Algorithms in modern mathematics and computer science

  • Donald E. Knuth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 122)


Computer Science Finite Subset Mathematical Thinking Transcendence Degree Missing Concept 
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  1. [1]
    A. D. Aleksandrov, A. N. Kolmogorov, and M. A. Lavrent'ev, eds., Mathematics: Its Content, Methods and Meaning 1 (Cambridge, Mass.: MIT Press, 1963). Translated by S. H. Gould and T. Bartha from Matematika: Eë Soderzhanie, Metody i Znachenie (Akad. Nauk SSSR, 1956).Google Scholar
  2. [2]
    Errett Bishop, Foundations of Constructive Analysis (N.Y.: McGraw-Hill, 1967).Google Scholar
  3. [3]
    Baldassarre Boncompagni, ed., Algoritml de Numero Indorum. Trattati D'Aritmetica 1 (Rome, 1857).Google Scholar
  4. [4]
    Solomon Gandz, "The Mishnat Ha Middot," Proc. Amer. Acad. for Jewish Research 4 (1933), 1–104. Reprinted in S. Gandz, Studies in Hebrew Astronomy and Mathematics (New York: Ktav, 1970), 295–400.Google Scholar
  5. [5]
    Solomon Gandz, "Sources of al-Khowârizmi's Algebra," Osiris 1 (1936), 263–277.CrossRefGoogle Scholar
  6. [6]
    Solomon Gandz, "The origin and development of the quadratic equations in Babylonian, Greek, and early Arabic algebra," Osiris 3 (1938), 405–557.CrossRefGoogle Scholar
  7. [7]
    Solomon Gandz, "The algebra of inheritance," Osiris 5 (1938) [sic], 319–391.CrossRefGoogle Scholar
  8. [8]
    Fred Gruenberger, "The role of education in preparing effective computing personnel," in F. Gruenberger, ed., Effective vs. Efficient Computing (Englewood Cliffs, N.J.: Prentice-Hall, 1973), 112–120.Google Scholar
  9. [9]
    A. P. fushkevich, "Arifmeticheskil traktat Mykhammeda Ben Musa Al-Khorezmi," Trudy Inst. Istorii Estestvoznaniia i tekhniki 1 (1954), 85–127.Google Scholar
  10. [10]
    Louis Charles Karpinski, ed., Robert of Chester's Latin Translation of the Algebra of Al-Khowärizmi. Univ. Michigan Humanistic Series 11, part 1 (Ann Arbor, 1915), 164 pp. Reprinted in 1930.Google Scholar
  11. [11]
    John L. Kelley, General Topology (Princeton: D. Van Nostrand, 1955).Google Scholar
  12. [2]
    E. S. Kennedy, "al-Biruni," Dictionary of Scientific Biography 2 (N.Y.: Charles Scribner's Sons, 1970), 147–158.Google Scholar
  13. [13]
    Stephen Cole Kleene, Introduction to Metamathematics (Princeton: D. Van Nostrand, 1952).Google Scholar
  14. [14]
    Donald E. Knuth, Fundamental Algorithms (Reading, Mass.: Addison-Wesley, 1968).Google Scholar
  15. [15]
    Donald E. Knuth and Luis Trabb Pardo, "The early development of programming languages," itEncyclopedia of Computer Science and Technology 7 (N.Y.: Marcel Dekker).Google Scholar
  16. [16]
    Iu. Kh. Kopelevich and B. A. Rosenfel'd, tr., Mukhammad al'-Khorezmi: Matematicheskie Traktaty (Tashkent: Akad. Nauk Uzbekskoγ SSR, 1964). [Includes al-Khwärizmi's arithmetic and algebra, with commentaries by B. A. Rosenfel'd.]Google Scholar
  17. [17]
    Seyyed Hossein Nasr et al., Historical Atlas of Iran (Tebran, 1971).Google Scholar
  18. [18]
    D. Pingree, review of [28], Math. Reviews 30 (July, 1965), No. 5.Google Scholar
  19. [19]
    G. Pólya and G. Szegö, Problems and Theorems in Analysis 1 (Berlin: Springer, 1972).Google Scholar
  20. [20]
    Ed. Sachau, "Algebraisches über das Schach bei Birûni," Zeitschrift d. Deutsche Morgenländische Gesellschaft 29 (1876), 148–156.Google Scholar
  21. [21]
    C. Edward Sachau, transl. and ed., al'Birûni's Chronology of Ancient Nations (London: William H. Allen and Co., 1879).Google Scholar
  22. [22]
    A. S. Saidan, The Arithmetic of al-Uqlidisi (Dordrecht: D. Reidel, 1975).Google Scholar
  23. [23]
    S. Kh. Sirazhdinov and G. P. Matvievskafa, Abu Raγkhan Beruni i Ego Matematicheskie Trudy (Moscow: Prosveshchenie, 1978).Google Scholar
  24. [24]
    D. J. Struik, ed., A Source Book in Mathematics, 1200–1800 (Cambridge, Mass.: Harvard University Press, 1969).Google Scholar
  25. [25]
    George B. Thomas, Calculus and Analytic Geometry, 2nd ed. (Cambridge, Mass.: Addison-Wesley, 1956).Google Scholar
  26. [26]
    G. J. Toomer, "al-Khwärizmτ," Dictionary of Scientific Biography 7 (N.Y.: Charles Scribner's Sons, 1973), 358–365.Google Scholar
  27. [27]
    J. F. Traub, Iterative Methods for the Solution of Equations (Englewood Cliffs, N.J.: Prentice-Hall, 1964).Google Scholar
  28. [28]
    Kurt Vogel, ed., Mohammed Ibn Musa Alchwarizmi's Algorismus, Das früheste Lehrbuch zum Rechnen mit indischen Ziffern (Aalen/Osnabruck: Otto Zeller Verlagsbuchhandlung, 1963). [This edition contains a facsimile of the manuscript, from which a correct transcription can be deduced.]Google Scholar
  29. [29]
    Oscar Zariski and Pierre Samuel, Commutative Algebra 1 (Princeton: D. Van Nostrand, 1958).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Donald E. Knuth
    • 1
  1. 1.Department of Computer ScienceStanford UniversityStanfordUSA

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