PDF Elementary Geometry for College Students Download
- Author: Daniel C. Alexander
- Publisher:
- ISBN: 9780395870556
- Category : Mathematics
- Languages : en
- Pages : 566
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One of the challenges many mathematics students face occurs after they complete their study of basic calculus and linear algebra, and they start taking courses where they are expected to write proofs. Historically, students have been learning to think mathematically and to write proofs by studying Euclidean geometry. In the author's opinion, geometry is still the best way to make the transition from elementary to advanced mathematics. The book begins with a thorough review of high school geometry, then goes on to discuss special points associated with triangles, circles and certain associated lines, Ceva's theorem, vector techniques of proof, and compass-and-straightedge constructions. There is also some emphasis on proving numerical formulas like the laws of sines, cosines, and tangents, Stewart's theorem, Ptolemy's theorem, and the area formula of Heron. An important difference of this book from the majority of modern college geometry texts is that it avoids axiomatics. The students using this book have had very little experience with formal mathematics. Instead, the focus of the course and the book is on interesting theorems and on the techniques that can be used to prove them. This makes the book suitable to second- or third-year mathematics majors and also to secondary mathematics education majors, allowing the students to learn how to write proofs of mathematical results and, at the end, showing them what mathematics is really all about.
Building on the success of its first four editions, the Fifth Edition of this market-leading text covers the important principles and real-world applications of plane geometry, with a new chapter on locus and concurrence and by adding 150-200 new problems including 90 designed to be more rigorous. Strongly influenced by both NCTM and AMATYC standards, the text takes an inductive approach that includes integrated activities and tools to promote hands-on application and discovery. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
ELEMENTARY GEOMETRY FOR COLLEGE STUDENTS, 7th Edition, is designed to help students develop a comprehensive vocabulary of geometry, an intuitive and inductive approach to the development of principles, and strong deductive skills to solve geometry-based real-world applications. Over 150 new exercises provide additional practice in writing proofs. Available with access to WebAssign, an online study tool that helps students master the course concepts.
The Student Study Guide with Solutions Manual provides additional practice problems for each section with solutions, as well as solutions to select odd-numbered problems from the text, along with section-by-section objectives.
The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.
This textbook provides an introduction to Euclidean geometry. While developing geometry for its own sake, the book also emphasizes the links between geometry and other branches of pure and applied mathematics.
Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Around 200 additional exercises, and a full solutions manual for instructors, available via www.springer.com ul