Foundations of Geometry
Published on 24. February 2005
Book
Paperback/Softback
448 pages
978-0-13-143700-5 (ISBN)
Description
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.
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.
More details
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
Professional and scholarly
Dimensions
Height: 180 mm
Width: 234 mm
Thickness: 17 mm
Weight
634 gr
ISBN-13
978-0-13-143700-5 (9780131437005)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Gerard Venema
Foundations of Geometry
Book
11/2011
2nd Edition
Pearson
€108.93
Shipment within 15-20 days
Content
(NOTE: Each chapter concludes with Exercises.)
1. Euclid's Elements.
2. Axiomatic Systems.
3. Theorems, Proofs, and Logic.
4. Set Theory and Real Numbers.
5. The Axioms of Plane Geometry.
6. Neutral Geometry.
7. Euclidean Geometry.
8. Hyperbolic Geometry.
9. Area.
10. Circles.
11. Constructions.
12. Transformations.
13. Models.
14. The Geometry of the Real World.
Appendix A: Euclid's Book I.
Definitions. Postulates. Common Notions. Propositions.
Appendix B: Other Systems of Axioms for Geometry.
Hilbert's Axioms. Birkhoff's Axioms. SMSG Axioms. UCSMP Axioms.
Appendix C: The Postulates Used in this Book.
The Undefined Terms. The Postulates of Neutral Geometry. The Parallel Postulates. The Area Postulates. The Reflection Postulate. Logical Relationships.
Appendix D: The Van Hiele Model of the Development of Geometric Thought.
Appendix E: Hints for Selected Exercises.
Bibliography.
Index.
1. Euclid's Elements.
2. Axiomatic Systems.
3. Theorems, Proofs, and Logic.
4. Set Theory and Real Numbers.
5. The Axioms of Plane Geometry.
6. Neutral Geometry.
7. Euclidean Geometry.
8. Hyperbolic Geometry.
9. Area.
10. Circles.
11. Constructions.
12. Transformations.
13. Models.
14. The Geometry of the Real World.
Appendix A: Euclid's Book I.
Definitions. Postulates. Common Notions. Propositions.
Appendix B: Other Systems of Axioms for Geometry.
Hilbert's Axioms. Birkhoff's Axioms. SMSG Axioms. UCSMP Axioms.
Appendix C: The Postulates Used in this Book.
The Undefined Terms. The Postulates of Neutral Geometry. The Parallel Postulates. The Area Postulates. The Reflection Postulate. Logical Relationships.
Appendix D: The Van Hiele Model of the Development of Geometric Thought.
Appendix E: Hints for Selected Exercises.
Bibliography.
Index.