Discrete Math

Finding the best route between two cities, given a complicated road network; or transmitting a message between two computers along a network of hundreds of computers, are all classified as 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. ...

Find the smallest integer $n$ that there must be either three mutual friends or three mutual strangers among $n$ people, suppose each pair of people are either friends or strangers? ...

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

Various ways of distributing balls into cells. ...

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. ...