Foundations of Geometry
Pearson (Verlag)
978-0-13-143700-5 (ISBN)
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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.
(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.
| Erscheint lt. Verlag | 24.2.2005 |
|---|---|
| Sprache | englisch |
| Maße | 234 x 180 mm |
| Gewicht | 634 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-13-143700-3 / 0131437003 |
| ISBN-13 | 978-0-13-143700-5 / 9780131437005 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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