Stephen Smale: The Mathematician Who Broke the Dimension Barrier PDF Download
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Author: Steve Batterson
Publisher: American Mathematical Soc.
ISBN: 0821826964
Category : Biography & Autobiography
Languages : en
Pages : 338
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Book Description
In 1957 Stephen Smale startled the mathematical world by showing that it is possible to turn a sphere inside out without cutting, tearing, or crimping. A few years later, from the beaches of Rio, he introduced the horseshoe map, demonstrating that simple functions could have chaotic dynamics. Despite his diverse accomplishments, Smales name is virtually unknown outside mathematics. One of the objectives of this book is to bring the life and work of this significant figure in intellectual history to the attention of a larger community.
Author: Steve Batterson
Publisher: American Mathematical Soc.
ISBN: 0821826964
Category : Biography & Autobiography
Languages : en
Pages : 338
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Book Description
In 1957 Stephen Smale startled the mathematical world by showing that it is possible to turn a sphere inside out without cutting, tearing, or crimping. A few years later, from the beaches of Rio, he introduced the horseshoe map, demonstrating that simple functions could have chaotic dynamics. Despite his diverse accomplishments, Smales name is virtually unknown outside mathematics. One of the objectives of this book is to bring the life and work of this significant figure in intellectual history to the attention of a larger community.
Author: Steve Batterson
Publisher: NYU Press
ISBN: 1685900372
Category : History
Languages : en
Pages : 139
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Book Description
Exposes the destruction of academic careers—and the complicity of educational institutions—in McCarthy's America The Prosecution of Professor Chandler Davis tells the true tale of a mathematician who found himself taking an involuntary break from chalking equations to sit opposite a row of self-righteous anti-Communist congressmen at the height of the McCarthy era. Courageously asserting the First Amendment to confront a system rapidly descending into fascism, Davis testified before the House Un-American Activities Committee (HUAC). He became one of a small number of left wingers who served time for contempt of Congress. In this fascinating and disturbing narrative, author Steve Batterson takes a deep dive into extant archival records generated by the FBI, HUAC, the University of Michigan, and repositories holding the papers of former Supreme Court justices. He examines the plights of six faculty and graduate students—including three future members of the National Academy of Sciences—whose careers were disrupted by the anticommunist actions of a wide range of personnel at the University of Michigan. He focuses on the seemingly conflicting Supreme Court decisions on labor leader John Watkins and Vassar College Psychology instructor Lloyd Barenblatt. And he examines the role played in the trial by Felix Frankfurter, a longtime Associate Justice on the Supreme Court, close advisor of Franklin D. Roosevelt, and co-founder of the ACLU. In the process, Batterson exposes the ways that McCarthy’s righteous emissaries relied on all kinds of institutions in 1950s America—from Hollywood studios to universities—to sabotage the careers of anyone with a trace of “Red.”
Author: Richard Kautz
Publisher: OUP Oxford
ISBN: 0191035548
Category : Science
Languages : en
Pages : 384
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Book Description
Based on only elementary mathematics, this engaging account of chaos theory bridges the gap between introductions for the layman and college-level texts. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle, the mathematical monster at the heart of chaos. The presentation is enhanced by many figures, animations of chaotic motion (available on a companion CD), and biographical sketches of the pioneers of dynamics and chaos theory. To ensure accessibility to motivated high school students, care has been taken to explain advanced mathematical concepts simply, including exponentials and logarithms, probability, correlation, frequency analysis, fractals, and transfinite numbers. These tools help to resolve the intriguing paradox of motion that is predictable and yet random, while the final chapter explores the various ways chaos theory has been put to practical use.
