Personal mathematics and computing: tools for the liberal arts
Computers can be effective tools for participating in the affairs of the world. They can also be used by the "experts" to erect barriers to participation. This book is a self-contained tutorial that can assist any reader with a background in high school mathematics in learning how to apply personal computing to enhance his or her understanding of modern quantitative methods in such areas as politics and economics, in environment and ecology, or in probability and statistics.The first part briefly introduces programming in True BASIC and includes eight programming projects that teach by example. These illustrate a variety of interesting applications and methods of computer-based quantitative reasoning - in lotteries and property taxes, in the law of supply and demand and the laws of chance (ESP, dice rolling, coin flipping, test taking), and in the use of peremptory challenges in jury selection.The remainder of the book applies mathematics and computing to real problems. Here the emphasis is on the art of expressing problems in ways that are amenable to computer analysis, with "assignments" for writing a number of computer programs for a wide variety of applications - in probability and statistics (a statistical comparison of two popular beers with the aid of a random number generator, a comparison of two roulette strategies, a statistical analysis of polling results, the Bell-Shaped Curve, and an analysis of a program aimed at reducing recidivism), in economic modeling (changing prices, inflation, mathematical tools for decision making, game theory), in optics (Fermat's principle, reflection and refraction, light caustics, funhouse mirrors, and an optical paradox), in Massachusetts local aid distribution, and in population models and ecology.Frank Wattenberg is Professor of Mathematics at the University of Massachusetts, Amherst.
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Eight Programming Projects
Probability and Statistics
8 other sections not shown
apparent position ation Population average per capita Bwinnings calculations capita EQV capita expenditures capita revenue resources capita WFTE choices choose cities and towns City or Town column communities computer program cost of ingredients cursor demand function equation equilibrium point equilibrium population equilibrium price event ex-prisoners exactly example Exercises Exercise expected payoff factors Fermat's Principle flip future value graph Heads Tails INPUT jury large number light ray linear regression logistic model look Lottery Formula Massachusetts mathematical mirror Modified demand Notice null hypothesis object output Pascal's Triangle peremptory challenges Player population multiplier possible present value price of Byties PRINT probability of spinning probability space property tax public services random number rise shown in Figure simulate slope species spinner spinning gray statement strategy subroutine supply function Tails Heads Tails Tails target Town Population trials True BASIC variable write