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This book has grown out of a course of lectures on elliptic functions, given in German, at the Swiss Federal Institute of Technology, Zurich, during the summer semester of 1982. Its aim is to give some idea of the theory of elliptic functions, and of its close connexion with theta-functions and modular functions, and to show how it provides an analytic approach to the solution of some classical problems in the theory of numbers. It comprises eleven chapters. The first seven are function-theoretic, and the next four concern arithmetical applications. There are Notes at the end of every chapter, which contain references to the literature, comments on the text, and on the ramifications, old and new, of the problems dealt with, some of them extending into cognate fields. The treatment is self-contained, and makes no special demand on the reader's knowledge beyond the elements of complex analysis in one variable, and of group theory.
Carl Ludwig Siegel gave a course of lectures on the Geometry of Numbers at New York University during the academic year 1945-46, when there were hardly any books on the subject other than Minkowski's original one. This volume stems from Siegel's requirements of accuracy in detail, both in the text and in the illustrations, but involving no changes in the structure and style of the lectures as originally delivered. This book is an enticing introduction to Minkowski's great work. It also reveals the workings of a remarkable mind, such as Siegel's with its precision and power and aesthetic charm. It is of interest to the aspiring as well as the established mathematician, with its unique blend of arithmetic, algebra, geometry, and analysis, and its easy readability.
Published for the Eidgenössische Technische Hochschule Zürich
Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid. De spite their apparent simplicity, lattices hide a rich combinatorial struc ture, which has attracted the attention of great mathematicians over the last two centuries. Not surprisingly, lattices have found numerous ap plications in mathematics and computer science, ranging from number theory and Diophantine approximation, to combinatorial optimization and cryptography. The study of lattices, specifically from a computational point of view, was marked by two major breakthroughs: the development of the LLL lattice reduction algorithm by Lenstra, Lenst...
The book presents the history of ICMI trough a prosopographical approach. In other words, it pays a lot of attention to the actors of the International movement. The portraits of the members of the ICMI Central Committees (1908-1936) and ICMI Executive Committees (1952-2008), and other eminent figures in ICMI history, who have passed away in the first 100 years of its life, are the guiding thread of the volume. Each portrait includes: · Biographical information · An outline of the various contributions made by the individual in question to the study of problems pertaining to mathematics teaching/education · Primary bibliography · Secondary with particular attention to the publications co...
This vividly illustrated history of the International Congress of Mathematicians- a meeting of mathematicians from around the world held roughly every four years- acts as a visual history of the 25 congresses held between 1897 and 2006, as well as a story of changes in the culture of mathematics over the past century. Because the congress is an int
This book is the fifth and final volume of Raoul Bott’s Collected Papers. It collects all of Bott’s published articles since 1991 as well as some articles published earlier but missing in the earlier volumes. The volume also contains interviews with Raoul Bott, several of his previously unpublished speeches, commentaries by his collaborators such as Alberto Cattaneo and Jonathan Weitsman on their joint articles with Bott, Michael Atiyah’s obituary of Raoul Bott, Loring Tu’s authorized biography of Raoul Bott, and reminiscences of Raoul Bott by his friends, students, colleagues, and collaborators, among them Stephen Smale, David Mumford, Arthur Jaffe, Shing-Tung Yau, and Loring Tu. Th...
This book offers an up-to-date insight into the early philosophical debate on Einsteinian relativity. The essays explore the reception and interpretation of Einstein’s ideas by some of the most important philosophical schools of the time, such as logical positivism (Reichenbach), neo-Kantianism (Cassirer, Natorp), critical realism (Sellars), and radical empiricism (Mach). The book is aimed at physicists and historians of science researching the epistemological implications of the theory of relativity, as well as to scholars in philosophy interested in understanding how leading philosophical figures of the early twentieth century reacted to the relativistic revolution.
Paul R. Halmos, eminent mathematician, is also a snapshot addict. For the past 45 years, Halmos has snapped mathematicians, their spouses, their brothers and sisters and other relatives, their offices, their dogs, and their carillon towers. From 6000 or so photographs in his collection, Halmos chose about 600 for this book. The pictures are candid shots showing mathematicians just being themselves, and the accompanying captions, in addition to identifying the subjects, contain anecdotes and bits of history that reveal Halmos' inimitable wit and insight.
The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.