Math Articles

Here is our every growing collection of expert math articles that deal with all mathematics disciplines. These cover all areas of math and all skill ranges from algebra to advanced calculus.

Maupertuis Principle

A Pure Hamiltonian Proof of the Maupertuis Principle

Here is another version of proof of Maupertuis's principle. This…
The Sum of Geometric Series from Probability Theory

The Sum of Geometric Series from Probability Theory

Here I present a simple (but to the best of my knowledge, new)…
lie algebra representations

Lie Algebras: A Walkthrough The Representations

  Part III: Representations  10. Sums and…
Lie Algebra Structure

Lie Algebras: A Walkthrough The Structures

  Part II: Structures5. Decompositions.Lie…
lie algebra basics

Lie Algebras: A Walkthrough The Basics

  Part I: Basics 1. Introduction. This article is…
stock options math

A Simplified Synthesis of Financial Options Pricing

Financial options (the right to purchase ("call") or sell ("put")…

Hilbert Spaces And Their Relatives: Operators

  Operators. The Maze Of Definitions. We will use…

Hilbert Spaces and Their Relatives: Basics

  Basics Language first: There is no such thing as…

Intransitive Dice with a Twist

Intransitive dice are sets of dice that don't follow the usual…

A Journey to The Manifold SU(2): Differentiation, Spheres and Fiber Bundles

Part 2  Differentiation, Spheres and Fiber Bundles Image…

How to Tell Operations, Operators, Functionals and Representations Apart

 All these concepts belong to the toolbox of physicists.…

Simple Geometry, Deep Math

IntroductionIt is a remarkable fact that consideration of…

Representations and Why Precision is Important

First of all: What is a representation? It is the description…

Can Angles be Assigned a Dimension?

1. Some Background on Dimensional Analysis ... if you are…

Exploring the Relationship Between Group Theory and Geometry

There is a very deep link between group theory and geometry.…

An Interesting Ramsey Theory Riddle

This insight will be about Ramsey theory. Ramsey theory has its…

Scientific Inference: Balancing Predictive Success with Falsifiability

  Bayes' Theorem: Balancing predictive success with…

Perfect Secrecy and the Unbreakable Cipher

Is it possible to design an unbreakable cipher? Do methods of…

The Monographic Substitution Cipher: From Julius Caesar to the KGB

A monographic substitution cipher works by replacing individual…

The Case for Learning Complex Math

Resistance to complex math seems to never die out.  I see it…

Things Which Can Go Wrong with Complex Numbers

At the first sight, there are many paradoxes in complex number…

Intro to the Millennium Prize Problems

In this Insight, I will go over the background information…

Axioms for the Natural Numbers

** Bloch Chapter 1.2The Peano system in Bloch has a special…

A Forward on Real Numbers and Real Analysis

It is important to realize that in standard mathematics, we attempt…

Trials and Tribulations of a Physicist who Became a Math Geek

How did I go from the brink of changing my major from physics…
math obvious

Teaching Math and the Obvious

My #1 goal, when I teach a math class, is to convey a certain…

A Brachistochrone Subway Is Not a Cost-effective Idea

It is apparent that a subway tunnel could be built without the…

Is Zero a Natural Number?

Using: Anderson-Feil Chapter 1.1Is zero a natural number?This…

What is a Property Formally

** Hrbacek-Jech Chapter 1.2Hrbacek and Jech do not go into…