The Nature and Growth of Modern Mathematics

Author: Edna Ernestine Kramer

Publisher: Princeton University Press

ISBN: 9780691023724

Category: Mathematics

Page: 758

View: 4749

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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: 6689

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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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Descartes' Natural Philosophy

Author: Stephen Gaukroger,John Schuster,John Sutton

Publisher: Routledge

ISBN: 1134600925

Category: Philosophy

Page: 784

View: 7364

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The most comprehensive collection of essays on Descartes' scientific writings ever published, this volume offers a detailed reassessment of Descartes' scientific work and its bearing on his philosophy. The 35 essays, written by some of the world's leading scholars, cover topics as diverse as optics, cosmology and medicine, and will be of vital interest to all historians of philosophy or science.
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New Theories of Everything

The Quest for Ultimate Explanation

Author: John D. Barrow

Publisher: OUP Oxford

ISBN: 0191579378

Category: Science

Page: 272

View: 8689

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Will we ever discover a single scientific theory that tells us everything that has happened, and everything that will happen, on every level in the Universe? The quest for the theory of everything - a single key that unlocks all the secrets of the Universe - is no longer a pipe-dream, but the focus of some of our most exciting research about the structure of the cosmos. But what might such a theory look like? What would it mean? And how close are we to getting there? In New Theories of Everything, John D. Barrow describes the ideas and controversies surrounding the ultimate explanation. Updating his earlier work Theories of Everything with the very latest theories and predictions, he tells of the M-theory of superstrings and multiverses, of speculations about the world as a computer program, and of new ideas of computation and complexity. But this is not solely a book about modern ideas in physics - Barrow also considers and reflects on the philosophical and cultural consequences of those ideas, and their implications for our own existence in the world. Far from there being a single theory uniquely specifying the constants and forces of nature, the picture today is of a vast landscape of different logically possible laws and constants in many dimensions, of which our own world is but a shadow: a tiny facet of a higher dimensional reality. But this is not to say we should give up in bewilderment: Barrow shows how many rich and illuminating theories and questions arise, and what this may mean for our understanding of our own place in the cosmos.
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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: 586

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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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Game Theory and Politics

Author: Steven J. Brams

Publisher: Courier Corporation

ISBN: 0486143635

Category: Mathematics

Page: 336

View: 6216

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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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Superior Beings

If They Exist, How Would We Know?

Author: BRAMS

Publisher: Springer Science & Business Media

ISBN: 1475718071

Category: Religion

Page: 202

View: 605

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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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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: 2599

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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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