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…
Calculus
The Dirichlet integral was first solved by the brilliant Leonhard Euler, it then achieved fame with Dirichlet’s work on Fourier series…
Geometry
An accidental introduction to field theory.
Analysis
Represent an ordered pair of integers with a single integer.
Analysis
Using only elementary methods we will prove the Fundamental Theorem of Algebra. Along the way, we’ll befriend some key ideas from…
Calculus
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
Let’s prove one of the most important theorems in elementary analysis! The only requirement is an elementary understanding of derivatives.
Analysis
In mathematics, it is often the case that we derive things through proof or previous results that we don’t fully understand.
Linear Algebra
Linear algebraic equations are one of the simplest equations that we can solve. If there is only one variable, then the solutions are…
Prime Numbers
Two simple proofs about the infinity of primes
Geometry
Where the sum of two squares meets the third.
Analysis
We discuss the concept of mathematical induction on the natural numbers and give some examples.
Set Theory
“No one will drive us from the paradise which Cantor created for us” — David Hilbert
Number Theory
Two Simple Proofs of the Irrationality of e
Analysis
…And the Foundations of Calculus
Analysis
The methods of finding roots of a quadratic equations are quite easy and are very well understood. There are all kinds of approaches…
Analysis
We take a deeper look at what Taylor Series does and how we can obtain polynomials for approximating non-polynomial functions.