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Quantum Computation

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• Number Theory (interactive Java applets)
  • Some number theoretic functions (greatest common divisor, the order of a number modulo n, the value of f(x) = m^x + c mod n.)
  • Graphs of f(x) = m^x + c mod n.
  • Graphs of f(x) = m^x + c mod n, with subsequent points joint by lines (Recognize patterns!?)
  • Prime factorization of numbers
  • The Euler totient function φ(n)
  • The Carmichael function λ(n)
  • Concerning RSA cryptography
    • Graphs of f(m) = m^e mod n.
    • Graphs of f(m) = m^e mod n, with subsequent points joint by lines.
    • Finding a public key (e, n) according to the RSA algorithm, given the secret key numbers (d, p, q).
  • The Riemann zeta function ζ(s) and the Riemann hypothesis
• Analysis
  • A function plotter.
• Astronomy and Physics
  • The shadows of black holes, explained and interactively computed by an applet.
• Operations Research
  • The knapsack problem, a classical algorithmic problem, solved by dynamic programming.
  • The Posten container problem, an extension of the knapsack problem, with three bottle-neck constraints.
• Mathematical Politics
  • The Banzhaf index of political power
    • The theory
    • An applet calculating the Banzhaf indices for arbitrary numbers of members.
    • A more comfortable applet calculating the Banzhaf indices which enables data exchange with a standard spread sheet program via copy-and-paste.
• Financial Mathematics
  • Loan redemption schedule of an annuity loan