesday, Feb. 6, Please turn in problems 74-78, 83-85, 86-95 and 97. The mandatory problems are 78, 84, 86, 89, 91, 92, 94, 97 (Hint to saving some work: note that #(G) is 1 if G is a tree, and that you can compute #(G) directly if G is a tree with extra edges. You might or might not run into loops, edges from a vertex to itself, in working the problem, depending on how you do it. Notice that a loop is never in a spanning tree, so you can delete loops as soon as they arise in computing spanning trees.) Problem 94 is likely to require a fair amount of thought, so although it is mandatory, I won't expect to see it on Feb. 6.

Thursday, Feb 7, Class in X-hour at 8:45. Please go over the review at the beginning of Chapter 3 and Problems 100-110 and be ready to discuss them in class.

Friday, Feb. 8 no class "carnival holiday."

Monday, Feb. 11, Please look over problems 111-123 and be prepared to discuss them in class.

Wednesday, Feb. 13,  Please turn in problems 100-123.  The mandatory problems are 102, 107, 108, 109, 111, 114, 115, 117, 119, 120.

Thursday, Feb. 14, 7:00PM Mid Term Exam (You will have until 9:00 if you need the time.)

Friday, Feb. 15,  Please look over problems 124-135 and be ready to discuss them in class.

Monday, Feb. 18,  Please look over problems 125-127 and 129-140 and be ready to discuss them in class.

Wednesday, Feb. 20,  Please turn in problems 124-127 and 129-140.  The mandatory problems are 124, as revised here, 126, 127, 129, 131, 134, 135, 138. If you are planning to get to Problem 203 by the end of the term, continue through problem 148 with Problem 144 and 146-148 mandatory.

Friday, Feb. 15,  please work your way through problems 141 to 149, reading the material on pages 65-67 as you go. If possible, I would like us to be able to introduce Problems 150 and 151 in class on Friday, because they are tricky to understand but easy once you understand them. If you are trying to get to Problem 203, I recommend that you try to get to at least problem 154. As a group you will want to decide whether to skip over problems 155 to 161 and come back to them if you have time after you get to 203. If you do want to do problems 155-161 for next Wednesday, I suggest you work on them simultaneously with doing problems 164-174 simultaneously, partly because most of them are pretty straightforward.

Monday, Feb. 25,  Please look over problems 149-154 and 162-174 and be ready to discuss them in class. If you are trying to get to Problem 203 by the end of the term, I suggest that you try to get to problem 183. That will give you a chance to finish off 155-161 if you want to.

Wednesday, Feb 27,  Please turn in Problem 131 as revised here, Problems 141-154 and 162-170.  The mandatory ones are Problems 144, 146, 147, 148, 151, 153, 165, 166, 168, 170.  If you are trying to get to Problem 203, I suggest you turn in Problems 149-154 and 162-183.  The mandatory ones are 151, 153, 165, 166, 168, 170, 173, 174, 175, 177, 180, 182.

Friday, March 1,  Please look over problems 171-83 and be ready to discuss them in class. If you are trying to get to Problem 203 by the end of the term, I suggest that you try to get to Problem 195.   (There is a lot of algebra in Problems 196-203.)

Monday March 4, If you are not trying to get to Problem 203, download the simplified version of Chapter 4 that was posted around noon Saturday and look over problems 191-201.  If you are trying to get to Problem 203, look over Problems 196-203, using the version of Chapter 4 you already have.  If you want to work on problems 155-161, now is the time to do it!

Wednesday, March 6.  In the new version of Chapter 4, please turn in Problems 171-183 and 191-201.  The mandatory problems are 173, 174, 175, 177, 179, 181, 193, 194, 198, 201.  If you are trying to get to Problem 203, please turn in Problems 184-203 in the old version of Chapter 4.  In this case, the mandatory problems are 173, 174, 175, 177, 179, 181, 185, 186, 189, 193, 194, 201, 203.