Ramsey Theory

  • Steven G. Krantz
  • Harold R. Parks


Counting is a big part of modern mathematics. Many mathematical problems necessitate the estimation of a particular, precisely specified number having a certain technical description. Certainly questions of airline scheduling, Internet routing, queueing theory, and crystalline structure are of this nature. For instance, how many different airline routes are there from San Francisco to Boston with not more than two stops along the way? This is a nontrivial question with a meaningful and useful answer. Along with Lejeune Dirichlet, Frank Ramsey was one of the pioneers of counting theory. His Ramsey’s theorem pervades large parts of mathematics.


Scarlet Fever Evil Spirit Pigeonhole Principle Ramsey Number Convex Quadrilateral 
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References and Further Reading

  1. [AZH 09]
    Aigner, M., Ziegler, G.M., Hoffman, K.H.: Proofs from the Book, 4th edn. Springer, New York (2009)Google Scholar
  2. [Exo 03]
    Exoo, G.: A Euclidean Ramsey problem. Discrete and Computational Geometry 29, 223–227 (2003)CrossRefMATHMathSciNetGoogle Scholar
  3. [GR 71]
    Graham, R.L., Rothschild, B.L.: Ramsey’s theorem for n-parameter sets. Transactions of the American Mathematical Society 159, 257–292 (1971)MATHMathSciNetGoogle Scholar
  4. [GRS 90]
    Graham, R.L., Rothschild, B.L., Spencer, J.H.: Spencer Ramsey Theory. Wiley, New York (1990)Google Scholar
  5. [GG 55]
    Greenwood, R.E. Jr, Gleason, A.M.: Combinatorial relations and chromatic graphs. Canadian Journal of Mathematics 7, 1–7 (1955)CrossRefMATHMathSciNetGoogle Scholar
  6. [Hof 98]
    Hoffman, P.: The Man Who Loved Only Numbers. Hyperion, New York (1998)MATHGoogle Scholar
  7. [Kra 02]
    Krantz, S.G.: Mathematical Apocrypha. Mathematical Association of America, Washington, DC (2002)MATHGoogle Scholar
  8. [Kra 05]
    Krantz, S.G.: Mathematical Apocrypha Redux. Mathematical Association of America, Washington, DC (2005)MATHGoogle Scholar
  9. [Ram 30]
    Ramsey, F.P.: On a problem of formal logic. Proceedings of the London Mathematical Society 30, 264–286 (1930)CrossRefMathSciNetGoogle Scholar
  10. [Ram 50]
    Ramsey, F.P.: The foundations of mathematics and other logical essays (edited by Richard Bevan Braithwaite, with a preface by George Edward Moore). The Humanities Press, New York (1950)Google Scholar
  11. [Sah 90]
    Sahlin, N.-E.: The Philosophy of F. P. Ramsey. Cambridge University Press, Cambridge (1990)Google Scholar
  12. [Tay 06]
    Taylor, G.: Frank Ramsey—a biographical sketch. In: Galavotti, M.C. (ed.) Cambridge and Vienna—Frank P. Ramsey and the Vienna Circle. Springer, New York (2006)Google Scholar
  13. [Wit 83]
    Wittgenstein, L.: Letters to C. K. Ogden with Comments on the English Translation of the “Tractatus Logico-Philosophicus”; Edited with an Introduction by Georg Henrik von Wright, and with an Appendix of Letters by Frank Plumpton Ramsey. Basil Blackwell/Routledge K. Paul, Oxford/Boston (1983)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Steven G. Krantz
    • 1
  • Harold R. Parks
    • 2
  1. 1.Department of MathematicsWashington University in St. LouisSt. LouisUSA
  2. 2.Department of MathematicsOregon State UniversityCorvalisUSA

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