Probability Theory
The Probabilistic Method
Maybe the most interesting proof method
Graph Theory
Graph Theory
City Planning Using Graph Theory
Strongly Connected Components Algorithm
Graph Theory
The Cycle Double Cover Conjecture
Delving into a deceptively simple-sounding problem that has gone unsolved for decades.
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.
Dynamic Programming
Exploring Monotone Subsequences With Dynamic Programming in Python
When computer science and dynamic programming meets math
Erdős
A Theorem of Erdős and Szekeres
A Theorem by two mathematical greats, which anybody, no maths experience required, can understand! An amazing, and beautiful, result…
Graph Theory
Solving a Handshaking Problem using Recursion
Let’s solve a nice problem brought to my attention by Lawrence Bryan. Thank you Lawrence :)
Graph Theory
Turán’s Theorem for Graphs
Using the Probabilistic Method and the Cauchy-Schwarz inequality
Graph Theory
Solving the Königsberg Bridge Problem
This proof is accessible to ANYONE — no mathematics knowledge required! (perfect for if you are a bit bored and in isolation, like me…
Graph Theory
Measuring Network Centrality
An Intro To Quantifying “Importance” Through Graph Theory
Graph Theory
Dijkstra’s Shortest Path Algorithm in Python
From GPS navigation to network-layer link-state routing, Dijkstra’s Algorithm powers some of the most taken-for-granted modern services…
Mathematics
The Four-Color Theorem
Its Surreal Simplicity & Critical Challenge To Re-Define The Modern Theorem