Solomon Garfunkel, coordinating editor
W.H. Freeman, 1996
ISBN 0-387-94612-8
800 pp, $60 list
sales of first three editions: 120,000 copies (not including editions in languages other than English)
The average student takes just one mathematics course in college. What should be in it? For All Practical Purposes is a response that presents mathematics through its contemporary applications. It answers the questions, "Just what is mathematics used for?" and What do mathematicians do, practice, or believe in?"
This book is designed for a one- or two-semester course in liberal arts mathematics or in courses that survey mathematical ideas. It assumes some ability in arithmetic, geometry, and elementary algebra.
Chapter-ending Exercises are now graded according to level of difficulty and categorized by subject, to help instructors make assignments and help students succeed at solving problems.
Chapter 4, Linear Programming, begins with a manufacturing problem involving only one resource, and all algebraic steps are now shown and described
In Chapter 5 , Producing Data, a new section on statistical estimation carefully introduces the concepts of sampling variability and margin of error. These topics are fortified with Examples of Gallup Poll surveys on crime. The discussion of probability has been deleted from Chapter 5 (a cohesive discussion of probability is now in Chapter 8, Probability, The Mathematics of Chance).
In Chapter 6, Describing Data, the discussion of variance and standard deviation is supported by Examples comparing metabolic rates for men and women.
Chapter 9, Identification Numbers and Bar Codes, now discusses only the most important bar codes, zip codes, and UPC codes.
Chapter 11, Social Choice: The Impossible Dream, is reorganized so that the chapter begins with elections involving two alternatives and then moves to elections involving three alternatives. Chapter 11 also features expanded coverage of plurality voting, the most common system in use today, and the Condorcet winner criterion. There is a new section on the Hare system of voting (currently used in Ireland and Australia), plus a summary of the pros and cons of the voting systems discussed in the chapter, which concludes with Arrow's Impossibility Theorem (which shows that there's no perfect system) and Approval Voting (the best approach?)
Chapter 12, Weighted Voting Systems, breaks ground with a discussion of the Banzhaf power indices for the electoral college.
Chapter 13 opens with a new section on a recently developed scheme for handling property settlements (called the Adjusted Winner Procedure), which uses the Trump divorce to illustrate the procedure. This is followed by another new section that discusses a popular method for dividing an inheritance if there are more than two heirs (called the Knaster Inheritance Procedure). An engaging new section called "Divide-and-Choose" sets the stage for the remainder of the chapter, which is devoted to other fair-division procedures.
A refocused Chapters 14 more clearly compares and contrasts the U.S. House of Representatives apportionment methods proposed by Hamilton, Jefferson, and Webster by showing specifically the apportionment that each method gives and the paradoxes involved. The chapter ends with a new section on the method currently used to apportion the House (called the Hill-Huntington Method) and a summary section discussing which apportionment method is best.
The ideas presented in Chapter 15, Game Theory: The Mathematics of Competition, are brought up to date in a new Chapter 16, The Theory of Moves, which shows how competitors from Samson and Delilah to Leno and Letterman resolve conflicts using a farsighted strategy and, perhaps, deception.
Chapter 18, Geometric Growth, features many new financial growth models, including certificates of deposit, money-market accounts, savings plans, sinking funds, inflation, and depreciation.
German version of 1st ed.: Mathematik in der Praxis (Spektrum der Wissenschaft, 1990)
Spanish version of 3rd ed.: Las matemáticas en la práctica (Addison-Wesley Iberoamericana España, 1997)
Paul J. Campbell / campbell@beloit.edu