Wednesday, June 19, 2019

Methods of Geometry (Free PDF)

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This book is a text for an upper-division general geometry course offered by many universities. It builds on knowledge gained in school and lowerdivision university courses, to introduce advanced geometry, emphasizing transformations and symmetry groups in two and three dimensions. These theories underly many fields of advanced mathematics, and are essential for application in science, engineering, and graphics. The book analyzes the content of the lower-level courses from an advanced standpoint, to lend prospective and in-service teachers insight into the structure of their subject as well as excitement about its beautiful methods and where they lead.

Mathematical preparation for this course should include vector and matrix algebra and the solution of square and nonsquare linear systems. Appendix C provides a streamlined summary of that material, with most of the nonobvious proofs. The book often uses simple concepts related to equivalence relations, described briefly in appendix A. Concepts related to transformations, their compositions and inverses, and transformation groups are developed in detail in section 6.1, but this book applies them only to isometries and similarities. The least upper bound principle is discussed in Appendix  and applied once in section 3.14, which is about ð.

About the author
1. Introduction
2. Foundations
3. Elementary Euclidean geometry
4. Exercises on elementary geometry
5. Some triangle and circle geometry
6. Plane isometrles and similarities
7. Three dimensional isometries and similarities
8. Symmetry
Appendix A Equivalence relations
Appendix  Least upper bound principle
Appendix C Vector and matrix algebra

Author Details
"James T. Smith"
San Francisco State University

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