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. |