Description
Book SynopsisTrade ReviewThe authors do an excellent job in bringing together the main techniques and results connected to the Erdős distance problem ... this is a useful book for the reader with sufficient mathematical experience who wishes to learn the principal techniques and results in the Erdős distance problem and related areas." -
Mathematical Reviews"This book...achieves the remarkable feat of providing an extremely accessible treatment of a classic family of research problems. ...The book can be used for a reading course taken by an undergraduate student (parts of the book are accessible for talented high school students as well), or as introductory material for a graduate student who plans to investigate this area further...Highly recommended." - M. Bona,
ChoiceTable of Contents
- Foreword
- Acknowledgments
- Introduction
- The √𝑛 theory
- The 𝑛^{2/3} theory
- The Cauchy-Schwarz inequality
- Graph theory and incidences
- The 𝑛^{4/5} theory
- The 𝑛^{6/7} theory
- Beyond 𝑛^{6/7}
- Information theory
- Dot products
- Vector spaces over finite fields
- Distances in vector spaces over finite fields
- Applications of the Erdős distance problem
- Hyperbolas in the plane
- Basic probability theory
- Jensen’s inequality
- Bibliography
- Biographical information
- Index of terminology
