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The Universe in Zero Words : The Story of Mathematics as Told through Equations: Mackenzie, Dana: BOOKS KINOKUNIYA
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The Universe in Zero Words : The Story of Mathematics as Told through Equations
The Universe in Zero Words : The Story of Mathematics as Told through Equations
著者名 Mackenzie, Dana
出版社 : Princeton Univ Pr
出版年月 : 2012/04
Binding : Hardcover
ISBN : 9780691152820

BookWeb価格 : MYR 117.65
会員価格 : MYR 105.88

在庫情報 : 専門取次会社からお取り寄せします。
通常、3週間以内に発送いたします。
言語 : English

内容情報
Source: ENG
Academic Descriptors: A51050000
Place of Publication: United States
Subject Development: History
Academic Level: Extracurricular
Review:
Choice Reviews 2012 November

Most popular books about science, and even about mathematics, tiptoe around equations as if they were something to be hidden from the reader's tender eyes. Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics - the universal language of science - keep the masterpieces of the subject hidden behind a veil? "The Universe in Zero Words" tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society - from the elementary (1+1=2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E=mc2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called 'a popular-science ace' by Booklist magazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives.Illustrated in color throughout, the book tells the human and often-surprising stories behind the invention or discovery of the equations, from how a bad cigar changed the course of quantum mechanics to why whales (if they could communicate with us) would teach us a totally different concept of geometry. At the same time, the book shows why these equations have something timeless to say about the universe, and how they do it with an economy (zero words) that no other form of human expression can match. "The Universe in Zero Words" is the ultimate introduction and guide to equations that have changed the world.

