Quantitative Reasoning and Problem Solving

Final Exam
Here is the take home final exam. The final exam will due in my office at 12:25 P.M. Friday Dec 22 but you may hand it in earlier.

First Exam Redux
You can view/upload the first exam here.

Grading policy

First Midterm Exam	100 points
First Exam Redo (Due Tuesday Oct 24)	100 points
Second Midterm Exam in class Thursday Dec 14	100 points
Final exam (Take Home: 12:25 P.M. Friday Dec 22)	100 points
Weekly Homework (see below)	100 points
Problems (see below)	300 points

The lectures will follow the text, and the exams will be be based on this material.

Syllabus and Homework
We will start with the Part VII of the text: Chapters 21-23. Then go through the text from the beginning and cover as much as seems feasible. The following table gives the date when a chapter from the text is covered, the homework assignment(s) from that chapter, and the date when each assignment is due. There will be about 7 assignments worth 20 points each. The homework is intended to help you learn the material. The grader will try to find your conceptual errors. Show respect for the grader. Do not hand in messy or incoherent work. The grader will not grade it.

Chapter	Start Date	Assignment	Due Date
21 Savings Models	T Sep 5	pp 825-831: 2-7,11,15,17,21,28	R Sep 21
22 Savings Models	T Sep 12	pp 829-832: 29-36, 43-45	T Sep 26
22 Borrowing Models	T Sep 12	pp 852-853:1,2,4,5,7,9,15-26	T Oct 3
1 Urban Services	T Oct 24	pp 25-30:1,2,18,22,25,26,27,28,31,39	T Oct 31
2 Business Efficiency	T Oct 31	pp 64-65:1-11	T Nov 2
2 Business Efficiency	T Oct 31	pp 66-75:14,15,16,17,23,33,34,35,41,42,44,48,51,53,68	T Nov 16
15 Game Theory	T Nov 9	pp 584-588:1-10, 17	T Nov 28
15 Apportionment	T Nov 28	pp 534-536: 8,9,10,15,16, 19-22	R Dec 7

Problems

Click this link to view/download a collection of problems. These problems require no specific knowledge beyond arithmetic and high school algebra, but they are not easy. The lectures and homework correspond to the textbook, but the problems do not. My hope is that you will struggle with them and that the struggle will benefit you. Each problem has a point value as indicated. The total point count is about 1000 points. You may earn up to 300 points. The following policy applies.

1. You may collaborate on these problems, but if you do, you must disclose who you worked with. If you worked alone, so indicate. If you received help from someone, so indicate. If you used some written source in solving a problem, so indicate. In any case, the final writeup of a problem must be your own. Your grade will not depend on whether or not you worked alone or received help or used a written source.

   The first page of any problem set that you hand in must disclose

   • who (if anyone) you worked with,
   • who (if anyone) helped you,
   • what (if any) other sources you use, or else
   • a declration that you worked alone.

   The reason for requiring disclosure is to reinforce academic honesty as a value. (Mathematicians frequently discuss their research with each other, but always acknowledge these discussions in the final product.)
2. For all these problems, it is not enough to simply state an answer; you must show your work in such a way that someone unfamiliar with this course (but reasonably skilled at arithmetic and high school algebra) can follow your reasoning. Your grade will be based in part on the clarity of the exposition.
3. You may ask me for help either by email, in class, or during office hours.
4. Show respect for the grader. Messy work will be marked down.
5. You may resubmit any problem. The problem will be graded as if it were the first submission, and the final grade on the problem will be the grade on the final submission.
6. In order to insure that you do not put off doing any problems until late in the semester the following deadlines are imposed. To earn the full 300 points you must
   • earn 150 points on work handed in before Tuesday October 2,
   • earn 200 points on work handed in before Tuesday October 31, and
   • earn all 300 points on work handed in before Thursday November 30.
   If you fail to meet these deadlines, your score will be reduced. For example, if you only earn 140 points on work handed in before Monday October 2 you will lose 10 points. However, if a problem is handed in before a deadline, and that same problem is later redone, the redone problem is treated as if it was handed in before the deadline.

Miscellaneous

• This website has some very nice material on some of the subjects we will study.
• The most important formula in Chapter 21 is

  A=P(1+r)^t

  for the amount A in an account after t years where r is the effective annual yield and P is the principal.
• There are a few errors in the text.
• Here (as promised) is the answer to problem 28 on page 828 of the text.
• Here is the rehash of the discussion on page 817 about inflation.
• These questions may help resolve an ambiguity in problem 45 on page 830.
• I really don't like the interpretation of problem 1 on page 852. Here is a correct treatment.
• Here, as promised, are the answers to the sample exam. Since the third exercise set has not yet been returned, the exam on Thursday October 12 will only contain questions from Chapter 21.
• Here are two websites on the apportionment problem. Apportionment I and Apportionment II.
• Here is something I wrote on apportionment while I was learning about it.
• I found this article by Balinski and Young on apportionment very interesting.
• This table should help you do Problem 10 on page 535 of the Comap Text.
• Here is the computer program I demonstrated in class. To use it you need to install the python programming language on your computer.
• Here is a proof that Kruskal's alogorithm works.