Journal for History of Mathematics (한국수학사학회지)

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

DOI QR Code

On Symmetric Functions

대칭함수의 유래

  • Received : 2021.03.25
  • Accepted : 2021.04.08
  • Published : 2021.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

One of the topics in school mathematics is the relation between the roots and the coefficients of equations. It deals with the way to find the roots out of the coefficients of equations. One of the concepts derived from the theory of equations is symmetric functions. Symmetry is a kind of functionality of human cognition. It is, in mathematics, geometrically related to the congruence and the similarity of figures, and algebraically a kind of invariants. We look at stories on the appearance of symmetric functions through the development of the theory of equations.

Keywords

References

  1. Martin Aigner, Gunter Ziegler, Proofs from THE BOOK, 3rd edition, Springer-Verlag, 2004. 이상욱, 고영미, 강미현 옮김, 하늘책의 증명, 교우사, 2008.
  2. George Andrews, Kimmo Eriksson, Integer Partitions, Cambridge University Press, 2014.
  3. Avner Ash, Robert Gross, Elliptic Tales, Princeton University Press, 2012.
  4. I. G. Bashmakova, G. S. Smirnova, The Beginnings & Evolution of Algebra, MAA, 2000.
  5. J. K. Baumgart, D. E. Deal, B. R. Vogeli, A. E. Hallerberg (eds.), Historical Topics for the Mathematics Classroom, NCTM, 1993 (originally, 1969).
  6. Jorg Bewersdorff, Galois Theory for Beginners: A Historical Pespective, AMS, 2006.
  7. Ben Blum-Smith, Samuel Coskey, The Fundamental Theorem on Symmetric Polynomials: History's First Whiff of Galois Theory. https://arxiv.org/abs/1301.7116v5
  8. David M. Bressoud, Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture, Cambridge University Press, 1999.
  9. Apostol Doxiadis, Uncle Petros and Goldbach's Conjecture: A Novel of Mathematical Obsession, Bloomsbury USA, 2001. 아포스톨로스 독시아디스 지음, 정희성 옮김, 강석진 감수, 사람들이 미쳤다고 말한 외로운 수학 천재 이야기, 생각의 나무, 2000.
  10. David Fontana, The Secret Language of Symbols: A Visual Key to Symbols Their Meanings, Chronicle Books, 1994. 데이비드 폰타나 지음, 공민희 옮김, 상징의 모든 것, 사람의 무늬, 2011.
  11. H. Gray Funkhouser, A Short Account of the History of Symmetric Functions of Roots of Equations, The American Mathematical Monthly 37(7)(1930), 357-365. https://doi.org/10.2307/2299273
  12. Hardy Grant, Israel Kleiner, Turning Points in the History of Mathematics, Birkhauser, 2015.
  13. Koh Youngmee, Kim Young Wook, Ree Sangwook (eds), 2014 KSHM-NIMS Summer School, Proceedings of the Korean Society for History of Mathematics 24(1)(2014).
  14. Matt D. Lunsford, Using Galois' Ideas in the Teaching of Abstract Algebra, in From Calculus to Computers (Shell-Gellasch and Jardine des.), MAA, 2005.
  15. Dana Mackenzie, The Universe in Zero Words: The Story of Mathematics as Told through Equations, Princeton University Press, 2012. 다나 매켄지 지음, 오채환, 이상욱, 이장주 옮김, 세상을 바꾼 방정식 이야기, 사람의무늬, 2014.
  16. Joseph Mazur, Enlighting Symbols: A Short History of Mathematical Notation and Its Hidden Powers, Princeton University Press, 2014.
  17. Paul J. Nahin, An Imaginary Tale: The Story of √-1, Princeton University Press, 1998.
  18. David J. Pengelley, Arthur Cayley and the First Paper on Group Theory, in From Calculus to Computers (Shell-Gellasch and Jardine des.), MAA, 2005.
  19. Ree Sangwook, Koh Youngmee, MaPhiA: Mathematics, Philosophy, and Artificial Intelligence, Journal for History of Mathematics 32(5)(2019), 217-231. https://doi.org/10.14477/JHM.2019.32.5.217
  20. Constance Reid, Hilbert, Springer-Verlag, 1996. 콘스탄스 리드, 이일해 옮김, 현대수학의 아버지 힐베르트, 사이언스북스, 2005.
  21. Bruce E. Sagan, The Symmetric Group: Representations, Combinatorial Algorithms and Symmetric Functions, Wadworth & Brooks/Cole, 1991.
  22. Amy Shell-Gellasch, Dick Jardine (eds.), From Calculus to Computers: Using the last 200 years of Mathematical History in the Classroom, MAA, 2005.
  23. Jacqueline Stedall, Symbolism, combinations, and visual imagery in the mathematics of Thomas Harriot, Historia Mathematica 34 (2007), 380--401. https://doi.org/10.1016/j.hm.2007.05.001
  24. Jacqueline Stedall, Mathematics Emerging: A Sourcebook 1540-1900, Oxford University Press, 2008.
  25. Jacqueline Stedall, From Cardano's geeat art to Lagrange's reflections: filling a gap in the history of mathematics, European Mathematical Society, 2011.
  26. Ian Stewart, Why Beauty is Truth: The History of Symmetry, Basic Books, 2007.
  27. John Stillwell, Mathematics and Its History (3rd ed.), UTM, Springer, 2010.
  28. Hermann Weyl, Symmetry, Princeton University Press, 1952.
  29. Wikipedia, Group theory. https://en.wikipedia.org/wiki/Group_theory (10 July 2020)
  30. Wikipedia, Symmetric polynomial. https://en.wikipedia.org/wiki/Symmetric_polynomial (10 July 2020)