Search Results for "five-golden-rules-great-theories-of-20th-century-mathematics-and-why-they-matter"

Five golden rules

Five golden rules

great theories of 20th-century mathematics and why they matter

  • Author: J. L. Casti
  • Publisher: Wiley
  • ISBN: N.A
  • Category: Mathematics
  • Page: 235
  • View: 2944
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Praise for Five Golden Rules "Casti is one of the great science writers of the 1990s. . . . If you'd like to have fun while giving your brain a first-class workout, then check this book out."-Keay Davidson in the San Francisco Examiner. "Five Golden Rules is caviar for the inquiring reader. . . . There is joy here in watching the unfolding of these intricate and beautiful techniques. Casti's gift is to be able to let the nonmathematical reader share in his understanding of the beauty of a good theory." -Christian Science Monitor. "Merely knowing about the existence of some of these golden rules may spark new, interesting-maybe revolutionary-ideas in your mind." -Robert Matthews in New Scientist (United Kingdom). "This book has meat! It is solid fare, food for thought. Five Golden Rules makes math less forbidding and much more interesting." -Ben Bova in the Hartford Courant "With this groundbreaking work, John Casti shows himself to be a great mathematics writer. Five Golden Rules is a feast of rare new delights all made perfectly comprehensible." -Rudy Rucker, author of The Fourth Dimension. "With the lucid informality for which he has become known, John Casti has written an engaging and articulate examination of five great mathematical theorems and their myriad applications." -John Allen Paulos, author of A Mathematician Reads the Newspaper.

Guide to Information Sources in Mathematics and Statistics

Guide to Information Sources in Mathematics and Statistics

  • Author: Martha A. Tucker,Nancy D. Anderson
  • Publisher: Libraries Unlimited
  • ISBN: 9781563087011
  • Category: Mathematics
  • Page: 348
  • View: 4812
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Publisher description: This book is a reference for librarians, mathematicians, and statisticians involved in college and research level mathematics and statistics in the 21st century. Part I is a historical survey of the past 15 years tracking this huge transition in scholarly communications in mathematics. Part II of the book is the bibliography of resources recommended to support the disciplines of mathematics and statistics. These resources are grouped by material type. Publication dates range from the 1800's onwards. Hundreds of electronic resources-some online, both dynamic and static, some in fixed media, are listed among the paper resources. A majority of listed electronic resources are free.

The Mathematical Century

The Mathematical Century

The 30 Greatest Problems of the Last 100 Years

  • Author: Piergiorgio Odifreddi
  • Publisher: Princeton University Press
  • ISBN: 9780691128054
  • Category: Mathematics
  • Page: 204
  • View: 6099
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The twentieth century was a time of unprecedented development in mathematics, as well as in all sciences: more theorems were proved and results found in a hundred years than in all of previous history. In The Mathematical Century, Piergiorgio Odifreddi distills this unwieldy mass of knowledge into a fascinating and authoritative overview of the subject. He concentrates on thirty highlights of pure and applied mathematics. Each tells the story of an exciting problem, from its historical origins to its modern solution, in lively prose free of technical details. Odifreddi opens by discussing the four main philosophical foundations of mathematics of the nineteenth century and ends by describing the four most important open mathematical problems of the twenty-first century. In presenting the thirty problems at the heart of the book he devotes equal attention to pure and applied mathematics, with applications ranging from physics and computer science to biology and economics. Special attention is dedicated to the famous "23 problems" outlined by David Hilbert in his address to the International Congress of Mathematicians in 1900 as a research program for the new century, and to the work of the winners of the Fields Medal, the equivalent of a Nobel prize in mathematics. This eminently readable book will be treasured not only by students and their teachers but also by all those who seek to make sense of the elusive macrocosm of twentieth-century mathematics.

Masters of Mathematics

Masters of Mathematics

The Problems They Solved, Why These Are Important, and What You Should Know about Them

