Maths and Musings

Analysis

Euler’s Log-Sine Integral

Let’s discover the ingenious, yet simple, solution to Euler’s Log-Sine integral

Calculus

Solving the Dirichlet Integral

The Dirichlet integral was first solved by the brilliant Leonhard Euler, it then achieved fame with Dirichlet’s work on Fourier series…

Practical Mathematics

How To Multiply Large Numbers Quickly

The Toom-Cook Algorithm

Analysis

An Elementary Proof of the Fundamental Theorem of Algebra

Using only elementary methods we will prove the Fundamental Theorem of Algebra. Along the way, we’ll befriend some key ideas from…

Graph Theory

Solving a Handshaking Problem using Recursion

Let’s solve a nice problem brought to my attention by Lawrence Bryan. Thank you Lawrence :)

Complex Analysis

Proving The Cauchy-Goursat Theorem

Let’s prove a beautiful Theorem from complex analysis!! For the determined amateur with some knowledge of 12th grade math and calculus.

Calculus

Solving the Gaussian Integral

Lord Kelvin wrote of this integral: “A mathematician is one to whom that is as obvious as that twice two makes four is to you. Liouville…

Analysis

Proving the Mean Value Theorem

Let’s prove one of the most important theorems in elementary analysis! The only requirement is an elementary understanding of derivatives.

Set Theory

What Is Zorn’s Lemma?

The quick and dirty guide to one of the stranger mathematical curiosities.

Set Theory

Proving Cantor’s Theorem

“No one will drive us from the paradise which Cantor created for us” — David Hilbert

Analysis

Understanding Why 0.99999… = 1

…And the Foundations of Calculus

Number Theory

Proving The Existence of Transcendental Numbers

… and how to compare the infinite?