Essential Advanced Precalculus

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.


Contents

1. Sets

2. The Real Number System

3. Functions

4. Graphs

5. Solutions


About the Author

Tim 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.