  • Author: Robert A. Nowlan
  • Publisher: Springer
  • ISBN: 9463008934
  • Category: Education
  • Page: 24
  • View: 8864
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The original title for this work was “Mathematical Literacy, What Is It and Why You Need it”. The current title reflects that there can be no real learning in any subject, unless questions of who, what, when, where, why and how are raised in the minds of the learners. The book is not a mathematical text, and there are no assigned exercises or exams. It is written for reasonably intelligent and curious individuals, both those who value mathematics, aware of its many important applications and others who have been inappropriately exposed to mathematics, leading to indifference to the subject, fear and even loathing. These feelings are all consequences of meaningless presentations, drill, rote learning and being lost as the purpose of what is being studied. Mathematics education needs a radical reform. There is more than one way to accomplish this. Here the author presents his approach of wrapping mathematical ideas in a story. To learn one first must develop an interest in a problem and the curiosity to find how masters of mathematics have solved them. What is necessary to be mathematically literate? It’s not about solving algebraic equations or even making a geometric proof. These are valuable skills but not evidence of literacy. We often seek answers but learning to ask pertinent questions is the road to mathematical literacy. Here is the good news: new mathematical ideas have a way of finding applications. This is known as “the unreasonable effectiveness of mathematics.”

The One True Platonic Heaven:

The One True Platonic Heaven:

A Scientific Fiction of the Limits of Knowledge

  • Author: John Casti
  • Publisher: National Academies Press
  • ISBN: 0309095107
  • Category: Science
  • Page: 224
  • View: 6034
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By the author of The Cambridge Quintet, John L. Casti's new book continues the tradition of combining science fact with just the right dose of fiction. Part novel, part science - wholly informative and entertaining. In the fall of 1933 the newly founded Institute for Advanced Study in Princeton, New Jersey, welcomed its first faculty member, Albert Einstein. With this superstar on the roster, the Institute was able to attract many more of the greatest scholars, scientists, and poets from around the world. It was to be an intellectual haven, a place where the most brilliant minds on the planet, sheltered from the outside world's cares and calamities, could study and collaborate and devote their time to the pure and exclusive pursuit of knowledge. For many of them, it was the "one, true, platonic heaven." Over the years, key figures at the Institute began to question the limits to what science could tell us about the world, pondering the universal secrets it might unlock. Could science be the ultimate source of truth; or are there intrinsic limits, built into the very fabric of the universe, to what we can learn? In the late 1940's and early 1950's, this important question was being asked and pondered upon by some of the Institute's deepest thinkers. Enter the dramatis personae to illuminate the science and the philosophy of the time. Mathematical logician Kurt Godel was the unacknowledged Grant Exalted Ruler of this platonic estate - but he was a ruler without a scepter as he awaited the inexplicably indefinite postponement of his promotion to full, tenured professor. Also in residence was his colleague, the Hungarian-American polymath, John van Neumann, developer of game theory, the axiomatic foundations of quantum mechanics, and the digital computer - stymied by the Institute's refusal to sanction his bold proposal to actually build a computer. One of Godel's closest friends figures large in this story: Albert Einstein, by common consensus the greatest physicist the 20th century had ever known. And, of course, the director the Institute, J. Robert Oppenheimer, the father of the atomic bomb, must by necessity be key to any story that focuses in on this time and place. Author Casti elegantly sets the stage and then masterfully directs this impressive cast of characters-with able assists by many "minor-character" icons like T. S. Eliot, Wolfgang Pauli, Freeman Dyson, and David Bohm, to tell a story of science, history, and ideas. As we watch events unfold (some of which are documented fact while others are creatively imagined fiction), we are witness to the discussions and deliberations of this august group… privy to wide-ranging conversations on thinking machines, quantum logic, biology as physics, weather forecasting, the structure of economic systems, the distinction between mathematics and natural science, the structure of the universe, and the powers of the human mind - all centered around the question of the limits to scientific knowledge. Imaginatively conceived and artfully executed, The One True Platonic Heaven is an accessible and intriguing presentation of some of the deepest scientific and philosophical ideas of the 20th century.

Reality Rules, The Fundamentals

Reality Rules, The Fundamentals

  • Author: John Casti
  • Publisher: John Wiley & Sons
  • ISBN: 9780471184355
  • Category: Mathematics
  • Page: 416
  • View: 8584
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"Casti Tours offers the most spectacular vistas of modern applied mathematics" â??Nature Mathematical modeling is about rulesâ??the rules of reality. Reality Rules explores the syntax and semantics of the language in which these rules are written, the language of mathematics. Characterized by the clarity and vision typical of the author's previous books, Reality Rules is a window onto the competing dialects of this languageâ??in the form of mathematical models of real-world phenomenaâ??that researchers use today to frame their views of reality. Moving from the irreducible basics of modeling to the upper reaches of scientific and philosophical speculation, Volumes 1 and 2, The Fundamentals and The Frontier, are ideal complements, equally matched in difficulty, yet unique in their coverage of issues central to the contemporary modeling of complex systems. Engagingly written and handsomely illustrated, Reality Rules is a fascinating journey into the conceptual underpinnings of reality itself, one that examines the major themes in dynamical system theory and modeling and the issues related to mathematical models in the broader contexts of science and philosophy. Far-reaching and far-sighted, Reality Rules is destined to shape the insight and work of students, researchers, and scholars in mathematics, science, and the social sciences for generations to come. Of related interest . . . ALTERNATE REALITIES Mathematical Models of Nature and Man John L. Casti A thoroughly modern account of the theory and practice of mathematical modeling with a treatment focusing on system-theoretic concepts such as complexity, self-organization, adaptation, bifurcation, resilience, surprise and uncertainty, and the mathematical structures needed to employ these in a formal system. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Alternate realities

