Algorithm The Power of Binary Search Binary search is ubiquitous. Even if you are not aware of it, you have most likely used some (approximate) version of binary search one way or another

Factorials Factorials and How to Compute Them I am sure you all remember the surprise you had the first time you saw a “5!” or “7!”

Number Theory Euclid’s Algorithm for Computing the Greatest Common Divisor An algorithm from ancient Greece

Linear Algebra Matrix Multiplication and the Ingenious Strassen’s Algorithm How Divide-And-Conquer Comes to the Rescue (again)

Analysis Matchings in Bipartite Graphs and the Kőnig-Egerváry Theorem via LP Duality We discuss how we can compute Maximum Matchings in bipartite graphs, and why these are equal to Minimum Vertex Covers.

Number Theory The Celebrated Harmonic Numbers and How to Approximate Them We discuss the famous harmonic sum and describe a simple way to approximate it.

Probability Theory The Coupon Collector Problem We discuss the well-known Coupon Collector problem, and provide two ways of computing the probability of winning.

Graph Theory Turán’s Theorem for Graphs Using the Probabilistic Method and the Cauchy-Schwarz inequality

Analysis Mathematical Induction: The Domino Effect in Natural Numbers We discuss the concept of mathematical induction on the natural numbers and give some examples.

Prime Numbers The Infinity of Primes We present two proofs of one of the great theorems in number theory, namely that there are infinitely many primes.

Applied Mathematics The Johnson-Lindenstrauss Lemma Why you don’t always need all of your coordinates

Probability Theory Beauty in Simplicity: Markov’s Elegant Inequality In this article, we introduce the simple but very useful Markov’s inequality for non-negative random variables.