Topics in Symmetry in Polynomial Roots and Factors, with Applications

Numbered in the order to learn them.

  1. Recap: Roots of Unity Filter (Basic Finite Fourier Analysis)

  2. Elementary Symmetric Sums and Vieta's Formulas

  3. Fundamental Theorem of Symmetric Sums

  4. Solving/Factoring "Simple" or Low-Degree Polynomials

  5. Discriminants and Resultants

  6. Newton Sums and Related Problems

  7. Exploiting Symmetry in Polynomial Coefficients

Type a concept, like “slope” or “photosynthesis”.

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