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Author: William A. Stein
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09/480b/topics

Math 480b Topics

Math 480b

Linear algebra

  • row reduction of matrices
  • solving systems of linear equations
  • computing determinants and characteristic polynomials
  • finding eigenvalues and eigenvectors
  • subspaces of vector spaces

Algebra

  • factoring polynomials
  • symbolically finding roots of polynomials
  • solving systems of polynomial equations
  • drawing cayley graphs of groups
  • number fields and Galois groups

Combinatorics, Probability, and Statistics

  • plotting graphs (vertices and edges)
  • computing invariants of graphs (automorphism group, shortest path, etc.)
  • solving Sudoku puzzles and Rubik's cube
  • counting and enumerating permutations, combinations, etc.
  • generating random numbers and random walks
  • computing the mean, variance, standard deviation, and plotting frequency histograms
  • predicting missing data (interpolation)

Calculus

  • plotting functions
  • computing limits and derivatives
  • finding min and max points of functions
  • computing symbolic integrals
  • computing definite integrals numerically
  • numerically finding roots of polynomials
  • summing infinite series
  • solving differential equations
  • parametric curves (plotting, arc length)

Number theory and Cryptography

  • enumerating and counting prime numbers
  • exchanging secret messages (Diffie-Hellman and RSA)
  • attacking RSA and Diffie-Hellman
  • elliptic curve cryptosystems
  • determining whether an integer is the area of a rational right triangle

2013-05-11 18:32