Produktdetaljer
Biografisk notat
Steven G. Krantz is a professor at Washington University in St. Louis where he teaches mathematics. He has previously taught at UCLA, Princeton University, and Penn State University. He earned his PhD from Princeton University in 1974. Prof. Krantz has directed 20 PhD students and 8 master's-degree students, and published over 130 books and over 300 scholarly articles. He is the holder of the Chauvenet Prize, the Beckenbach Book Award, and the Kemper Prize, and he is a fellow of the American Mathematical Society.
This book is an ambitious but optimistic treatment of the subject of topology. Not only does Elements of Topology: Theory and Practice, Second Edition treat the standard basic material on point-set topology, but it also gives an introduction to algebraic topology, a treatment of manifolds, a discussion of function spaces, and some ideas of knot theory. Even the exciting new topic of the Jones polynomial is covered.
After discussing the key ideas of topology, the author examines the more advanced topics of algebraic topology and manifold theory. He also explores meaningful applications in several areas, including the traveling salesman problem, digital imaging, mathematical economics, and dynamical systems.
Topic coverage has been reduced in this second edition, and exercise sets have been added at the end of each section. The book as a whole—and the first two chapters in particular— offer many examples. Solutions to selected exercises are included at the end.
Today’s students need a text that speaks to them in their own language, and at a pace with which they are comfortable. That is the goal of this edition. Taking a fresh and accessible approach to a venerable subject, this text provides excellent representations of topological ideas. It forms the foundation for further mathematical study in real analysis, abstract algebra, and beyond.
Now in its second edition, this book is an ambitious but optimistic treatment of the subject of topology. Topic coverage has been reduced in this new edition, and exercise sets have been added at the end of each section. Today’s students need a text that speaks to them in their own language, and at a pace with which they are comfortable.
1. Fundamentals 2. Advanced Properties 3. Basic Algebraic Topology 4. Manifold Theory 5. Function Spaces 6. Knot Theory
Produktdetaljer
Biografisk notat
Steven G. Krantz is a professor at Washington University in St. Louis where he teaches mathematics. He has previously taught at UCLA, Princeton University, and Penn State University. He earned his PhD from Princeton University in 1974. Prof. Krantz has directed 20 PhD students and 8 master's-degree students, and published over 130 books and over 300 scholarly articles. He is the holder of the Chauvenet Prize, the Beckenbach Book Award, and the Kemper Prize, and he is a fellow of the American Mathematical Society.