Modelling Disease Spread

SIR model and other models

• What is the probability that a person has the disease after he was tested positive?
• What is the probability that a person does not have the disease after she was tested negative?

Finding recurrences

1. Extended Euclidean Algorithm
2. Modular Arithmetic
3. Diffie-Hellman Key Exchange
4. Public Key Cryptography

The linear optimization is explained on a practical industrial case. The Simplex Algorithm is presented. The Excel Solver is described.

I describe the Earth-centered (ECEF) cartesian and spherical coordinates as well as local ENU coordinates. I also derive transformations between them.

I derive the equation of the great circle on the spherical Earth, the formula for the shortest distance and other related formulas.

I derive equations of the torus and present an Octave program to draw it.

I present a simple zero-knowledge proof of map coloring with 3 colors.

My contributions to Math.Stackexchange.