This no-nonsense guide provides students and self-learners with a clear and readable study of the most important ideas of precalculus mathematics. Tim Hill's distraction-free approach combines decades of tutoring experience with the proven methods of his Russian math teachers. The result: learn in a few weeks what conventional schools stretch into months. - 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. The Real Line and Coordinate Plane 2. Straight Lines 3. Circles and Parabolas 4. Functions 5. Graphs 6. Trigonometry 7. Solutions

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

This is a mathematics textbook that covers mostly precalculus topics with some introductory calculus, as well as more advanced topics that are often not covered by a standard high school curriculum. A chapter proceeds by first establishing some central definitions and then further mathematical consequences, gradually developing the topic from scratch in the process. Unlike many other textbooks in precalculus, this book places emphasis on the art of mathematical proof, with an abundant supply of theorems, lemmas, and other problems that require such proofs. Detailed solutions and proofs are supplied as well.The main purpose is to aid readers who wish to learn precalculus and advanced supplemental topics through a more theoretical and abstract perspective and challenge their mathematical critical thinking skills rather than solve simple computational problems. The book is intended to develop the reader's conceptual understanding of the subject, as well as harness their curiosity in exploring such advanced topics. Furthermore, the book can be used as a supplementary text for students currently taking a precalculus or similar level math class who wish to learn more and go beyond the standard precalculus chapters, and into more abstract, advanced topics that are often not taught in many high schools at all.

ÒGeometry is a very beautiful subject whose qualities of elegance, order, and certainty have exerted a powerful attraction on the human mind for many centuries. . . Algebra's importance lies in the student's future. . . as essential preparation for the serious study of science, engineering, economics, or for more advanced types of mathematics. . . The primary importance of trigonometry is not in its applications to surveying and navigation, or in making computations about triangles, but rather in the mathematical description of vibrations, rotations, and periodic phenomena of all kinds, including light, sound, alternating currents, and the orbits of the planets around the sun.Ó In this brief, clearly written book, the essentials of geometry, algebra, and trigonometry are pulled together into three complementary and convenient small packages, providing an excellent preview and review for anyone who wishes to prepare to master calculus with a minimum of misunderstanding and wasted time and effort. Students and other readers will find here all they need to pull them through.