Author: Robert A. Meyers
Publisher: Springer Science & Business Media
ISBN: 1461418054
Category : Mathematics
Languages : en
Pages : 1885
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Book Description
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Author: Christophe Letellier
Publisher: World Scientific
ISBN: 9814434876
Category : Mathematics
Languages : en
Pages : 364
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Book Description
The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto Rössler, René Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively. Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical — not necessarily widely known — contributions (about the different types of chaos introduced by Rössler and not just the “Rössler attractor”; Gumowski and Mira's contributions in electronics; Poincaré's heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology, etc. Contents:Introduction to Topological Analysis (Christophe Letellier & Robert Gilmore)Emergence of a Chaos Theory:The Peregrinations of Poincaré (R Abraham)A Toulouse Research Group in the “Prehistoric” Times of Chaotic Dynamics (Christian Mira)Can We Trust in Numerical Computations of Chaotic Solutions of Dynamical Systems? (René Lozi)Chaos Hierarchy — A Review, Thirty Years Later (Otto E Rössler & Christophe Letellier)Development of the Topology of Chaos:The Mathematics of Lorenz Knots (Joan S Birman)A Braided View of a Knotty Story (Mario Natiello & Hernán Solari)How Topology Came to Chaos (Robert Gilmore)Reflections From the Fourth Dimension (Marc Lefranc)The Symmetry of Chaos (Christophe Letellier)Applications of Chaos Theory:The Shape of Ocean Color (Nicholas Tufillaro)Low Dimensional Dynamics in Biological Motor Patterns (Gabriel B Mindlin)Minimal Smooth Chaotic Flows (Jean-Marc Malasoma)The Chaotic Marriage of Physics and Financial Economics (Claire Gilmore)Introduction of the Sphere Map with Application to Spin-Torque Nano-Oscillators (Keith Gilmore & Robert Gilmore)Robert Gilmore, a Portrait (Hernán G Solari) Readership: Graduate students and researchers interested in topological analysis of nonlinear dynamical systems producing chaotic attractors. Keywords:Chaos;Topology;Nonlinear DynamicsKey Features:Historical survey, main concepts and some applicationsIncludes contributions from most of the main scientists in the field (Rössler, Birman, and Lefranc)An introduction for beginners is included
Author: M. Norton Wise
Publisher: Duke University Press
ISBN: 9780822333197
Category : Science
Languages : en
Pages : 358
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Book Description
For much of the twentieth century scientists sought to explain objects and processes by reducing them to their components—nuclei into protons and neutrons, proteins into amino acids, and so on—but over the past forty years there has been a marked turn toward explaining phenomena by building them up rather than breaking them down. This collection reflects on the history and significance of this turn toward “growing explanations” from the bottom up. The essays show how this strategy—based on a widespread appreciation for complexity even in apparently simple processes and on the capacity of computers to simulate such complexity—has played out in a broad array of sciences. They describe how scientists are reordering knowledge to emphasize growth, change, and contingency and, in so doing, are revealing even phenomena long considered elementary—like particles and genes—as emergent properties of dynamic processes. Written by leading historians and philosophers of science, these essays examine the range of subjects, people, and goals involved in changing the character of scientific analysis over the last several decades. They highlight the alternatives that fields as diverse as string theory, fuzzy logic, artificial life, and immunology bring to the forms of explanation that have traditionally defined scientific modernity. A number of the essays deal with the mathematical and physical sciences, addressing concerns with hybridity and the materials of the everyday world. Other essays focus on the life sciences, where questions such as “What is life?” and “What is an organism?” are undergoing radical re-evaluation. Together these essays mark the contours of an ongoing revolution in scientific explanation. Contributors. David Aubin, Amy Dahan Dalmedico, Richard Doyle, Claus Emmeche, Peter Galison, Stefan Helmreich, Ann Johnson, Evelyn Fox Keller, Ilana Löwy, Claude Rosental, Alfred Tauber
Author: Reuben Hersh
Publisher: Princeton University Press
ISBN: 9781400836116
Category : Mathematics
Languages : en
Pages : 432
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Book Description
Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life. These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment--as well as of those rare individuals driven to insanity and even murder by an obsession with math. This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.
Author: Margaret W. Rossiter
Publisher: JHU Press
ISBN: 1421402335
Category : Biography & Autobiography
Languages : en
Pages : 465
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Book Description
With the thoroughness and resourcefulness that characterize the earlier volumes, she recounts the rich history of the courageous and resolute women determined to realize their scientific ambitions.
Author: Luke Hodgkin
Publisher: OUP Oxford
ISBN: 0191664367
Category : Mathematics
Languages : en
Pages : 296
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Book Description
A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwarizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader.
Author: David E. Zitarelli
Publisher: American Mathematical Soc.
ISBN: 1470448297
Category : Education
Languages : en
Pages : 474
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Book Description
This is the first truly comprehensive and thorough history of the development of mathematics and a mathematical community in the United States and Canada. This first volume of the multi-volume work takes the reader from the European encounters with North America in the fifteenth century up to the emergence of a research community the United States in the last quarter of the nineteenth. In the story of the colonial period, particular emphasis is given to several prominent colonial figures—Jefferson, Franklin, and Rittenhouse—and four important early colleges—Harvard, Québec, William & Mary, and Yale. During the first three-quarters of the nineteenth century, mathematics in North America was largely the occupation of scattered individual pioneers: Bowditch, Farrar, Adrain, B. Peirce. This period is given a fuller treatment here than previously in the literature, including the creation of the first PhD programs and attempts to form organizations and found journals. With the founding of Johns Hopkins in 1876 the American mathematical research community was finally, and firmly, founded. The programs at Hopkins, Chicago, and Clark are detailed as are the influence of major European mathematicians including especially Klein, Hilbert, and Sylvester. Klein's visit to the US and his Evanston Colloquium are extensively detailed. The founding of the American Mathematical Society is thoroughly discussed. David Zitarelli is emeritus Professor of Mathematics at Temple University. A decorated and acclaimed teacher, scholar, and expositor, he is one of the world's leading experts on the development of American mathematics. Author or co-author of over a dozen books, this is his magnum opus—sure to become the leading reference on the topic and essential reading, not just for historians. In clear and compelling prose Zitarelli spins a tale accessible to experts, generalists, and anyone interested in the history of science in North America.
