Cyptography and Number Theory

  1. Shift ciphers
  2. Relative frequencies of letters in English
  3. Viginère ciphers
  4. Breaking Viginère ciphers with monographic frequency counts
  5. The sieve of Eratosthenes in action
  6. Generating primes by sieving
  7. The Jacobi symbol
  8. Bezout's equation
  9. Primality testing with Fermat's little theorem
  10. Multiple precision arithmetic
  11. Multiple precision arithmetic using strings
  12. Multiple precision arithmetic using Java
  13. "Stupidest known algorithm" for factoring


  1. Graphs of derivatives   Java applet. You pull a graph around, it draws the derivative.
  2. Draw the derivative   Java applet. You try to draw the derivative of a given graph.


  1. Interest
  2. Present value

Modern algebra and other things

  1. Elliptic curves
  2. Division algorithm in Z[√2]
  3. Counting Gaussian integers in a disk
  4. Bezout's equation for Z
  5. Bezout's equation for Gaussian integers
  6. Bezout's equation for Gaussian integers and Z[√2]
  7. Pascal's triangle modulo n
  8. Pascal's triangle
  9. Equivalence of antilogisms
  10. Continued fractions
  11. Manipulating poynomials in two variables
  12. Umbral calculus modulo p
  13. Sums of cubes x3 + y3 + z3 = w3
  14. Fibonacci sequences with Java
  15. Pell's equation from Ray Mines
  16. The Saint Petersburg Paradox for class on mathematical ideas.

Liberal arts mathematics

  • Table of contents   Red sections are generally links to JavaScripts.

    One shot mysterious stuff

    1. Powers of 3 checked for repeated multisets of digits
    2. Something about general syllogisms
    3. Bounce