Discrete Math

Problems like finding the optimal route between two cities on a complex road network, or transmitting a message between two nodes across a sprawling computer network, are all instances of the shortest path problem. ...

Given $n$ workers and $n$ jobs, and the cost $c_{ij}$ to train the $i$-th worker for the $j$-th job, find an assignment of one worker to each job which minimized the total training cost. ...

Problem: What is the smallest integer $n$ such that in any group of $n$ people, where each pair consists of either mutual friends or mutual strangers, there must be a subgroup of three mutual friends or three mutual strangers? ...

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects. ...

This note explores the combinatorial problem of distributing balls into boxes, which provides a natural introduction to Stirling numbers of the first and second kind. ...

It is extremely difficult, and often impossible, to prevent errors when data are stored, retrieved, operated on, or transmitted. ...

Any mathematical system containing all the theorems of arithmetic is an incomplete system. ...