# Traveling Salesman Problem

## Series: Linear Optimization

Solution using Branch and Bound.

# Langford problem

## Series: Linear Optimization

Three different solutions.

# Who Betrayed Dune’s Duke Leto?

## Series: Riddler Puzzles

A FiveThirtyEight Riddler puzzle.

# Flowfree

## Series: Linear Optimization

Solution using constratint programming.

# Riddle of the pilgrims

## Series: Linear Optimization

Solution using integer programming.

# Unusual Crossword

An unusual crossword based on the first 30 digits of pi.

# Problems for children from 5 to 15 by V.I. Arnold

My solutions to a select number of problems.

# A curious identity involving $e$ and $\pi$

## Series: Infinite Series

An infinite series problem.

# Problems by Ramanujan

Submitted to the Journal of the Indian Mathematical Society (JIMS).

# Problems in summation of series

## Series: Infinite Series

Problem 1 Find a closed form solution for $f(z) = \sum_{n=1}^\infty \sum_{k=1}^n \frac{1}{k}z^n = z + \frac{3}{2}z^2 + \frac{11}{6}z^3 + \dots$. Solution We have \begin{align*} f(z) - zf(z) &= z + \frac{z^2}{2} + \frac{z^3}{3} + \dots \ &= \int \frac{1}{1-z}dz = -ln(1-z) \ \implies f(z) &= -\frac{ln(1-z)}{1-z} \end{align*} Problem 2 Evaluate $\sum_{n=0}^{\infty} \frac{(-1)^n)}{3^n(2n + 1)}$.