A funny, marvelously readable portrait of one of the most brilliant and eccentric men in history." --The Seattle Times Paul Erdos was an amazing and prolific mathematician whose life as a world-wandering numerical nomad was legendary. He published almost 1500 scholarly papers before his death in 1996, and he probably thought more about math problems than anyone in history. Like a traveling salesman offering his thoughts as wares, Erdos would show up on the doorstep of one mathematician or another and announce, "My brain is open." After working through a problem, he'd move on to the next place, the next solution. Hoffman's book, like Sylvia Nasar's biography of John Nash, A Beautiful Mind, reveals a genius's life that transcended the merely quirky. But Erdos's brand of madness was joyful, unlike Nash's despairing schizophrenia. Erdos never tried to dilute his obsessive passion for numbers with ordinary emotional interactions, thus avoiding hurting the people around him, as Nash did. Oliver Sacks writes of Erdos: "A mathematical genius of the first order, Paul Erdos was totally obsessed with his subject--he thought and wrote mathematics for nineteen hours a day until the day he died. He traveled constantly, living out of a plastic bag, and had no interest in food, sex, companionship, art--all that is usually indispensable to a human life." The Man Who Loved Only Numbers is easy to love, despite his strangeness. It's hard not to have affection for someone who referred to children as "epsilons," from the Greek letter used to represent small quantities in mathematics; a man whose epitaph for himself read, "Finally I am becoming stupider no more"; and whose only really necessary tool to do his work was a quiet and open mind. Hoffman, who followed and spoke with Erdos over the last 10 years of his life, introduces us to an undeniably odd, yet pure and joyful, man who loved numbers more than he loved God--whom he referred to as SF, for Supreme Fascist. He was often misunderstood, and he certainly annoyed people sometimes, but Paul Erdos is no doubt missed. --Therese Littleton
This volume is dedicated to Paul Erdos, who has profoundly influenced mathematics in this century, with over 1200 papers on number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks is the host of stimulating problems and conjectures, to many of which he has attached monetary prices, in accordance with their notoriety. A feature of this volume is a collection of some fifty outstanding unsolved problems, together with their "values.
This volume is dedicated to Paul Erdos, who has profoundly influenced mathematics in this century, with over 1200 papers on number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks is the host of stimulating problems and conjectures, to many of which he has attached monetary prices, in accordance with their notoriety. A feature of this volume is a collection of some fifty outstanding unsolved problems, together with their "values.
Number theory, the branch of mathematics that studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. In this book, the authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive.
A funny, marvelously readable portrait of one of the most brilliant and eccentric men in history." --The Seattle Times Paul Erdos was an amazing and prolific mathematician whose life as a world-wandering numerical nomad was legendary. He published almost 1500 scholarly papers before his death in 1996, and he probably thought more about math problems than anyone in history. Like a traveling salesman offering his thoughts as wares, Erdos would show up on the doorstep of one mathematician or another and announce, "My brain is open." After working through a problem, he'd move on to the next place, the next solution. Hoffman's book, like Sylvia Nasar's biography of John Nash, A Beautiful Mind, reveals a genius's life that transcended the merely quirky. But Erdos's brand of madness was joyful, unlike Nash's despairing schizophrenia. Erdos never tried to dilute his obsessive passion for numbers with ordinary emotional interactions, thus avoiding hurting the people around him, as Nash did. Oliver Sacks writes of Erdos: "A mathematical genius of the first order, Paul Erdos was totally obsessed with his subject--he thought and wrote mathematics for nineteen hours a day until the day he died. He traveled constantly, living out of a plastic bag, and had no interest in food, sex, companionship, art--all that is usually indispensable to a human life." The Man Who Loved Only Numbers is easy to love, despite his strangeness. It's hard not to have affection for someone who referred to children as "epsilons," from the Greek letter used to represent small quantities in mathematics; a man whose epitaph for himself read, "Finally I am becoming stupider no more"; and whose only really necessary tool to do his work was a quiet and open mind. Hoffman, who followed and spoke with Erdos over the last 10 years of his life, introduces us to an undeniably odd, yet pure and joyful, man who loved numbers more than he loved God--whom he referred to as SF, for Supreme Fascist. He was often misunderstood, and he certainly annoyed people sometimes, but Paul Erdos is no doubt missed. --Therese Littleton
The authors' aim is to present a review of experimental and theoretical research that has been done to establish and to explain the physical properties of actinide compounds. The book is aimed at physicists and chemists. It was thought useful to collect a large selection of diagrams of experimental data scattered in the literature. Experiment and theory are presented separately, with cross references. Not all work has been included: rather, typical examples are discussed. We apologize to all researchers whose work has not been quoted. Since we report on an active field of research, clearly the data and their interpretation are subject to change. We benefitted greatly from discussions with many of our colleagues, particularly with Drs. G. H. Lander and W. Suski. The help of Mrs. C. Bovey and Ch. Lewis in the preparation of the manuscript, and the artwork and photo graphic work of Ms. Y. Magnenat and E. Spielmann of the Institute of Experi mental Physics of the University of Lausanne, are gratefully acknowledged. Our particular thanks are due to Ms. J. Ubby for her skillful and patient editorial work.
