Foundations of Geometry
G. Venema

For sophomore/junior-level courses in Geometry; especially appropriate for students that will go on to teach high-school mathematics. This text comfortably serves as a bridge between lower-level mathematics courses (calculus and linear algebra) and upper-level courses (real analysis and abstract algebra). It fully implements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers. Foundations of Geometry particularly teaches good proof-writing skills, emphasizes the historical development of geometry, and addresses certain issues concerning the place of geometry in human culture. Implementation of "The Mathematical Education of Teachers (MET)"-Achieves the goals of MET within the context of a traditional axiomatic approach to geometry. Prepares students to teach high school geometry by making connections that enable a deeper understanding of the subject. Comprehensive coverage of most of Euclid's Elements-Covers almost all of the material in the first six books of that work. Gives students a wide range of geometric topics. Careful statements of the axioms. Aids students' understanding of how the theorems of geometry are built on the axioms. Coverage of transformations and the transformational approach to the foundations-Contains a complete classification of rigid motions of the plane and an explanation of how the Reflection Postulate can substitute for the Side-Angle-Side Postulate. Helps students understand the transformational perspective and how it can be incorporated into the axioms. A complete construction of the traditional models for Hyperbolic Geometry. Gives students a model that helps them understand the relationships spelled out in the axioms. A study of geometry in the real world-Looks at some non-traditional models and curved spaces. Helps students arrive at answers to the questions that naturally arise about the relationship between non-Euclidean geometry and the geometry of the real world. An introduction to proof-Acts as a bridge between lower-level courses in which technique is emphasized to upper-level courses in which proof and the understanding of concepts are emphasized. Enables students to experience the axiomatic method and study careful proofs that characterize more advanced mathematics. Emphasis on how to write proofs-Provides many model proofs as well as commentary on key proofs. Provides students with an excellent introductory chapter on how to write proofs, and provides more advanced techniques as they progress through the course. Includes many proofs that are exercises, with hints given so that students know roughly how the proof should be structured. Enables students to concentrate on how to organize and communicate the proof.Careful attention to the historical development of geometry-Discusses certain cultural and philosophical issues; and demonstrates the changes that the foundations have gone through over time. Helps students see that mathematics is a human activity. Use of technology-Encourages the use of such tools as Geometer's Sketchpad. Provides an aid for visualizing geometric relationships and a way to explore possible relationships.  Comprehensive appendices-Includes Euclid's Book I, Other Systems of Axioms for Geometry; Postulates; the Van Hiele Model of the Development of Geometric Thought, and Hints for Selected Exercises. Enables students to continue to use this book in their future careers as a convenient desk reference.

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Wydawnictwo: angielskie
Data wydania: b.d
Kategoria: Popularnonaukowe
ISBN: 978-0-13-143700-5
Liczba stron: 0