Essential Advanced Precalculus: A Self-Teaching Guide

Can a set be a member of itself? How do we know that the square root of 2 is irrational? Can a graph really represent a function accurately? Is a function just a rule? Does canceling (crossing out) terms mask important algebraic properties? This entirely practical book is for the student who wants a complete command of the prerequisite material on the first day of calculus class.Success in calculus depends on having a reasonable command of all that went before, yet most precalculus students are taught only simple tools and techniques, leaving them with a superficial understanding of problem-solving. Tim Hill explains why things are true and encourages students to go beyond merely memorizing ways of solving a few problems to pass exams.Teaches general principles that can be applied to a wide variety of problems.Avoids the mindless and excessive routine computations that characterize conventional textbooks.Treats the subject as a logically coherent discipline, not as a disjointed collection of techniques.Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking.Omits digressions, excessive formalities, and repetitive exercises.Provides exceptional preparation for a calculus course.Includes problems (with all solutions) that extend your knowledge rather than merely reinforce it.Contents1. Sets2. The Real Number System3. Functions4. Graphs5. SolutionsAbout the AuthorTim Hill is a statistician living in Boulder, Colorado. He holds degrees in mathematics and statistics from Stanford University and the University of Colorado. Tim has written self-teaching guides for Algebra, Trigonometry, Geometry, Precalculus, Advanced Precalculus, Permutations & Combinations, Mathematics of Money, and Excel Pivot Tables. When he's not crunching numbers, Tim climbs rocks, hikes canyons, and avoids malls. Read more