Steven Senger – författare

The Erd s problem asks, What is the smallest possible number of distinct distances between points of a large finite subset of the Euclidean space in dimensions two and higher? The main goal of this book is to introduce the reader to the techniques, ideas, and consequences related to the Erd s problem. The authors introduce these concepts in a concrete and elementary way that allows a wide audience--from motivated high school students interested in mathematics to graduate students specializing in combinatorics and geometry--to absorb the content and appreciate its far-reaching implications. In the process, the reader is familiarized with a wide range of techniques from several areas of mathematics and can appreciate the power of the resulting symbiosis. The book is heavily problem oriented, following the authors' firm belief that most of the learning in mathematics is done by working through the exercises. Many of these problems are recently published results by mathematicians working in the area. The order of the exercises is designed both to reinforce the material presented in the text and, equally importantly, to entice the reader to leave all worldly concerns behind and launch head first into the multifaceted and rewarding world of Erd s combinatorics.

A physician who is treating a patient confronts a complex and incompletely understood living system that is sensitive to pain. An engineer or programmer who develops a new device, on the other hand, operates within the less emotional domains of materials and mathematics. The Medicine Meets Virtual Reality (MMVR) conference brings together physicians, scientists, engineers, educators, students, and others to bridge the gap between clinicians and technologists, and to create collaborative solutions to healthcare challenges. This book presents the proceedings of the Medicine Meets Virtual Reality conference (MMVR19), held in Newport Beach, California, USA, in February 2012. It includes papers on modeling and simulation, imaging, data visualization and fusion, haptics, robotics, telemedicine and medical intelligence networking, virtual and augmented reality, psychotherapy and physical rehabilitation tools, serious games, and other topics.MMVR stimulates interaction between developers and end users and promotes unorthodox problem-solving as a complement to rigorous scientific methodology. This book will interest all who are involved with the future of medicine.