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Math Tools for Economists-Econ 1078-100 Steve Thorpe University of Colorado-Boulder Spring 1996 Office: ECON 107 Phone: 492-7908 E-mail: [email protected] Office hours: Mondays and Wednesdays , 2:00-3:50; Fridays, 9:00-10:50; by appointment. Introduction Let me begin this course with a challenge: find an issue or topic that does not in any way involve mathematics. I think that you will be surprised to find out just how ubiquitous math is in our world. Note that this does not imply that all issues are equally interesting to all people. I do believe, however, that each of us finds something interesting. [n this course, we will strive to use our interests (yours and mine) to our advantage in order to learn the mathematical tools necessary to live in our complex society. Although math is everywhere, it is more prevalent in some areas-Bconomics, for example-than in other areas. Most issues in economics are inherently quantitative. For example, you care not only that you earn interest on your savings, but also about how much interest you get. Some issues are qualitative: If interest rates rise, would you expect the price of a share of Nintendo stock to rise or fall? You could think about this question as follows: A Nintendo share is worth something because it will pay dividends, and because you can sell it later. Imagine that the money you use to buy the share would otherwise be put into a savings account. If the interest rate on the savings account is higher, then savings is more attractive and, correspondingly, the Nintendo stock is less attractive. Thus. the price of a Nintendo stock falls when interest rates rise because fewer people will want to hold Nintendo stocks. We are still left with the question of how much the stock price will fall. In this course, we will answer questions like these , and many other types, using mathematical models. Resources There is no single "textbook" for the course. Rather, we will spend time reading and analyzing the mathematical aspects of everyday economic issues found in newspapers and magazines, and on television. A student subscription to a good newspaper such as The Wall Street Journal or The New York Times is strongly recommended. There is, however, one required resource for the course: A Mathematical Skills Primer, by John Martin. You should treat this volume as a reference book. Keep it next to your dictionary and thesaurus. (Unless you have trouble sleeping at night, don't try to read through the primer as a textbook or a novel.) Grades Your final letter grade for the course will be based primarily on your performance on three exams, two midterm exams and a final exam (30% each), and on your scores on periodically assigned problem sets. The final exam is scheduled by the University for Monday, May 13th, from 7:30 to 10:30 a.m. If you cannot make this exam do not take this course. General Course Outline* Material Comprising Exam 1: The Basics • Number systems • Fractions, decimals, and percents • Exponents and Logarithms • Scientific notation and unit conversions • Algebra • Sets • Graphing Material Comprising Exam 2: Modeling • Functions and equations • Simultaneous equations • Matrices • Linear programming Material Comprising Exam 3 (final exam): Information for Making Choices • Simple and compound interest • Present value/discounting • Probability and statistics *Since we are not using a traditional textbook for this course, the order of the topics is not set in stone. In general, we will cover the topics in an order in which they are needed for the issues we are discussing at the time. ,..,