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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.
A book that explains the fundamentals of geometry, algebra, and trigonometry with as fewest words as the author deems it possible.
"The text is suitable for a typical introductory algebra course, and was developed to be used flexibly. While the breadth of topics may go beyond what an instructor would cover, the modular approach and the richness of content ensures that the book meets the needs of a variety of programs."--Page 1.
Sheldon Axler's Precalculus: A Prelude to Calculus, 3rd Edition focuses only on topics that students actually need to succeed in calculus. This book is geared towards courses with intermediate algebra prerequisites and it does not assume that students remember any trigonometry. It covers topics such as inverse functions, logarithms, half-life and exponential growth, area, e, the exponential function, the natural logarithm and trigonometry.
"Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of OpenStax College Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. OpenStax will also be releasing College Algebra and Algebra and trigonometry titles tailored to the particular scope, sequence, and pedagogy of those courses."--Preface.
A review of plane geometry, numerical trigonometry, geometric and trigonometric analysis, and limits emphasizes the graphic representation of problems to be solved by combined methods.
Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by clearly-defined learning objectives, and includes worked examples that demonstrate problem-solving approaches in an accessible way. Coverage and Scope Precalculus contains twelve chapters, roughly divided into three groups. Chapters 1-4 discuss various types of functions, providing a foundation for the remainder of the course. Chapter 1: Functions Chapter 2: Linear Functions Chapter 3: Polynomial and Rational Functions Chapter 4: Exponential and Logarithmic Functions Chapters 5-8 focus on Trigonometry. In Precalculus, we approach trigonometry by first introducing angles and the unit circle, as opposed to the right triangle approach more commonly used in College Algebra and Trigonometry courses. Chapter 5: Trigonometric Functions Chapter 6: Periodic Functions Chapter 7: Trigonometric Identities and Equations Chapter 8: Further Applications of Trigonometry Chapters 9-12 present some advanced Precalculus topics that build on topics introduced in chapters 1-8. Most Precalculus syllabi include some of the topics in these chapters, but few include all. Instructors can select material as needed from this group of chapters, since they are not cumulative. Chapter 9: Systems of Equations and Inequalities Chapter 10: Analytic Geometry Chapter 11: Sequences, Probability and Counting Theory Chapter 12: Introduction to Calculus
This no-nonsense guide provides students and self-learners with a clear and readable study of geometry's most important ideas. 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 days what conventional schools stretch into months. Covers classical and analytic geometry. 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 geometry 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. Includes problems (with solutions) that extend your knowledge rather than merely reinforce it. Contents 1. Triangles 2. Circles 3. Cylinders 4. Cones 5. Spheres 6. Analytic Geometry 7. Solutions 8. Geometry Cheat Sheet 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 and combinations, debt, mortgages, and Excel pivot tables. When he's not crunching numbers, Tim climbs rocks, hikes canyons, and avoids malls.
The fundamental shapes of geometry can be built into the grand sweeps of the Sydney Opera House or something as small as a snowflake. This title takes geometric concepts like polygons, platonic solids, and angles and demonstrates their myriad appearances in the world around us. From the Great Pyramid of Giza to sinking a bank shot in pool, geometry abounds.