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