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Introduction to Topology and Geometry

Introduction to Topology and Geometry

ISBN: 978-0-471-66260-0

Nov 2004

480 pages

Description

A sweeping yet uniquely accessible introduction to a variety of central geometrical topics

Covering over two centuries of innovations in many of the central geometrical disciplines, Introduction to Topology and Geometry is the most comprehensive introductory-level presentation of modern geometry currently available.

Unique in both style and scope, the book covers an unparalleled range of topics, yet strikes a welcome balance between academic rigor and accessibility. By including subject matter previously relegated to higher-level graduate courses in mathematics and making it both interesting and accessible, the author presents a complete and cohesive picture of the science for students just entering the field. Historical notes throughout provide readers with a feel for how mathematical disciplines and theorems come into being.

Students and teachers will benefit from a uniquely unified treatment of such topics as:

  • Homeomorphism
  • Graph theory
  • Surface topology
  • Knot theory
  • Differential geometry
  • Riemannian geometry
  • Hyperbolic geometry
  • Algebraic topology
  • General topology

Using a variety of theorems to tie these seemingly disparate topics together, the author demonstrates the essential unity of mathematics.

A logical yet flexible organization makes the text useful for courses in basic geometry as well as those with a more topological focus, while exercises ranging from the routine to the challenging make the material accessible at varying levels of study.

Preface.

Acknowledgment.

1. Informal Topology.

2. Graphs.

3. Surfaces.

4. Graphs and Surfaces.

5. Knots and Links.

6. The Differential Geometry of Surfaces.

7. Riemann Geometries.

8. Hyperbolic Geometry.

9. The Fundamental.

10. General Topology.

Appendix A: Curves.

Appendix B: A Brief Survey of Groups.

Appendix C: Permutations.

Appendix D: Modular Arithmetic.

Appendix E: Solutions and Hints to Selected Exercises.

References and Resources.

Index.

"This is a nice collection of topics that are not usually present in a single text…I am glad that the book is on my bookshelf." (MAA Reviews, January 1, 2006)

“…a very useful textbook…stimulating and never boring to read, illustrating once more the richness and beauty of the field.” (Zentralbaltt MATH, July 2005)

"Stahl...proves a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." (CHOICE, June 2005)