Sergei Yakovenko's blog: on Math and Teaching

Monday, April 25, 2011

Lectures 5-6, April 26-May 3, 2011

Filed under: lecture,Rothschild Course "Symmetry" — Sergei Yakovenko @ 3:59
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Symmetric polynomials in several variables

Because of the numerous mathematical formulas and no figures, the notes for these lectures are provided in the pdf format.

For your convenience, the list of sections is supplied.

  1. Multi-index notation
  2. Definition of symmetric polynomials in several variables
  3. Construction of symmetric polynomials: averaging over the group. Young tableaux
  4. Elementary symmetric polynomials
  5. Main theorem on representation of symmetric polynomials: formulation
  6. Symmetry break and lexicographic order of monomials. Proof of the Main theorem
  7. Power sums, a.k.a Newton sums a.k.a. symmetric powers
  8. Generating functions and representation of symmetric powers
  9. Miscellaneous problems concerning symmetric polynomials

Enjoy the notes and let me know if any problems arise.


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