A Course in Abstract Algebra Inspired by History

  • Israel Kleiner


Division Ring Diophantine Equation Galois Theory Abstract Algebra Algebraic Number Theory 
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  1. 1.
    W. W. Adams and L. J. Goldstein, Introduction to Number Theory, Prentice-Hall, 1976.Google Scholar
  2. 2.
    G. Birkhoff, Current trends in algebra, Amer. Math. Monthly 1973, 80: 760–782.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    G. Birkhoff and S. MacLane, A Survey of Modern Algebra, 5th ed., A K Peters, 1996.Google Scholar
  4. 4.
    D. M. Burton and D. H. Van Osdol, Toward the definition of an abstract ring, in Learn from the Masters, ed. by F. Swetz et al, Math. Assoc. of America, 1995, pp. 241–251.Google Scholar
  5. 5.
    A. Clark, Elements of Abstract Algebra, Dover, 1984.Google Scholar
  6. 6.
    R. A. Dean, Elements of Abstract Algebra, Wiley, 1966.Google Scholar
  7. 7.
    A. Fraenkel, Über die Teiler der Null und die Zerlegung von Ringen, Jour. für die Reine und Angew. Math. 1914, 145: 139–176.Google Scholar
  8. 8.
    L. J. Goldstein, Abstract Algebra: A First Course, Prentice-Hall, 1973.Google Scholar
  9. 9.
    G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford Univ. Press, 1938.Google Scholar
  10. 10.
    I. N. Herstein, Topics in Algebra, Blaisdell, 1964.Google Scholar
  11. 11.
    D. Hilbert, Über den Zahlbegriff, Jahresb. der Deut. Math. Verein. 1900, 8: 180–184.Google Scholar
  12. 12.
    A. Jones, S. A. Morris, and K. R. Pearson, Abstract Algebra and Famous Impossibilities, Springer-Verlag, 1991.Google Scholar
  13. 13.
    I. L. Kantor and A. S. Solodovnikov, Hypercomplex Numbers, Springer-Verlag, 1989. (Translated from the Russian by A. Shenitzer.)Google Scholar
  14. 14.
    I. Kleiner, The roots of commutative algebra in algebraic number theory, Math. Magazine 1995, 68: 3–15.MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    I. Kleiner, Thinking the unthinkable: The story of complex numbers (with a moral), Math. Teacher 1988, 81: 583–592.Google Scholar
  16. 16.
    M. Kline, Mathematics in Western Culture, Oxford Univ. Press, 1964.Google Scholar
  17. 17.
    N. H. McCoy and G. J. Janusz, Introduction to Modern Algebra, Wm. C. Brown, 1992.Google Scholar
  18. 18.
    H. Pollard and H. G. Diamond, The Theory of Algebraic Numbers, Math. Assoc. of America, 1975.Google Scholar
  19. 19.
    19. H. Pycior, George Peacock and the British origins of symbolical algebra, Hist. Math. 1981, 8: 23–45.CrossRefMathSciNetGoogle Scholar
  20. 20.
    I. Richards, An application of Galois theory to elementary arithmetic, Advances in Math. 1974, 13: 268–273.MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    F. Richman, Number Theory: An Introduction to Algebra, Brooks/Cole, 1971.Google Scholar
  22. 22.
    I. Stewart, Concepts of Modern Algebra, Penguin, 1975.Google Scholar
  23. 23.
    I. Stewart, Galois Theory, 3rd ed., Chapman & Hall, 2004.Google Scholar
  24. 24.
    J. M. Thomas, Theory of Equations, McGraw Hill, 1938.Google Scholar
  25. 25.
    J. P. Tignol, Galois Theory of Algebraic Equations, Wiley, 1988.Google Scholar
  26. 26.
    B . L. van der Waerden, A History of Algebra, Springer-Verlag, 1985.Google Scholar
  27. B . L. van der Waerden, Hamilton’s discovery of quaternions, Math. Magazine 1976, 49: 227–234.Google Scholar
  28. 28.
    P. L. Wantzel, Recherches sur les moyens de reconnaitre si un Problème de Géométrie peut se résoudre avec la règle et le compass, Journ. de Math. Pures et Appl. 1837, 2: 366–372.Google Scholar

Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • Israel Kleiner
    • 1
  1. 1.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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