Anonymous
Posted October 30, 2005
Serge Lang's presents the mathematics he thinks high school students should know when they begin their study of college mathematics. As such, it provides a good means to supplement what you learned in high school with material not normally covered in the high school curriculum that will serve you well if you study mathematics in college. The book is divided into four sections: algebra, intuitive geometry, coordinate geometry, and miscellaneous topics. The algebra section begins with a discussion of the integers, rational numbers, and real numbers. Linear equations, systems of linear equations, powers and roots, and inequalities are also covered. A brief discussion of logic precedes a section on geometry that covers distance, angles, isometries, and area. The coordinate geometry section covers rectangular and polar coordinates, dilations and reflections, segments, rays, lines, parametric equations, trigonometry, and conic sections. The final section addresses functions, more general mappings, complex numbers, mathematical induction proofs, summations, geometric series, and determinants. Topics are well motivated and clearly presented. The book gives you insight into the deeper structure of mathematics. However, the presentation of the material is marred by numerous typographical errors. The problems range from routine calculations to proofs. Some problems are quite challenging and require considerable ingenuity to solve. Answers to some of the exercises are included in the back of the text.
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More About This Textbook
Overview
This text in basic mathematics is ideal for high school or college students. It provides a firm foundation in basic principles of mathematics and thereby acts as a springboard into calculus, linear algebra and other more advanced topics. The information is clearly presented, and the author develops concepts in such a manner to show how one subject matter can relate and evolve into another.
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Table of Contents
1: Numbers. 2: Linear Equations. 3: Real Numbers. 4: Quadratic Equations. 5: Distance and Angles. 6: Isometries. 7: Area and Applications. 8: Coordinates and Geometry. 9: Operations on Points. 10: Segments, Rays, and Lines. 11: Trigonometry. 12: Some Analytic Geometry. 13: Functions. 14: Mappings. 15: Complex Numbers. 16: Inductins and Summations. 17: Determinants.