Ramanujan


Book Description

The letters that Ramanujan wrote to G. H. Hardy on January 16 and February 27, 1913, are two of the most famous letters in the history of mathematics. These and other letters introduced Ramanujan and his remarkable theorems to the world and stimulated much research, especially in the 1920s and 1930s. This book brings together many letters to, from, and about Ramanujan. The letters came from the National Archives in Delhi, the Archives in the State of Tamil Nadu, and a variety of other sources. Helping to orient the reader is the extensive commentary, both mathematical and cultural, by Berndt and Rankin; in particular, they discuss in detail the history, up to the present day, of each mathematical result in the letters. Containing many letters that have never been published before, this book will appeal to those interested in Ramanujan's mathematics as well as those wanting to learn more about the personal side of his life. Ramanujan: Letters and Commentary was selected for the CHOICE list of Outstanding Academic Books for 1996.







The Neuroscience of Autism Spectrum Disorders


Book Description

Autism is no longer considered a rare disease, and the Center for Disease Control now estimates that upwards of 730,000 children in the US struggle with this isolating brain disorder. New research is leading to greater understanding of and ability to treat the disorder at an earlier age. It is hoped that further genetic and imaging studies will lead to biologically based diagnostic techniques that could help speed detection and allow early, more effective intervention. Edited by two leaders in the field, this volume offers a current survey and synthesis of the most important findings of the neuroscience behind autism of the past 20 years. With chapters authored by experts in each topic, the volume explores etiology, neuropathology, imaging, and pathways/models. Offering a broad background of ASDs with a unique focus on neurobiology, the volume offers more than the others on the market with a strictly clinical focus or a single authored perspective that fails to offer expert, comprehensive coverage. Researchers and graduate students alike with an interest in developmental disorders and autism will benefit, as will autism specialists across psychology and medicine looking to expand their expertise. Uniquely explores ASDs from a neurobiological angle, looking to uncover the molecular/cellular basis rather than to merely catalog the commonly used behavioral interventions Comprehensive coverage synthesizes widely dispersed research, serving as one-stop shopping for neurodevelopmental disorder researchers and autism specialists Edited work with chapters authored by leaders in the field around the globe - the broadest, most expert coverage available




State-chartered Credit Unions


Book Description




Foundations of Logic and Mathematics


Book Description

This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.




Godel


Book Description

Kurt Gödel was an intellectual giant. His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Shattering hopes that logic would, in the end, allow us a complete understanding of the universe, Gödel's theorem also raised many provocative questions: What are the limits of rational thought? Can we ever fully understand the machines we build? Or the inner workings of our own minds? How should mathematicians proceed in the absence of complete certainty about their results? Equally legendary were Gödel's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first book for a general audience on this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life.




The Annenbergs


Book Description

"This is the colorful and dramatic biography of two of America's most controversial entrepreneurs: Moses Louis Annenberg, 'the racing wire king, ' who built his fortune in racketeering, invested it in publishing, and lost much of it in the biggest tax evasion case in United States history; and his son, Walter, launcher of TV Guide and Seventeen magazines and former ambassador to Great Britain."--Jacket.




Discrete Groups


Book Description

This book deals with geometric and topological aspects of discrete groups. The main topics are hyperbolic groups due to Gromov, automatic group theory, invented and developed by Epstein, whose subjects are groups that can be manipulated by computers, and Kleinian group theory, which enjoys the longest tradition and the richest contents within the theory of discrete subgroups of Lie groups. What is common among these three classes of groups is that when seen as geometric objects, they have the properties of a negatively curved space rather than a positively curved space. As Kleinian groups are groups acting on a hyperbolic space of constant negative curvature, the technique employed to study them is that of hyperbolic manifolds, typical examples of negatively curved manifolds. Although hyperbolic groups in the sense of Gromov are much more general objects than Kleinian groups, one can apply for them arguments and techniques that are quite similar to those used for Kleinian groups. Automatic groups are further general objects, including groups having properties of spaces of curvature 0. Still, relationships between automatic groups and hyperbolic groups are examined here using ideas inspired by the study of hyperbolic manifolds. In all of these three topics, there is a ``soul'' of negative curvature upholding the theory. The volume would make a fine textbook for a graduate-level course







Infinite Homotopy Theory


Book Description

This book deals with algebraic topology, homotopy theory and simple homotopy theory of infinite CW-complexes with ends. Contrary to most other works on these subjects, the current volume does not use inverse systems to treat these topics. Here, the homotopy theory is approached without the rather sophisticated notion of pro-category. Spaces with ends are studied only by using appropriate constructions such as spherical objects of CW-complexes in the category of spaces with ends, and all arguments refer directly to this category. In this way, infinite homotopy theory is presented as a natural extension of classical homotopy theory. In particular, this book introduces the construction of the proper groupoid of a space with ends and then the cohomology with local coefficients is defined by the enveloping ringoid of the proper fundamental groupoid. This volume will be of interest to researchers whose work involves algebraic topology, category theory, homological algebra, general topology, manifolds, and cell complexes.