I have a passion for numbers and symbolic calculations. Since my teenage years, I have been interested in recreational mathematics, mathematical puzzles, fundamental properties of numbers (number theory), series, polynomials, and integrals. Here is a list of topics that kept me busy for a while. For some of them, the outcome of my calculations is available in XHTML/MathJax or XHTML/MathML format by clicking on the topic (some of these pages are huge and may take a long time to download).
General Topic | Especially... |
---|---|
Bernoulli numbers | |
Carmichael numbers | |
Chebyshev polynomials | |
Congruent numbers | |
Continued fractions | Continued fraction expansions of square roots |
Diophantine equations | Pell's equation |
Eight queens puzzle | Amazons on NxN chessboard |
Euclidean algorithm | |
Euler's totient function | |
Feigenbaum constants | |
Fermat's little theorem | |
Fractals | Mandelbrot set, Julia set |
Game of life | |
Generating functions | |
Graphs | |
Integrals | Indefinite integrals, Abelian integrals |
Legendre polynomials | |
Magic squares | |
Ordinary differential equations | Canonical ODEs |
Overhanging dominoes | |
Pi decimals | |
Polynomial congruences | |
Polynomial division | |
Polynomial interpolation | Cotesian numbers |
Polynomial recurrences | |
Prime numbers | Large primes, Mersenne primes, Prime factors |
Primitive roots modulo n | |
Quadratic residues | |
Riemann zeta function ζ(s) | |
Series | Power series, Taylor series, Maclaurin series, Laurent series, Formal power series, Closed-form expressions |
Sums of powers | Faulhaber's formula |
Tiling puzzles | Squared squares |
Trigonometric identities | Multiple-angle formulas: sin(2a), sin(3a), sin(4a), etc. |