Here are some other topics and problems I find interesting.
  • Celestial mechanics. I have written some notes on the basics of Newtonian gravitation, Kepler's laws, the motion of planets, asteroids, ..., and ephemeris calculation.
  • Kaggle. I have worked on some projects/competitions, see the documentation in the GitHub-repo.
  • CitiBikes. A lot of data is available online, I have done some analysis and visualizations here.
  • Image compression. I have implemented¬†
  • Pythagorean triples. Derivation and proof of Euclid's formula for Pythagorean triples, using complex numbers.
  • Optimization of production - a variational problem. Suppose that a factory produces a certain product, let it here be bricks. A fraction of the produced bricks can be re-invested into the company to build now brick-ovens, which increases the rate at which the bricks are produced. The remaining bricks can be sold for profit. Re-investing bricks into the factory-expansion is usually a good idea, since it will increase profit on the long run. But which (time-dependent) fraction of the production should be re-invested in order to maximize profit until a given time? This is a variational problem with interesting properties. I discuss its solvability and show that it possesses a unique maximizer in the set of piecewise continuous functions. Find the full discussion with proofs here.
  • Depot problem. Only a limited amount of fuel can be transported at once by a truck. The truck can create depots to store fuel on the way. However, transporting fuel there consumes fuel as well. I address the question of how to place the depots such that the truck maximizes the distance that it can reach by creating depots and using the fuel at the depots, until all initial fuel is used up. Full discussion is here.