This volume contains a collection of papers in Analytic and Elementary Number Theory in memory of Professor Paul Erdös, one of the greatest mathematicians of this century. Written by many leading researchers, the papers deal with the most recent advances in a wide variety of topics, including arithmetical functions, prime numbers, the Riemann zeta function, probabilistic number theory, properties of integer sequences, modular forms, partitions, and q-series. Audience: Researchers and students of number theory, analysis, combinatorics and modular forms will find this volume to be stimulating.
A comprehensive introduction to mathematical and agent-based modeling of social behavior This book provides a unified, theory-driven introduction to key mathematical and agent-based models of social dynamics and cultural evolution, teaching readers how to build their own models, analyze them, and integrate them with empirical research programs. It covers a variety of modeling topics, each exemplified by one or more archetypal models, and helps readers to develop strong theoretical foundations for understanding social behavior. Modeling Social Behavior equips social, behavioral, and cognitive scientists with an essential tool kit for thinking about and studying complex social systems using mathematical and computational models. Combines both mathematical and agent-based modeling of social behavior Integrates cognitive science, social science, and cultural evolution Covers topics such as the philosophy of modeling, collective movement, segregation, contagion, polarization, the evolution of cooperation, the emergence of norms, networks, and the scientific process Discusses more advanced topics, including how to use models to build a more robust empirical research program An ideal introductory textbook for graduate students or advanced undergraduates An invaluable resource for practitioners
From small beginnings in the early 1970s, the study of complement regulatory proteins has grown in the last decade to the point where it dominates the complement field. This growth has been fueled by the discovery of new regulators, the cloning of old and new regulators, the discovery that many of the regulators are structurally and evolutionarily related to each other and the development of recombinant forms for use in therapy. There are now more proteins known to be involved in controlling the complement system than there are components of the system and the list continues to grow. The time is ripe for a comprehensive review of our current knowledge of these intriguing proteins. This book does just that. The first few chapters discuss the "nuts-and-bolts" of the complement regulators, describing their structures, functional roles and modes of action. The roles of the complement regulators in vivo are then described, focusing on the consequences of deficiency, roles in the reproductive system, interactions with pathogens and exploitation for therapy. The interesting developments in defining the complement regulators expressed in other species are also discussed. The book is written as a monograph, albeit by two people. The text is as readable as possible without compromising on scientific accuracy and completeness. The conversational style very evident in some sections is deliberate! Placing all references in a single bibliography at the end of the text further improves readability. The reader will go to the book to discover a specific fact but be persuaded to read more and derive pleasure from the process. The authors' enthusiasm for the subject comes over strongly in the text, and this enthusiasm proves infectious. - Complement regulators--structure, functional roles and mode of action - Comprehensive reviews of each of the individual regulators - Roles of Complement regulators in vivo,in health and disease: - Consequences of deficiency - Roles in the reproductive system - Interactions with pathogens - Exploitation for therapy - Complement regulators in other species
The MAA was founded in 1915 to serve as a home for The American Mathematical Monthly. The mission of the Association-to advance mathematics, especially at the collegiate level-has, however, always been larger than merely publishing world-class mathematical exposition. MAA members have explored more than just mathematics; we have, as this volume tries to make evident, investigated mathematical connections to pedagogy, history, the arts, technology, literature, every field of intellectual endeavor. Essays, all commissioned for this volume, include exposition by Bob Devaney, Robin Wilson, and Frank Morgan; history from Karen Parshall, Della Dumbaugh, and Bill Dunham; pedagogical discussion from Paul Zorn, Joe Gallian, and Michael Starbird, and cultural commentary from Bonnie Gold, Jon Borwein, and Steve Abbott. This volume contains 35 essays by all-star writers and expositors writing to celebrate an extraordinary century for mathematics-more mathematics has been created and published since 1915 than in all of previous recorded history. We've solved age-old mysteries, created entire new fields of study, and changed our conception of what mathematics is. Many of those stories are told in this volume as the contributors paint a portrait of the broad cultural sweep of mathematics during the MAA's first century. Mathematics is the most thrilling, the most human, area of intellectual inquiry; you will find in this volume compelling proof of that claim.
Understanding Deviance' provides an indispensable guide to the major themes and theories which have come to form the sociology of crime and deviance, from their origins in the research of the University of Chicago sociology department in the 1920s to the most recent work in cultural criminology.
Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.
This book is a tribute to Paul Erd\H{o}s, the wandering mathematician once described as the "prince of problem solvers and the absolute monarch of problem posers." It examines -- within the context of his unique personality and lifestyle -- the legacy of open problems he left to the world after his death in 1996. Unwilling to succumb to the temptations of money and position, Erd\H{o}s never had a home and never held a job. His "home" was a bag or two containing all his belongings and a record of the collective activities of the mathematical community. His "job" was one at which he excelled: identifying a fundamental roadblock in some particular line of approach and capturing it in a well-chosen, often innocent-looking problem, whose solution would likewise provide insight into the underlying theory. By cataloguing the unsolved problems of Erd\H{o}s in a comprehensive and well-documented volume, the authors hope to continue the work of an unusual and special man who fundamentally influenced the field of mathematics.
Number theory, the branch of mathematics that studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. In this book, the authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive.
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