Erdos Distance Problem

Julia Garibaldi, Alex Iosevich University of Rochester, Rochester, NY, USASteven Senger, University of Missouri-Columbia, Columbia, MO, Columbia, MO, USA

• ForewordAcknowledgmentsIntroductionThe √𝑛 theoryThe 𝑛^{2/3} theoryThe Cauchy-Schwarz inequalityGraph theory and incidencesThe 𝑛^{4/5} theoryThe 𝑛^{6/7} theoryBeyond 𝑛^{6/7}Information theoryDot productsVector spaces over finite fieldsDistances in vector spaces over finite fieldsApplications of the Erdős distance problemHyperbolas in the planeBasic probability theoryJensen’s inequalityBibliographyBiographical informationIndex of terminology

The 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, Choice