Skip to main content

Algorithms in modern mathematics and computer science

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 122))

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. Errett Bishop, Foundations of Constructive Analysis (N.Y.: McGraw-Hill, 1967).

    Google Scholar 

  3. Baldassarre Boncompagni, ed., Algoritml de Numero Indorum. Trattati D'Aritmetica 1 (Rome, 1857).

    Google Scholar 

  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. Solomon Gandz, "Sources of al-Khowârizmi's Algebra," Osiris 1 (1936), 263–277.

    Article  Google Scholar 

  6. Solomon Gandz, "The origin and development of the quadratic equations in Babylonian, Greek, and early Arabic algebra," Osiris 3 (1938), 405–557.

    Article  Google Scholar 

  7. Solomon Gandz, "The algebra of inheritance," Osiris 5 (1938) [sic], 319–391.

    Article  Google Scholar 

  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. A. P. fushkevich, "Arifmeticheskil traktat Mykhammeda Ben Musa Al-Khorezmi," Trudy Inst. Istorii Estestvoznaniia i tekhniki 1 (1954), 85–127.

    Google Scholar 

  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. John L. Kelley, General Topology (Princeton: D. Van Nostrand, 1955).

    Google Scholar 

  12. E. S. Kennedy, "al-Biruni," Dictionary of Scientific Biography 2 (N.Y.: Charles Scribner's Sons, 1970), 147–158.

    Google Scholar 

  13. Stephen Cole Kleene, Introduction to Metamathematics (Princeton: D. Van Nostrand, 1952).

    Google Scholar 

  14. Donald E. Knuth, Fundamental Algorithms (Reading, Mass.: Addison-Wesley, 1968).

    Google Scholar 

  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. 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. Seyyed Hossein Nasr et al., Historical Atlas of Iran (Tebran, 1971).

    Google Scholar 

  18. D. Pingree, review of [28], Math. Reviews 30 (July, 1965), No. 5.

    Google Scholar 

  19. G. Pólya and G. Szegö, Problems and Theorems in Analysis 1 (Berlin: Springer, 1972).

    Google Scholar 

  20. Ed. Sachau, "Algebraisches über das Schach bei Birûni," Zeitschrift d. Deutsche Morgenländische Gesellschaft 29 (1876), 148–156.

    Google Scholar 

  21. C. Edward Sachau, transl. and ed., al'Birûni's Chronology of Ancient Nations (London: William H. Allen and Co., 1879).

    Google Scholar 

  22. A. S. Saidan, The Arithmetic of al-Uqlidisi (Dordrecht: D. Reidel, 1975).

    Google Scholar 

  23. S. Kh. Sirazhdinov and G. P. Matvievskafa, Abu Raγkhan Beruni i Ego Matematicheskie Trudy (Moscow: Prosveshchenie, 1978).

    Google Scholar 

  24. D. J. Struik, ed., A Source Book in Mathematics, 1200–1800 (Cambridge, Mass.: Harvard University Press, 1969).

    Google Scholar 

  25. George B. Thomas, Calculus and Analytic Geometry, 2nd ed. (Cambridge, Mass.: Addison-Wesley, 1956).

    Google Scholar 

  26. G. J. Toomer, "al-Khwärizmτ," Dictionary of Scientific Biography 7 (N.Y.: Charles Scribner's Sons, 1973), 358–365.

    Google Scholar 

  27. J. F. Traub, Iterative Methods for the Solution of Equations (Englewood Cliffs, N.J.: Prentice-Hall, 1964).

    Google Scholar 

  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. Oscar Zariski and Pierre Samuel, Commutative Algebra 1 (Princeton: D. Van Nostrand, 1958).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Andrei P. Ershov Donald E. Knuth

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Knuth, D.E. (1981). Algorithms in modern mathematics and computer science. In: Ershov, A.P., Knuth, D.E. (eds) Algorithms in Modern Mathematics and Computer Science. Lecture Notes in Computer Science, vol 122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11157-3_26

Download citation

  • DOI: https://doi.org/10.1007/3-540-11157-3_26

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11157-3

  • Online ISBN: 978-3-540-38621-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics