Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
권호 표지
DOI QR코드

DOI QR Code

On Functional Equations

함수방정식의 유래

  • Received : 2021.09.16
  • Accepted : 2021.10.19
  • Published : 2021.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

A functional equation is an equation which is satisfied by a function. Some elementary functional equations can be manipulated with elementary algebraic operations and functional composition only. However to solve such functional equations, somewhat critical and creative thinking ability is required, so that it is educationally worth while teaching functional equations. In this paper, we look at the origin of functional equations, and their characteristics and educational meaning and effects. We carefully suggest the use of the functional equations as a material for school mathematics education.

Keywords

Acknowledgement

본 논문은 2020학년도 수원대학교 학술진흥연구비 지원에 의한 논문임.

References

  1. J. Aczel, Lectures on Functional Equations and Their Applications, Translated by Scripta Technica Inc., Edited by Hansjorg Oser, Academic Press, 1966.
  2. J. Aczel, Functional Equations: History, Applications and Theory, D. Reidel Publishing Company, 1984.
  3. J. Aczel, On history, applications and theory of functional equations, Functional Equations: History, Applications and Theory, D. Reidel Publishing Company, 1984, 3-12.
  4. Cl. Alsina, The esthetics and usefulness of functional equations, Functional Equations: History, Applications and Theory, D. Reidel Publishing Company, 1984, 13-15.
  5. I. G. Bashmakova, G. S. Smirnova, The Beginning & Evolution of ALGEBRA, MAA, 2000.
  6. Jorg Bewersdorff, Galois Theory for Beginners: A Historical Perspective, AMS, 2006.
  7. J. G. Dhombres, On the historical role of functional equations, Functional Equations: History, Applications and Theory, D. Reidel Publishing Company, 1984, 17-31.
  8. Ronald L. Graham, Donald E. Knuth, Oren Patashnik, Concerete Mathematics, 2nd edition, Addison-Wesley Publishing Company, Inc., 1994.
  9. Koh Youngmee, Ree Sangwook, On Symmetric Functions, Journal for History of Mathematics 34(2)(2021), 39-54. 고영미, 이상욱, 대칭함수의 유래, Journal for History of Mathematics 34(2)(2021), 39-54.
  10. Marek Kuczma, A Survey of the Theory of Functional Equations, Publikacije Elektrotehnickog fakulteta, Serija Matematika i fizika (Mathematiques et Physique) 130(1964), 1-64, University of Belgrade, Serbia. https://www.jstor.org/stable/43667209?seq=1 or http://pefmath2.etf.rs/files/60/130.pdf
  11. Adam C. McBride, Book review of "Aczel, J. (ed.), Functional equations: history, applications and theory (D. Reidel, Dordrecht 1984), pp. ix+244, Dfl. 125." Proceedings of the Edinburgh Society 27(1984), 345-346.
  12. Paul J. Nahin, An Imaginary Tale: The Story of ${\sqrt{-1}}$, Princeton University Press, 1998.
  13. Prasanna K. Sahoo, Palaniappan Kannappan, Introduction to Functional Equations, CRC Press, 2011.
  14. P. K. Sahoo, T. Riedel, Mean Value Theorems and Functional Equations, World Scientific, 1998.
  15. Christopher G. Small, Functional Equations and How to Solve Them, Springer, 2007.
  16. Jacqueline Stedall, Matheamtics Emerging: A Sourcebook 1540-1900, Oxford University Press, 2008.
  17. Jacqueline Stedall, From Cardano's Art to Lagrange's Resolution: filling a gap in the history of mathematics, European Mathematical Society, 2011.
  18. Herbert Wilf, generatingfunctionology, Academic Press, 1990.