Logic  

The question of whether mathematics could be reduced to logic, or whether it could be reduced only to set theory, remained open.

  1. Whitehead, Alfred North, and Bertrand Russell (1910, 1912, 1913), "Principia Mathematica", 3 vols, Cambridge: Cambridge University Press. Second edition, 1925 (Vol. 1), 1927 (Vols 2, 3). Abridged as Principia Mathematica to *56, Cambridge: Cambridge University Press, 1962.
  2. Russell, Bertrand (1903) Principles of Mathematics, Cambridge: Cambridge University Press.
  3. Russell, Bertrand (1919) Introduction to Mathematical Philosophy, London: George Allen and Unwin.
  4. Russell, Bertrand (1948) "Whitehead and Principia Mathematica," Mind, 57, 137-138.
  5. Russell, Bertrand (1959) My Philosophical Development, London and New York: Routledge.
  6. Urquhart, Alasdair (1988) "Russell's Zig-Zag Path to the Ramified Theory of Types," Russell, 8, 82-91.
  7. Whitehead, Alfred North (1898) A Treatise on Universal Algebra, Cambridge: Cambridge University Press.
  8. Whitehead, Alfred North (1906) On Mathematical Concepts of the Material World, London: Dulau.
  9. Douglas R. Hofstadter, ``Godel Escher Bach: An Eternal Golden Braid,'' Basic Books, 1999.
  10. Richard Jeffrey, Formal Logic: Its Scope and Limits. 3rd ed. McGraw Hill, 1990. ISBN 0-07-032357-7
  11. Richard Jeffrey, Formal Logic: Its Scope and Limits. 4th ed., John P. Burgess (editor), Hackett Publishing, 2006, ISBN-10: 0872208133; ISBN-13: 978-0872208131
  12. Richard Jeffrey, The Logic of Decision. 2nd ed. University of Chicago Press, 1990. ISBN 0-226-39582-0
  13. Richard Jeffrey, Computability and Logic (with George Boolos and John P. Burgess). 4th ed. Cambridge University Press, 2002. ISBN 0-521-00758-5

Set Theory

  1. T.J. Jech, "Set theory" , Acad. Press (1978) (Translated from German)
  2. E.J. Lemmon, "Introduction to axiomatic set theory" , Routledge & Kegan Paul (1968)
  3. G. Takeuti, W.M. Zaring, "Introduction to axiomatic set theory" , Springer (1971)
  4. K. Gödel, "The consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory" , Princeton Univ. Press (1940)

Methodology

  1. George Polya, ``Mathematical discovery: on understanding, learning, and teaching problem solving,'' New York: Wiley, 1981. 
  2. George Polya, ``How to solve it : a new aspect of mathematical method,'' 2d ed., Princeton, N.J. : Princeton University Press, 1973.
  3. George Polya, ``Mathematics and plausible reasoning,'' Princeton, N.J.: Princeton University Press, 1954.  Two volumes.

History

Math for engineers

  1. Dean G. Duffy, ``Advanced engineering mathematics,'' 2nd ed., CRC, 2003. 
  2. Daniel Zwillinger, "CRC standard mathematical tables and formulae," 31st ed., CRC, 2002.

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