Alternate realities

mathematical models of nature and man

  • Author: J. L. Casti
  • Publisher: Wiley-Interscience
  • ISBN: N.A
  • Category: Mathematics
  • Page: 493
  • View: 9824
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Praise for Alternate Realities Mathematical Models of Nature and Man "â¦covers the major topics completely and accurately within the context of current knowledge. Indeed, to my knowledge, there is no book which does so nearly as completely and well." âGeorge Leitmann, University of California, Berkeley "Surveys an extensive amount of modern mathematicsâ¦introduces and outlines some of these basic modern ideas for the non-specialist." âDonald G. Saari, Northwestern University "A sophisticated and modern text on mathematical modellingâ¦much more comprehensive than any of its competitors currently on the market." âGeorge Klir, State University of New York at Binghamton "Castiâs approach is fearless in constructing conceptual mappings between reality and mathematical notions. The book is pioneering in nature." âMyron B. Allen, University of Wyoming An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Godel

Godel

A Life Of Logic, The Mind, And Mathematics

  • Author: John L. Casti,Werner DePauli,L Casti
  • Publisher: Basic Books
  • ISBN: 9780786747603
  • Category: Science
  • Page: 224
  • View: 8730
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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.

How Mathematicians Think

How Mathematicians Think

Using Ambiguity, Contradiction, and Paradox to Create Mathematics

  • Author: William Byers
  • Publisher: Princeton University Press
  • ISBN: 9780691145990
  • Category: Mathematics
  • Page: 424
  • View: 1537
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To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.

World Link

World Link

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Economic policy
  • Page: N.A
  • View: 7276
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How to win friends & influence people

How to win friends & influence people

  • Author: Dale Carnegie
  • Publisher: Diamond Pocket Books Pvt Ltd
  • ISBN: 9352613937
  • Category: Self-Help
  • Page: 224
  • View: 8526
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Mood Matters

Mood Matters

From Rising Skirt Lengths to the Collapse of World Powers

  • Author: John L Casti
  • Publisher: Springer Science & Business Media
  • ISBN: 3642048358
  • Category: Business & Economics
  • Page: 250
  • View: 3352
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"Mood Matters" makes the radical assertion that all social events ranging from fashions in music and art to the rise and fall of civilizations are biased by the attitudes a society holds toward the future. When the "social mood" is positive and people look forward to the future, events of an entirely different character tend to occur than when society is pessimistic. The book presents many examples from every walk of life in support of this argument. In addition, methods are given to actually measure the social mood and to project it into the future in order to forecast what’s likely or not over varying periods of time. Casti's writing is a pleasure to read and its contents an eye-opener. "They [the chapters] tell an engrossing story, and the mystery heightens as it goes. . . . it's chatty and knowing." Greg Benford, Physicist and science-fiction writer, author of "Timescape" and "Deep Time" "I am struck by how thought-provoking it all is. I am sure that your book will draw a lot of attention" Tor Norretranders, Science writer, author of "The Generous Man" and "The User Illusion".

Paradigms Lost

Paradigms Lost

Images of Man in the Mirror of Science

  • Author: John L. Casti
  • Publisher: N.A
  • ISBN: 9780349105444
  • Category: Science
  • Page: 565
  • View: 1651
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Intended for both the layman and the scientist, this book presents an overview of some of today's great scientific questions, from the way in which we acquire language and the fundamental nature of our thinking processes, to the possible existence of life elsewhere in the universe. Each chapter is constructed in the form of a trial, with the conventional scientific wisdom presented by the prosecution and alternative views put forward by the defence . The author, who aims to be both informative and entertaining, subsequently steps in to act as juror , offering explanations of his verdicts.

