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The role of algorithms in the teaching of algebra

Part of the Lecture Notes in Mathematics book series (LNM,volume 697)

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References

  1. E.R. Berlekamp, "Factoring polynomials over finite fields", Bell System Tech. J. 46 (1967), 1853–1859.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. William W. Boone, "Certain simple, unsolvable problems of group theory", K. Nederl. Akad. Wetensch. Proc. Ser. A [Indag. Math.] I 57 [16] (1954), 231–237

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. II 57 [16] (1954), 492–497

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. III 58 [17] (1955), 252–256

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. IV 58 [17] (1955), 571–577

    CrossRef  MATH  Google Scholar 

  6. V 60 [19] (1957), 22–27

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. VI 60 [19] (1957), 227–232.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Grete Herman, "Die Frage der endlichen vielen Schritte in der Theorie der Polynomideale", Math. Ann. 95 (1926), 736–788.

    CrossRef  MathSciNet  Google Scholar 

  9. David Hilbert, "Ueber die Theorie der algebraischen Formen", Math. Ann. 36 (1890), 473–534.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Nathan Jacobson, Lectures in Abstract Algebra. I: Basic Concepts; II: Linear Algebra; III: Theory of Fields and Galois Theory (The University Series in Higher Mathematics. Van Nostrand, Princeton, New Jersey; Toronto; New York; London; 1951, 1953, 1964. Reprinted: Graduate Texts in Mathematics, 30, 31, 32. Springer-Verlag, New York, Heidelberg, Berlin, 1975.

    Google Scholar 

  11. Donald E. Knuth, The Art of Computer Programming. Vol. 2: Seminumerical Algorithms (Addison-Wesley Series in Computer Science and Information Processing. Addison-Wesley, Reading, Mass.; Menlo Park, California; London; Don Mills, Ontario; 1969).

    MATH  Google Scholar 

  12. Serge Lang, Algebra (Addison-Wesley Series in Mathematics. Addison-Wesley, Reading, Mass., 1965).

    MATH  Google Scholar 

  13. Saunders Mac Lane, Garrett Birkhoff, Algebra (Macmillan, New York; Collier-Macmillan, London, 1967).

    MATH  Google Scholar 

  14. П.С. Новиков [P.S. Novikov], "Об алгоритмичесной неразрешимости проблемы тождества слов в теории групп" [On the algorithmic insolvability of the word problem in group theory], Trudy Mat. Inst. Steklov. 44 (1955), 3–143; Amer. Math. Soc. Transl. (2) 9 (1958), 1–122.

    Google Scholar 

  15. Michael O. Rabin, Probabilistic Algorithms, Algorithms and Complexity (Proc. Sympos. Carnegie-Mellon University, Pittsburgh, 1976, 21–39. Academic Press [Harcourt Brace Jovanovich], New York, London, 1976).

    Google Scholar 

  16. Charles C. Sims, "Some group-theoretic algorithms", these proceedings, 108–124.

    Google Scholar 

  17. Richard P. Standuhar, "The determination of Galois groups", Math. Comp. 27 (1973), 981–996.

    CrossRef  MathSciNet  Google Scholar 

  18. B.L. van der Waerden, Moderne Algebra, I, II (Unter Benutzung von Vorlesungen von E. Artin und E. Noether. Die Grundlehren der Mathematischen Wissenschaften, 23, 24. J. Springer, Berlin, 1930, 1931. English editions: translated by Fred Blum and John R. Schulenberger. Frederick Unger, New York, 1970).

    Google Scholar 

  19. Heinrich Weber, Lehrbuch der Algebra, I, II, III (F. Vieweg, Braunschweig, 1895, 1896, 1891. 2nd Editions: F. Vieweg, Braunschweig, 1898, 1899, 1908. Reprinted: Chelsea, New York, 1961). Original Title, 1891: Elliptische Functionen und Algebraische Zahlen.

    MATH  Google Scholar 

  20. Horst G. Zimmer, Computational Problems, Methods, and Results in Algebraic Number Theory (Lecture Notes in Mathematics, 262. Springer-Verlag, Berlin, Heidelberg, New York, 1972).

    MATH  Google Scholar 

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© 1978 Springer-Verlag

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Sims, C.C. (1978). The role of algorithms in the teaching of algebra. In: Newman, M.F., Richardson, J.S. (eds) Topics in Algebra. Lecture Notes in Mathematics, vol 697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103125

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  • DOI: https://doi.org/10.1007/BFb0103125

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09103-5

  • Online ISBN: 978-3-540-35549-6

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