Analysis – Cantor's Archive

Geometry

Visualizing Mathematical Equations and Operations

Capture the Essence of an Equation and Solve it Visually by Using Mathematical Graphs

Series

The Mind-Boggling Properties of the Alternating Harmonic Series

Riemann’s simple algorithm to approximate computationally any real number

Series

The Basel Problem: 1+1/2² + 1/3² +… = π²/6

Solving the Basel problem, using an elementary introduction to Fourier series! Part 0: Motivation, some History, and Welcome! Hello and welcome! We are going to be tackling a beautiful problem, the ‘Basel Problem’. It was posed in 1650 by Pietro Mengoli, and it took 84 years to solve it, when

Analysis

The Chessboard Puzzle and the Mathematics of Invariants

Here we crack a tricky yet simple problem at the intersection of computer science and mathematics. It also gives a lovely insight into how…

Analysis

Distributions: What Exactly is the Dirac Delta “Function”?

The theory of distributions , also known as generalized functions, often remains something of an enigma…

Popular Science

A Totally New, Very Old Method for Finding Square Roots

A new iterative method to approximate square roots — actually shown to be centuries old!

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.

Analysis

A Comprehensible Introduction To Mathematical Induction

Since you’ve come here, chances are you need to learn about mathematical induction. You probably couldn’t care any less about it, but your nagging teacher makes you learn it anyway.

Analysis

This Math Problem Will Test Your Attentiveness To Detail

Are positive numbers and their negative counterparts equal?

Analysis

Mathematics Analysis For Coders

An intro to mathematical analysis, using ideas familiar to coders

Prime Numbers

Erdős’ Proof of the Infinitude of Primes

Let’s take a look at an unusual proof that there are infinitely many prime numbers.

Analysis

The Link Between Hypothesis Testing and Proof by Contradiction

Hypothesis testing has some similarities with one of the simplest methods of proof from mathematical logic: Proof by contradiction…