One of the greatest mathematicians and computer scientist we were contemporary with was Edsger W. Dijkstra. Among many of his contributions to these fields he let us a wonderful simple algorithm which helps us finding the shortest path between two…

## When to use a Venn diagram

Venn diagram is not just that simple but ingenious tool that helps you to solve those complicated set problems. Venn diagram is a powerful tool. A Venn diagram or set diagram is a diagram that shows all possible logical relations…

## Solving ordinary differential equations (ODE)

Introduction In Algebra we have what is called algebraic equation that is an mathematical expression described in terms of an unknown variable x. For instance is an algebraic equation of first order(because the highest order of the x term is…

## Bridge probability of card distribution

Summer is here and some days are more rainy than others. What to do? What to do? Take three of your friends (why not one of yours best friends and two 'enemies') and play a bridge game, for example the…

## Combinatorics and probability

I think that one of the most beautiful branches of mathematics is discrete mathematic, and here I would emphasize the combinatorics and probability theory. Background Introduction Counting How many they are? Factorial Permutations Combinations Probability Background While I was…

## Finding the lexicographic order of permutations

Given a finite alphabet (e.g. {A,B,C,...,Z}) how many different words can you create from these letters knowing that each letter can be used only once? This is just a typical problem of combinatorics and the answer it's quite simple: n!…

## Poker probability

Have you ever wondered what are the chances that you get a quads (four of a kind) when playing poker? Well, that depends on how many cards the hand has because there are several poker variants, right? These kind of…

## The quiz of the day

As I've started reading more about pure and discrete mathematics I've encountered a very interesting problem and thus I thought it would be just an interesting quiz for this weekend. The quiz of the day What is the number that…

## Differential equations: estimating the time of death

For those who still haven't found the usefulness/beauty of math (and in particular calculus) I propose a small real-life application inspired by a CSI episode: estimating the time of death. The problem Let's suppose that you are a crime investigator…