Contents
Preface 6 IntroductionEquations of Antiquity 16 1. Why we believe in arithmetic: the world's simplest equation 20 2. Resisting a new concept: the discovery of zero 26 3. The square of the hypotenuse: the Pythagorean theorem 30 4. The circle game: the discovery of pi 40 5. From Zeno's paradoxes to the idea of infinity 46 6. A matter of leverage: laws of levers 52 Part Two: Equations in the age of exploration 56 7. The stammerer's secret: Cardano's formula 60 8. Order in the heavens: Kepler's laws of planetary motion 68 9. Writing for eternity: Fermat's Last Theorem 74 10. An unexplored continent: the fundamental theorem of calculus 80 11. Of apples, legends ... and comets: Newton's laws 90 12. The great explorer: Euler's theorems 96 Part Three: Equations in a promethean age 104 13. The new algebra: Hamilton and quaternions 108 14. Two shooting stars: group theory 114 15. The geometry of whales and ants: non-Euclidean geometry 122 16. In primes we trust: the prime number theorem 128 17. The idea of spectra: Fourier series 134 18. A god's-eye view of light: Maxwell's equations 142 Part Four: Equations in our own time 150 19. The photoelectric effect: quanta and relativity 154 20. From a bad cigar to Westminster Abbey: Dirac's formula 164 21. The empire-builder: the Chern-Gauss-Bonnet equation 174 22. A little bit infinite: the Continuum Hypothesis 182 23. Theories of chaos: Lorenz equations 194 24. Taming the tiger: the Black-Scholes equation 204 Conclusion: What of the future? 214 Acknowledgments 218 Bibliography 219 Index 222Four Faith Models Chapter Twenty: Striving for Justice and Peace on Earth, Catholic Peace Initiatives Ismael Muvingi Chapter Twenty-One: Peacebuilding Principles and Values in Islam: Beyond the Basic Framework Mohammed Abu-Nimer Chapter Twenty-Two: Peace on Earth: The Anabaptist-Mennonite Perspective Lois Edmund Chapter Twenty-Three: Neve Shalom/Wahat al-Salam: the 'Oasis of Peace' Deanna Armbruster Chapter Twenty-Four: Conclusions: Peace on Earth Revisited Hamdesa Tuso, Jessica Senehi, and Sean Byrnezum Rechtsstreit Anschutz & Co. gegen Sperry-Gyroscope Company" Editorial Note: Einstein on Ampere's Molecular Currents 145 13. "Experimental Proof of Amp6re's Molecular Currents" 151 (with Wander J. de Haas), 19 February 1915 "Experimenteller Nachweis der Ampereschen Molekularstrome" Deutsche Physikalische Gesellschaft. Verhandlungen 17 (1915) 14. "Experimental Proof of the Existence of Ampere's Molecular Currents" (with Wander J. de Haas), 23 April 1915 172 Koninklijke Akademie van Wetenschappen to Amsterdam. Section of Sciences. Proceedings 18 (1915-16) 15. "Experimental Proof of Ampere's Molecular Currents," 7 May 1915 190 "Experimenteller Nachweis der Ampereschen Molekularstrome" Die Naturwissenschaften 3 (1915) 16. "Correction of My Joint Paper with J. W. de Haas: 'Experimental Proof of Ampere's Molecular Currents'," 10 May 1915 194 "Berichtigung zu meiner gemeinsam mit Herrn J. W. de Haas veroffentlichten Arbeit ,,Experimenteller Nachweis der Ampereschen Molekularstrome" " Deutsche Physikalische Gesellschaft. Verhandlungen 17 (1915) 17. "Comment on the Essay Submitted by Knapp: 'The Shearing of the Light-Ether ...'," 15 June 1915 197 "Ausserung zu dem von Herrn Knapp eingereichten Aufsatze ,,Die Scherung des Lichtathers ..." 18. "Response to a Paper by M. von Laue: 'A Theorem in Probability Calculus and Its Application to Radiation Theory'," 24 June 1915 198 "Antwort auf eine Abhandlung M. v. Laues ,,Ein Satz der Wahrscheinlichkeitsrechnung und seine Anwendung auf die Strahlungstheorie" " Annalen der Physik 47 (1915) 19. "Supplementary Expert Opinion," 7 August 1915 "Nachtragsgutachten" 207 20. "My Opinion on the War," 23 October-11 November 1915 211 "Meine Meinung Uber den Krieg" 21. "On the General Theory of Relativity," 4 November 1915 214 "Zur allgemeinen Relativitatstheorie" Koniglich Preuaische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1915) 22. "On the General Theory of Relativity (Addendum)," 11 November 1915 225 "Zur allgemeinen Relativitatstheorie (Nachtrag)" Koniglich Preuaische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1915) 23. "Comment on Our Paper: 'Experimental Proof of Ampere's Molecular Currents"' (with Wander J. de Haas), 15 November 1915 230 "Notiz zu unserer Arbeit ?Experimenteller Nachweis der Ampereschen Molekularstrome" Deutsche Physikalische Gesellschaft. Verhandlungen 17 (1915) 24. "Explanation of the Perihelion Motion of Mercury from the General Theory of Relativity," 18 November 1915 233 "Erklarung der Perihelbewegung des Merkur aus der allgemeinen Relativitatstheorie" Koniglich Preuaische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1915) 25. "The Field Equations of Gravitation," 25 November 1915 244 "Die Feldgleichungen der Gravitation" Koniglich Preuaische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1915) 26. "On the Theory of Tetrode and Sackur for the Entropy Constant," ca. 14 January 1916 250 "Zur Tetrode-Sakkur'schen Theorie der Entropie-Konstante" 27. "A New Formal Interpretation of Maxwell's Field Equations of Electrodynamics," 3 February 1916 263 "Eine neue formale Deutung der Maxwellschen Feldgleichungen der Elektrodynamik" Koniglich Preuaische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1916) 28. "A Simple Experiment to Demonstrate Ampere's Molecular Currents," 25 February 1916 270 "Ein einfaches Experiment zum Nachweis der Ampereschen Molekularstrome" Deutsche Physikalische Gesellschaft. Verhandlungen 18 (1916) 29. "Ernst Mach," 14 March 1916 277 Physikalische Zeitschrift 17 (1916) 30. "The Foundation of the General Theory of Relativity," 20 March 1916 283 "Die Grundlage der allgemeinen Relativitatstheorie" Annalen