Course Goals

The main idea of this course is to give ``non-math people" the benefits that the study of mathematics offers toward being an educated person. We will look at several types of problems which, if we tried to do them using ordinary ``everyday thinking," would hopelessly baffle us. Mathematics, the Einsteinian ``refinement," will allow us to organize these problems so that they become not only possible but (after a lot of hard practice) easy to solve. This ideology of formalizing a problem to make it more doable is a technique that should be in the intellectual toolbox of every educated individual.

A second major goal is to familiarize you with some types of mathematical thinking which are used in the alleged ``real world." Every day scholars, professionals, community leaders, businesspeople, and citizens are confronted with a dizzying array of situations where somebody is trying to push something on them. In a stunning variety of these situations, mathematics is used, either in the background or to lend authority to the claims being made. An educated individual should be comfortable enough with mathematics to ask when the math really means something and when it's a cover-up for greed and bad ideology.

Course Content

Text: L. J. Goldstein, D. I. Schneider, and M. J. Siegel, Finite Mathematics and its Applications, 7ed, Prentice-Hall 2001.

We will start with chapter 5, which will serve as an introduction to techniques in formalizing and solving problems, and which is foundational to the rest of the course. Typical problems will involve sorting through a lot of information (there are so many students who have a computer, so many who have high debt burdens, so many who have both, and so many who have neither) to find the part we want (how many have no computer but do have a high debt burden?).

Chapters 6 and 7 cover probability and statistics, two of the primary areas in which the evil try to take advantage of the uneducated. Important applications will include the lottery (a tax on the uneducated), car insurance (why do we have to pay more until we're 25?), and election polls (Dewey defeats Truman?).

After this, we will turn our attention to chapter 1, where we will study linear equations and inequalities. Most of the material will probably be review for most people, so we will move through it rather quickly. It will be used extensively in the material that follows.

In chapter 3 we will look at a certain kind of optimization problems. Classical problems in this chapter are things like ``Say you own a factory that can produce TV's, computer monitors, and army-contracted ray guns. Here is a table of the materials each one needs and the profit margin on each. You can obtain up to so much of each of these materials. How many TV's, how many monitors, and how many ray guns should you produce to maximize profit?" They're quite daunting until we have a way to organize the problem.

We will look at some material from chapter 2, on matrices and matrix arithmetic. These are very powerful tools, and are useful far beyond what we'll do with them. However, they are quite important in game theory.

Last year's academy award winning film ``A Beautiful Mind" told the story of one of the pioneers of our next topic. We will study game theory in chapter 9. Game situations are translated into matrices, and a certain optimization (of the kind we will do in chapter 3) will help us find the best strategy for each player. Much of the original development of the field was in the 1940's through 1960's to study the strategy of nuclear warfare, but it is now used extensively in economics, finance, law, and political science. We'll talk about some of these applications.

Course Activities

Class meets Monday, Wednesday, and Friday, 1:55-2:45 PM, in DeBartolo 136.

Homework will be assigned daily or almost daily and will be collected weekly, on Wednesdays. It is wise to work on the homework as it is assigned, for a couple of reasons. First, there will be enough of it that it will not be practical to just sit down and do the whole week's worth in an evening. Second (and more importantly), the material builds on itself, so that a few days without working through at least some of the problems may find you feeling a little lost.

Cooperation on homework is strongly encouraged. There will almost certainly be problems on which it is necessary. Talk with each other, talk with me, talk with friends, use any resource. I do ask that you be careful to give credit where it is due. In mathematics, as in all academic disciplines, no idea is ever purely our own, but common decency calls for a parenthetical note like ``(joint work with Katie McIrish)" or ``(found in K. Rosen, Discrete Mathematics and its Applications)" where that reflects the way you got the solution you're presenting. Such citations will not adversely affect your grade in any way. Also, it is important to be sure that you understand the solution you present. In designing the tests, I will assume thorough familiarity with all homework problems due before the date of the exam.

You are encouraged to visit me in my office (see note on office hours above) or to call or e-mail me. Also, First Year of Studies offers workshops and tutoring that may be helpful to you. There is a TA for the class, Stephanie Zabela, who will hold regular help sessions at a time and location to be announced.

More details on the projects will follow. They will generally involve some in-depth analysis of a problem relating to course material. One of the main goals of these projects will be to call on you to write about math in English.

There will be some short pop quizzes from time to time. A perfect score on one will result in extra credit. They will be mainly intended to give you (and me) a little more of an idea how well you are understanding the material.

Exams will be given in the regularly scheduled class time and place on September 18, October 4, and November 20. The final exam will be given on December 17, 1:45 - 3:45 PM at place to be announced. The final will consist of two parts. The first will focus on material covered since the last exam, and the second will be cumulative. Of course, no cooperation can be permitted on exams.

Grading

Grades will be calculated from

Homework	50
Projects	50
Midterm exams (3 @ 100pts each)	300
Final Exam
(covering the last course material)	75
(cumulative part)	75
	550

Failure to attend class regularly will certainly adversely affect your grades on each of these factors.

I will make the following guarantees about letter grades. I may decide to lower these standards (i.e. give a higher grade than the one shown here), but will never raise them. Check here throughout the semester for updates.