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.
Analysis
Analysis
Four Curious, Counter-Intuitive Mathematical Truths
In mathematics, it is often the case that we derive things through proof or previous results that we don’t fully understand.
Linear Algebra
A Method of Counting The Number of Solutions
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
How to Prove the Infinity of Primes
Two simple proofs about the infinity of primes
Geometry
Pythagoras’ Theorem With Proof
Where the sum of two squares meets the third.
Analysis
Mathematical Induction: The Domino Effect in Natural Numbers
We discuss the concept of mathematical induction on the natural numbers and give some examples.
Set Theory
Proving Cantor’s Theorem
“No one will drive us from the paradise which Cantor created for us” — David Hilbert
Number Theory
How to Prove That e is Irrational
Two Simple Proofs of the Irrationality of e
Analysis
Understanding Why 0.99999… = 1
…And the Foundations of Calculus
Analysis
Mighty Ruler Conquers Quadratic Equations
The methods of finding roots of a quadratic equations are quite easy and are very well understood. There are all kinds of approaches…
Analysis
Taylor Series And The Power Of Approximation
We take a deeper look at what Taylor Series does and how we can obtain polynomials for approximating non-polynomial functions.
Analysis
Root-Finding Algorithms
Ways of determining when an equation is equal to zero