Description : New functions are introduced in number theory, and for each one a general description, examples, connections, and references are given.
Description : This book chronicles the Society's activities over fifty years, as membership grew, as publications became more numerous and diverse, as the number of meetings and conferences increased, and as services to the mathematical community expanded. To download free chapters of this book, click here.
Description : After three decades since the first nearly complete edition of John von Neumann's papers, this book is a valuable selection of those papers and excerpts of his books that are most characteristic of his activity, and reveal that of his continuous influence.The results receiving the 1994 Nobel Prizes in economy deeply rooted in Neumann's game theory are only minor traces of his exceptionally broad spectrum of creativity and stimulation.The book is organized by the specific subjects-quantum mechanics, ergodic theory, operator algebra, hydrodynamics, economics, computers, science and society. In addition, one paper which was written in German will be translated and published in English for the first time.The sections are introduced by short explanatory notes with an emphasis on recent developments based on von Neumann's contributions. An overall picture is provided by Ulam's, one of his most intimate partners in thinking, 1958 memorial lecture. Facsimilae and translations of some of his personal letters and a newly completed bibliography based on von Neumann's own careful compilation are added.
Description : The mathematical works of Fritz John whose deep and original ideas have had a great influence on the development of various fields in mathema tical analysis are made available with these volumes. His works are certainly well known to the experts, but knowledge of his contributions may not have spread as widely as it should have. For example, the concept of functions of bounded mean oscillations plays a central role in harmonic analysis today, but it is perhaps less known that this class of functions was introduced by John as early as 1961, motivated by his work in elasticity theory. With the publication of this collection, a wider circle of mathematicians will become familiar with, and appreciate, the fertile ideas of Fritz John. The organization of these two volumes was undertaken in consultation with the author. It was decided not to present the papers in chronological order, but rather to subdivide them into ten sections representing different mathematical topics to which John has contributed. Commentaries made by experts in the fields are appended to each section. Since the division into sec tions could, of course, not be made sharply, there are several overlaps. For instance, the comments of Louis Nirenberg refer to Elasticity Theory VI, Geometric Inequalities VIII, and Functions of Bounded Mean Oscillations IX. To help the reader, cross-references and remarks by the author will be found at the end of each section.
Description : There exists a history of great expectations and large investments involving artificial intelligence (AI). There are also notable shortfalls and memorable disappointments. One major controversy regarding AI is just how mathematical a field it is or should be. This text includes contributions that examine the connections between AI and mathematics, demonstrating the potential for mathematical applications and exposing some of the more mathematical areas within AI. The goal is to stimulate interest in people who can contribute to the field or use its results. Included in the work by M. Newborn on the famous Deep BLue chess match. He discusses highly mathematical techniques involving graph theory, combinatorics and probability and statistics. G. Shafer offers his development of probability through probability trees with some of the results appearing here for the first time. M. Golumbic treats temporal reasoning with ties to the famous Frame Problem. His contribution involves logic, combinatorics and graph theory and leads to two chapters with logical themes. H. Kirchner explains how ordering techniques in automated reasoning systems make deduction more efficient. Constraint logic programming is discussed by C. Lassez, who shows its intimate ties to linear programming with crucial theorems going back to Fourier. V. Nalwa's work provides a brief tour of computer vision, tying it to mathematics - from combinatorics, probability and geometry to partial differential equations. All authors are gifted expositors and are current contributors to the field. The wide scope of the volume includes research problems, research tools and good motivational material for teaching.