Book Review Digest

Book Review Digest

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Bibliography
  • Page: N.A
  • View: 9181
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Would-be worlds

Would-be worlds

how simulation is changing the frontiers of science

  • Author: John L. Casti
  • Publisher: Wiley
  • ISBN: N.A
  • Category: Computers
  • Page: 256
  • View: 6210
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Critical acclaim for How Simulation Is Changing the Frontiers of Scienc "John Casti is one of the great science writers of the 1990s." —San Francisco Examiner "A popular account of the enormous change computers have brought to the everyday practice of science . . . an easy and enjoyable read." —Nature "As we approach a new century, modelling through new mathematical insights and powerful computers grows apace . . . .John Casti has written a truly important book." —The Sunday Times

The Cambridge Quintet

The Cambridge Quintet

A Work of Scientific Speculation

  • Author: John L. Casti
  • Publisher: Little Brown GBR
  • ISBN: 9780349108537
  • Category: Artificial intelligence
  • Page: 181
  • View: 3064
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By 1949, the idea of duplicating human thought processes in a computer was starting to surface, as the outgrowth of code-breaking work done by Alan Turing and others in Britain during the Second World War. This ingenious work of speculative scientific fiction reconstructs what might have been said during the animated conversation flowing around Snow's rooms that fateful in Cambridge. The quintet's debate anticipates all of the basic questions which have surrounded artificial intelligence in the fifty years since. Can a machine think or merely process information? Is the brain simply a symbol-processing machine, as Turing suggests, and if so, what is the nature of meaning? Can there be, as Wittgenstein proposes, no thought without language, and no language without the social interaction of human beings?

Complexification

Complexification

explaining a paradoxical world through the science of surprise

  • Author: J. L. Casti
  • Publisher: Harpercollins
  • ISBN: 9780060168889
  • Category: Mathematics
  • Page: 320
  • View: 8339
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A mathematician explores how complexity arises, showing how the universe consists of unpredictable "dynamical systems" so subtle that human logic cannot fathom them and laying the groundwork for a "Science of Surprise." 30,000 first printing. $30,000 ad/promo. Tour.

Mathematical Mountaintops

Mathematical Mountaintops

The Five Most Famous Problems of All Time

  • Author: J. L. Casti
  • Publisher: Oxford University Press, USA
  • ISBN: N.A
  • Category: Mathematics
  • Page: 177
  • View: 8580
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In Mathematical Mountaintops, John Casti brilliantly recreates the solutions to the five greatest mathematical problems of all time: The Four-Color Map Problem, Fermat's Last Theorem, The Continuum Hypothesis, Kepler's Conjecture, and Hilbert's Tenth Problem. Casti recounts these mathematical quests with great verve. In retelling the story of Hilbert's Tenth Problem, for instance, he sweeps from Britain to New York to Leningrad and introduces us to such luminaries as Alan Turing, before turning to the young Soviet researcher who credited his breakthrough to a 700-year-old Italian problem about rabbits. He describes how Fermat's Last Theorem tantalized generations of scientists, who tried for three centuries to answer it, and relates how the final solution was greeted with the unprecedented front-page headlines, prize money, and international celebration--before a flaw (soon resolved) turned up. Casti's account of the struggle to solve Kepler's Conjecture wittily revealshow the "proof of the obvious" sometimes eludes us for centuries. And his discussion of The Continuum Hypothesis movingly portrays the tragic figure of Georg Cantor, the troubled genius who created the first truly original mathematics since the Greeks, yet died insane in an institution. Casti closes with a preview of the "Magnificent Seven"--the greatest unsolved mathematical mysteries, each of which carries a million-dollar bounty from the Clay Mathematics Institute--including the Poincare Conjecture, the Yang-Mills Existence and Mass Gap (why physicists can't isolate quarks), and the Reimann Hypothesis ("the granddaddy of all mathematical mysteries"). Mathematical Mountaintops is a brilliant account of mathematicians in action--seeking hidden patterns and structures, forging elegant chains of reasoning--as they struggle with problems that challenged the greatest minds for decades, if not centuries.

The Elements of Euclid

The Elements of Euclid

  • Author: Euclid
  • Publisher: N.A
  • ISBN: N.A
  • Category: Geometry
  • Page: 416
  • View: 3252
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Poincare's Prize

Poincare's Prize

The Hundred-Year Quest to Solve One of Math's Greatest Puzzles

  • Author: George G. Szpiro
  • Publisher: Penguin
  • ISBN: 1440634289
  • Category: Mathematics
  • Page: 320
  • View: 5156
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The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.