# Math Section Articles

## Collection by Math Section

15
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All articles from the Math Section can be found here.

Learn about the most fundamental Graph Theory definitions and the most interesting applications of Graph Theory in everyday life.

Maps can always be colored with only four colors in such a way that no two adjacent regions of the map share the same color. This is the Four Color Theorem, a highly controversial mathematical theorem that was proved using computer-assistance. A first in mathematics. We delve into the controversy, explain the proof concept, and present ways to make maps that are still not 4-colorable.

Speeding tickets issued by the police are a real-life application of the mean value theorem. In this article, we explain the mathematics behind the example.

We explain the basic idea of the Simplex Algorithm, present linear programming, and discuss the underlying geometric ideas used to solve LP-problems.

How long is the coast of Britain? This question was of utmost importance in the process of creation of the field of fractal geometry. We explain the coastline paradox, fractal geometry and dimension, and how we use fractal geometry to measure coastlines. #Fractals #Geometry #Coastlines #Fry #Lewis #Richardson #Dimension

We approximate pi using a Monte-Carlo method in Matlab, explain the code, provide the program for you to try for yourself, and present an error analysis. #Pi #Matlab #Tutorial

Your friends are on average more popular than you. That fact is the Friendship Paradox. We give a mathematical proof for this statement, explain the relevant graph-theoretic terms, and present an example of an application of the Friendship Paradox in real life, the early detection of flu outbreaks. #Graph #Theory #Friendship #Paradox

A game-theoretic discussion of doping. We discuss possible methods for solving the doping dilemma, introduce the Nash equilibrium, and establish the mathematical concept of doping games.

In this article, you can learn about how you can apply the secretary problem, optimal stopping theory, and probability theory to dating in order to optimize your love life. #Love #Life #Marriage #Optimization #Stopping #Theory #Secretary #Problem #Probability

We present an example of a problem from theoretic computer science and epistemic logic, the Byzantine general problem.

This article serves as a follow-up to the article titled Friendship Paradox. We consider the complement graph which creates the Inverse Friendship Paradox.

Leonhard Euler created graph theory by walking across the seven bridges of Königsberg. We follow Euler's path and discuss this directed graph problem.

We explain the German Tank Problem that the Allies faced in World War 2, derive a solution by analyzing serial numbers, and provide insight with an example. #Probability #Theory #World #War #2 #German #Tank #Problem #Allies

We prove by contradiction that there are infinitely many prime numbers. This fact was already known to Euclid and our proof is based on his.

We introduce the shortest path algorithm by Dijkstra, pathfinding, and ultimately explain how Google Maps finds the shortest route from point A to point B.