Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
1 primary work • 2 total works
Book 114
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition "...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 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.
With its logical, yet flexible, organization, the Second Edition: * Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being * Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods * Bridges seemingly disparate topics by creating thoughtful and logical connections * Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition 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.
With its logical, yet flexible, organization, the Second Edition: * Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being * Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods * Bridges seemingly disparate topics by creating thoughtful and logical connections * Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition 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.
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.
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.