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Introduction to Topology and Geometry (2E) by Saul Stahl, Catherine Stenson
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About this book :-
Introduction to Topology and Geometry (2E) written by
Saul Stahl, Catherine Stenson
This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications.
This text is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.
Book Detail :-
Title: Introduction to Topology and Geometry
Edition: Second Edition
Author(s): Saul Stahl, Catherine Stenson
Publisher:
Series:
Year: 2013
Pages: 518
Type: PDF
Language: English
ISBN: 9781118108109,9781118545904
Country: US
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About Author :-
The author Colin Conrad Adams (born 1942) was an American Professor of mathematics, author and educator. He worked as a professor of mathematics at the University of Kansas for almost thirty-four years. Saul Stahl received his B. A degree from Brooklyn College of the City University of New York in 1963, a M. A. from the University of California, Berkeley in 1966, and a Doctor of Philosophy from Western Michigan University in 1975. Education period of Saul Stahl in Brooklyn College of the City University of New York Education period of Saul Stahl in University of California, Berkeley Education period of Saul Stahl in Western Michigan University
Saul Stahl start his career as teacher of volunteer high school and college in Nepal as a part of the United States Peace Corps in 1965. Three years later he was appointed as a systems programmer at International Business Machines Co. He served at Wright State University as an assistant professor of mathematics from 1975 to 1977. In 1977 Stahl became a professor of mathematics at the University of Kansas and worked there for almost thirty-four years, becoming a Professor Emeritus.
The author Catherine Stenson , PhD, is Professor of Mathematics at Juniata College in Huntingdon, Pennsylvania.
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Book Contents :-
Introduction to Topology and Geometry (2E) written by
Saul Stahl, Catherine Stenson
cover the following topics.
1. Informal Topology
2. Graphs
2.1 Nodes and Arcs
2.2 Traversability
2.3 Colorings
2.4 Planarity
2.5 Graph Homeomorphisms
3. Surfaces
3.1 Polygonal Presentations
3.2 Closed Surfaces
3.3 Operations on Surfaces
3.4 Bordered Surfaces
3.5 Riemann Surfaces
4. Graphs and Surfaces
4.1 Embeddings and Their Regions
4.2 Polygonal Embeddings
4.3 Embedding a Fixed Graph
4.4 Voltage Graphs and Their Coverings
Appendix
5. Knots and Links
5.1 Preliminaries
5.2 Labelings
5.3 From Graphs to Links and on to Surfaces
5.4 The Jones Polynomial
5.5 The Jones Polynomial and Alternating Diagrams
5.6 Knots and Surfaces
6. The Differential Geometry of Surfaces
6.1 Surfaces, Normals, and Tangent Planes
6.2 The Gaussian Curvature
6.3 The First Fundamental Form
6.4 Normal Curvatures
6.5 The Geodesic Polar Parametrization
6.6 Polyhedral Surfaces I
6.7 Gauss
s Total Curvature Theorem
6.8 Polyhedral Surfaces II
7. Riemann Geometries
8. Hyperbolic Geometry
8.1 Neutral Geometry
8.2 The Upper Half-plane
8.3 The Half-Plane Theorem of Pythagoras
8.4 Half-Plane Isometries
9. The Fundamental Group
9.1 Definitions and the Punctured Plane
9.2 Surfaces
9.3 3-Manifolds
9.4 The Poincaré Conjecture
10. General Topology
10.1 Metric and Topological Spaces
10.2 Continuity and Homeomorphisms
10.3 Connectedness
10.4 Compactness
11. Polytopes
11.1 Introduction to Polytopes
11.2 Graphs of Polytopes
11.3 Regular Polytopes
11.4 Enumerating Faces
Appendix
A.Parametrization of Curves and Arclength
B.Brief Survey of Groups
C.Permutations
D.Modular Arithmetic
E.Solutions and Hints to Selected Exercises
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