The Nature and Growth of Modern Mathematics

Author: Edna Ernestine Kramer

Publisher: Princeton University Press

ISBN: 9780691023724

Category: Mathematics

Page: 758

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Now available in a one-volume paperback, this book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story--ultimately linked to modern digital computers--the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful "ideals" of Dedekind and Emmy Noether; and the importance of "purifying" mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail.
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A Bridge to Advanced Mathematics

Author: Dennis Sentilles

Publisher: Courier Corporation

ISBN: 0486277585

Category: Mathematics

Page: 416

View: 9713

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This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.
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Metaphor and Analogy in the Sciences

Author: F. Hallyn

Publisher: Springer Science & Business Media

ISBN: 9401594422

Category: Philosophy

Page: 244

View: 5411

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This collection of papers contains historical case studies, systematic contributions of a general nature, and applications to specific sciences. The bibliographies of the contributions contain references to all central items from the traditions that are relevant today. While providing access to contemporary views on the issue, the papers illustrate the wide variety of functions of metaphors and analogies, as well as the many connections between the study of some of these functions and other subjects and disciplines.
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Superior Beings

If They Exist, How Would We Know?

Author: BRAMS

Publisher: Springer Science & Business Media

ISBN: 1475718071

Category: Religion

Page: 202

View: 4352

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The central question I pose in this book is: If there existed a supe rior being who possessed the supernatural qualities of omni science, omnipotence, immortality, and incomprehensibility, how would he/she act differently from us, and would these differences be knowable? (ßecause God, the superior being in the Judeo Christian tradition, is generally described as a male, I shall hence forth use the masculine pronoun form for convenience, but I intend no invidious gender distinctions, whether applied to super natural or natural beings.l Theologians, philosophers of religion, and erudite scholars in other disciplines have addressed this and related questions before, but their answers, generally speaking, have not been informed by any systematic or rigorous theory. I believe the mathematical theory of games, which has little to do with the frivolity and playfulness we normally associate with games, provides a powerful tool for clarifying the key theo logical concepts in my central question and drawing out their implications in games played between human and superior beings. I am fully aware that not everybody will agree that omni science, omnipotence, immortality, and incomprehensibility are what I say they are, but I invite them to propose their own defi- Preface viii nitions and derive their own conclusions with the aid of the theory. By endowing these protean concepts with unambiguous meanings, I will try to show how game theory can breathe life into questions that have been dismissed too quickly simply because they are metaphysical-outside the world of experience.
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Game Theory and Politics

Author: Steven J. Brams

Publisher: Courier Corporation

ISBN: 0486143635

Category: Mathematics

Page: 336

View: 6114

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DIVMany illuminating and instructive examples of the applications of game theoretic models to problems in political science appear in this volume, which requires minimal mathematical background. 1975 edition. 24 figures. /div
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The Mathematical Experience, Study Edition

Author: Philip Davis,Reuben Hersh,Elena Anne Marchisotto

Publisher: Springer Science & Business Media

ISBN: 0817682945

Category: Mathematics

Page: 500

View: 7697

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Winner of the 1983 National Book Award! "...a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition) Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications. The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto ([email protected]) upon request.
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From Natural Philosophy to the Sciences

Writing the History of Nineteenth-Century Science

Author: David Cahan

Publisher: University of Chicago Press

ISBN: 9780226089270

Category: Science

Page: 456

View: 5772

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During the nineteenth century, much of the modern scientific enterprise took shape: scientific disciplines were formed, institutions and communities were founded, and unprecedented applications to and interactions with other aspects of society and culture occurred. In this book, eleven leading historians of science assess what their field has taught us about this exciting time and identify issues that remain unexamined or require reconsideration. They treat both scientific disciplines—biology, physics, chemistry, the earth sciences, mathematics, and the social sciences—in their specific intellectual and sociocultural contexts as well as the broader topics of science and medicine; science and religion; scientific institutions and communities; and science, technology, and industry. Providing a much-needed overview and analysis of a rapidly expanding field, From Natural Philosophy to the Sciences will be essential for historians of science, but also of great interest to scholars of all aspects of nineteenth-century life and culture. Contributors: Bernadette Bensaude-Vincent, Jed Z. Buchwald, David Cahan, Joseph Dauben, Frederick Gregory, Michael Hagner, Sungook Hong, David R. Oldroyd, Theodore M. Porter, Robert J. Richards, Ulrich Wengenroth
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The Pentagon Wars

Reformers Challenge the Old Guard

Author: James Burton

Publisher: Naval Institute Press

ISBN: 1612513697

Category: Political Science

Page: 336

View: 6486

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From the late 1960s through the mid-1980s, a small band of military activists waged war against corruption in the Pentagon, challenging a system they believed squandered the public’s money and trust. The book examines the movement and its proponents and describes how the system responded to the criticisms and efforts to change accepted practices and entrenched ways of thinking. The author, an air force colonel and part of the movement, worked in the pentagon for fourteen years. He presents a view of the Department of Defense that only an insider could offer. He exposes serious flaws in the military policy-making process, particularly in weapons development and procurement. The details he gives on the unrelenting push for high-tech weapons, despite their ineffectiveness and extraordinary cost-overruns, provide a strong case for the charge of ethical bankruptcy. The second half of the book deals with the author’s attempts to get frontline equipment tested under combat conditions. For the first time, readers learn the nasty details of his battle with the army over line-fire testing of the Bradley Fighting Vehicle—a battle that he eventually won, leading to the personnel carrier’s redesign and the saving of many lives. Never reluctant to name names and reveal details, James G. Burton presents a forceful case. And his revelations offer insights not found elsewhere into the motivations and actions of the people who wield power from within. Nor does he stop at the walls of the Pentagon. In his epilogue he tells what happened in the field during the final hours of the Gulf War that allowed Hussein’s elite Republican Guard to escape. Now back in print after having inspired a feature HBO film, this explosive account of insider corruption is sure to serve policy-makers for generations to come.
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