der Physik 49 (1916) 31. "Appendix. Formulation of the Theory on the Basis of a Variational Principle," before 20 March 1916 340 "Anhang. Darstellung der Theorie ausgehend von einem Variationsprinzip" 32. "Approximative Integration of the Field Equations of Gravitation," 22 June 1916 347 "Naherungsweise Integration der Feldgleichungen der Gravitation" Koniglich Preuaische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1916) 33. "Einstein's Memorial Lecture on Karl Schwarzschild," 29 June 1916 358 "Gedachtnisrede des Hrn. Einstein auf Karl Schwarzschild" Koniglich Preuaische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1916) 34. "Emission and Absorption of Radiation in Quantum Theory," 17 July 1916 363 "Strahlungs-Emission und -Absorption nach der Quantentheorie" Deutsche Physikalische Gesellschaft. Verhandlungen 18 (1916) 35. "Preface" to Erwin Freundlich, The Foundations of Einstein's Theory of Gravitation, ca. August 1916 371 36. Review of H. A. Lorentz, Statistical Theories in Thermodynamics: Five Lectures ... 11 August 1916 374 Les theories statistiques en thermodynamique Die Naturwissenschaften 4 (1916) 37. "Author's Summary of The Foundation of the General Theory of Relativity, 11 August 1916 378 Die Naturwissenschaften 4 (1916) 38. "On the Quantum Theory of Radiation," after 24 August 1916 381 "Zur Quantentheorie der Strahlung" Physikalische Gesellschaft Zurich. Mitteilungen 18 (1916) 39. "Elementary Theory of Water Waves and of Flight," 25 August 1916 "Elementare Theorie der Wasserwellen und des Fluges" 399 Die Naturwissenschaften 4 (1916) 40. "On Friedrich Kottler's Paper: 'On Einstein's Equivalence Hypothesis and Gravitation'," October 1916 403 "Uber Friedrich Kottlers Abhandlung ,,Uber Einsteins Aquivalenzhypothese und die Gravitation" Annalen der Physik 51 (1916) 41. "Hamilton's Principle and the General Theory of Relativity," 26 October 1916 409 "Hamiltonsches Prinzip und allgemeine Relativitatstheorie" Koniglich Preuaische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1916) Editorial Note: Einstein's Popular Book on Relativity 417 42. On the Special and the General Theory of Relativity (A Popular Account), December 1916 420 Uber die spezielle und die allgemeine Relativitatstheorie (Gemeinverstandlich). Braunschweig: Vieweg, 1917 43. "Cosmological Considerations in the General Theory of Relativity," 8 February 1917 540 "Kosmologische Betrachtungen zur allgemeinen Relativitatstheorie" Koniglich Preuaische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1917) 44. "Reply to the Plaintiff's Written Statement of 27 December 1916," 17 February 1917 553 "Antwort auf die Schrift der Klagerin vom 27. December 1916" 45. "On the Quantum Theorem of Sommerfeld and Epstein," 11 May 1917 "Zum Quantensatz von Sommerfeld und Epstein" 555 Deutsche Physikalische Gesellschaft. Verhandlungen 19 (1917) 46. Review of Hermann von Helmholtz, Two Lectures on Goethe, 2 November 1917 568 Zwei Vortrage uber Goethe Die Naturwissenschaften 5 (1917) 47. "A Derivation of Jacobi's Theorem," 22 November 1917 "Eine Ableitung des Theorems von Jacobi" Koniglich Preuaische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1917) 48. "Marian von Smoluchowski," 14 December 1917 576 Die Naturwissenschaften 5 (1917) 49. "The Nightmare," 25 December 1917 580 "Der Angst-Traum" Berliner Tageblatt, 25 December 1917 APPENDIXES A. Summaries of Einstein's Courses, University of Berlin 583 B. Nachschrift of Einstein's Wolfskehl Lectures, summer 1915 586 Literature Cited 591 Indexes 607Murdered or Driven to Suicide by the Nazis 358 1.3. List of German-Speaking Mathematicians Persecuted in Other Manners (Includes Teachers of Mathematics and Is Probably Incomplete) 360 Appendix 2: Excerpt from a Letter by George David Birkhoff rom Paris (1928) to His Colleague-Mathematicians at Harvard Concerning the Possibility of or Desirability to Hire Foreigners 366 Appendix 3.1: Report Compiled by Harald Bohr "Together with Different German Friends" in May 1933 Concerning the Present Conditions in German Universities, in Particular with Regard to Mathematics and Theoretical Physics 368 Appendix 3.2: Translation of a Letter from Professor Karl Lowner of the University of Prague to Professor Louis L. Silverman (Dartmouth College) Dated August 2, 1933 372 Appendix 3.3: Richard von Mises's "Position toward the Events of Our Time" in November 1933 374 Appendix 3.4: Report by Artur Rosenthal (Heidelberg) from June 1935 on the Boycott of His and Heinrich Liebmann's Mathematical Courses 376 Appendix 3.5: Max Pinl--Later the Author of Pioneering Reports (1969-72) on Mathematical Refugees--in a Letter to Hermann Weyl on the Situation in Czechoslovakia Immediately after the Munich Dictate of September 29, 1938 378 Appendix 4.1: A Letter by Emmy Noether of January 1935 to the Emergency Committee in New York Regarding Her Scientific and Political Interests during Emigration 380 Appendix 4.2: Richard Courant's Resignation from the German Mathematicians'Association DMV in 1935 381 Appendix 4.3: Von Mises in His Diary about His Second Emigration, from Turkey to the USA, in 1939 383 Appendix 4.4: Hermann Weyl to Harlow Shapley on June 5, 1943, Concerning the Problems of the Immigrant from Gottingen, Felix Bernstein 388 Appendix 5.1: Richard Courant in October 1945 to the American Authorities Who Were Responsible for German Scientific Reparation 390 Appendix 5.2: Max Dehn's Refusal to Rejoin the German Mathematicians' Association DMV in 1948 393 Appendix 6: Memoirs for My Children (1933/1988) by Peter Thullen 394 Archives, Unprinted Sources, and Their Abbreviations 415 References 421 Photographs Index and Credits 445 Subject Index 449 Name Index 461