Math 181 C1 Home Page, Fall 2008

This is the home page for Math 181, A Mathematical World, Section C1 This class meets for the Fall 2008 semester MWF 10:00-10:50 in 341 Altgeld Hall. My intention is to provide, at the very least, an archive for all of the TeX-d handouts in the course and a guide to the semester, class-by-class.

Fourth week items

  • A student writes, regarding the Third Homework, Due Monday, Sept. 22: For question number 24 on p. 365, I reviewed the definition of independance of irrelevant alternatives to try and help myself better understand it. But, what I don't understand is how the winner of this problem would not change if people changed their votes. Perhaps I am understanding the question incorrectly? I appreciate your help.
  • My reply: The point here is that nobody changes their preferences regarding the relative ordering of A and B and yet the outcome differs. It's most worthwhile for you to write out what you think happens in each of the two cases and each of the two systems. Notice that the last voter changes slightly.
  • No other homework questions as of 2:30 pm 9/21/08.

    • Third week items

  • We basically finished Chapter 9, to the extent we'll be covering it, subject to any questions you might have on Monday. Our next topic will be Chapter 1 and graphs.
  • Lots of handouts, including an adjusted winner problem (the wedding of Pat and Chris) to work out for Wednesday.
  • I meant to post the Second Homework, Due Monday, Sept. 15 on the day I assigned it. Sorry.
  • Wednesday and Friday's handouts were a grab-bag of old exam questions on voting, a relic of local politics and an open-ended ballot (with 209 voters) whose point was that, if a weighted count of (t,1,0) is given to (1st,2nd,3rd), and t = 2, 5 and 11, then each of the candidates might win. The moral of the story is that the rules can make a huge difference in determining the winner

    • Second week items

  • We covered sections 13.4 and 13.5. We'll finish Chapter 13 on Monday and move on to Chapter 9, on voting systems.
  • There were three handouts. A blank template of Bob, Carol and Ted's preferences, an explitictly worked out version of how it should be split if Carol cuts, using the Steinhaus lone divider, and homework solutions. I won't link homework solutions. Come to class!
  • A student writes: I am trying to work on the hw due friday but I am stuck on the last two problems. I am not quite sure how to go about them. Thanks!
  • My reply: OK. What I mean is in #8, suppose this was an adjusted winner, and Bob gave 40 pts to the pension, 30 pts to the house, etc, and Carol gave 40 pts to the house, 30 pts to the investments, etc. How would this be allocated? In #9, we have a Knaster inheritance, with Bob saying the pension is worth $40,000, the house is worth $30,000, etc, and Carol says the house is worth $40,000, the investments are worth $30,000, etc. How would the items be split?

  • A student writes: if there is an equal bid on the vehicles how do you go about solving?
  • My reply: Make a decision and explain what you did.

    • First week items

  • We covered sections 13.1 through 13.3.
  • Information for the course is contained in the Course Organization. There was also a questionnaire (unlinked) and a Problem-solving template. The article from which I took the picture of the Konigsberg bridges is more technical than you'll probably want to read, but it can be found at Bridges, (The illustrations are at the end.) The Math 181 study list will not be put on the web for security reasons.
  • Here is a worked version of the book's 13.1 Example. Please note that there is a typo on p.2: the last two items in the last two columns should be 100 and 0, not 0 and 100. My apologies.
  • I passed out a couple of problems for you to work on in an "active learning" format on Friday -- two old exam questions.
  • Finally: First Homework, Due Friday, Sept. 5.
  • Bring questions to class on Wednesday and read sections 13.4 through 13.6.
  • Some correspondence on the second of the old exam questions:
    A student writes: I went through and attempted to complete the second sample worksheet you gave us on Friday that deals with the adjusted winner procedure (it is #9). Since there are six items, do bob &carol each receive three since there is an even amount? The numbers I got were that Bob would think he received 55% of the total and that Carol would think she received 60%. Am I correct or way off? I just want to see if I am doing it wrong before I complete the homework.

    My reply: In this problem, there is one place going down the column where the split is 55-60 for one person, and then the next place gives the split 65-50 the other way. When that happens, you have to do a little algebra and solve the equation to figure out how to split the item in the middle. I will talk about this problem in class on Wednesday.

    A student writes: I was wondering if before I begin to do the homework problems, if you could tell me if the solution I came up with for the second in class assignment is correct. Actually, the reason for this e-mail is that I am pretty sure it is not correct. I came up with:
    B gets 30+13+12(1-x)
    C gets 10+20+20+10(x)
    So, 43+12-12x=60+10x
    55-12x=60+10x
    55=60+22x
    x= -5/22.
    I don't understand why or how I could have come up with a negative fraction here. I would appreciate an explaination before I do all the homework probblems and do them all completely wrong, too.

    My reply: OK let's rearrange and set things up
    Item B C ratio
    1 30 20 1.50
    5 13 10 1.30
    6 12 10 1.20
    4 10 10 1.00
    3 15 20 .75
    2 20 30 .67
    If we split so that B gets 156 and C gets 432, then B thinks he's gotten 30+13+12 = 55 and C thinks she's gotten 10+20+30=60, so C gets too much. If we split so that B gets 1564 and C gets 32, then B thinks he's gotten 30+13+12+10 = 65 and C thinks she's gotten 20+30=50, so C gets too much. This means it's item 4 that you have to split. I'm not sure where you're getting the numbers for C.

    • Top of Page