### The Pantheon of Derivatives - Part IV

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Lie Derivatives A Lie derivative is in general the…

### The Pantheon of Derivatives - Part III

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Some Topology Whereas the terminology of vector…

### The Pantheon of Derivatives - Part II

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Generalizations Beyond ##\mathbb{R}## and ##\mathbb{C}## As…

### The Pantheon of Derivatives - Part I

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Differentiation in a Nutshell I want to gather the…

### Trick to Solving Integrals Involving Tangent and Secant

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This little trick is used for some integration problems involving…

### Simple Geometry, Deep Math

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Introduction It is a remarkable fact that consideration of…

### Using the Fourier Series To Find Some Interesting Sums

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Preliminaries If f(x) is periodic with period 2p and f’(x)…

### Representations and Why Precision is Important

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

### Can Angles be Assigned a Dimension?

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

### Partial Differentiation Without Tears

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Differentiation is usually taught quite well. Perhaps that's…

### Solving the Cubic Equation for Dummies

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Everybody learns the "quadratic formula" for solving equations…

### Omissions in Mathematics Education: Gauge Integration

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The current (pure) mathematics curriculum at the university is…

### General Brachistochrone Problem

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Consider a problem about the curve of fastest descent in the…

### Some Misconceptions on Indefinite Integrals

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Integration is an incredibly useful technique taught in all calculus…

### Groups and Geometry

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

### How to Self-Study Algebra. Part II: Abstract Algebra

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There are three big parts of mathematics: geometry, analysis…

### Friends, Strangers, 7825 and Computers

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

### Irrationality for Dummies

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On one of my restless wanderings around the Internet, I came…

### Scientific Inference P3: Balancing Predictive Success with Falsifiability

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Bayes' Theorem: Balancing predictive success with…

### How to Self-study Analysis. Part II: Intermediate Analysis

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If you wish to follow this guide, then you should know how to…

### How to Self-study Algebra: Linear Algebra

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In this insight I will give a roadmap to learn the basics of…

### Resources for High School Math at Home

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The popularity of home schooling and failures of the public schools…

### In High School and Want to Do Advanced Mathematics?

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This insight is written for high school students who don't feel…

### Perfect Secrecy and the Unbreakable Cipher

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

### The Monographic Substitution Cipher: From Julius Caesar to the KGB

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A monographic substitution cipher works by replacing individual…

### How to Self Study Geometry. Part I: Pure Geometry

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Geometry is one of the oldest parts of mathematics. It has been…

### How to Self Study Analysis. Part I: Intro Analysis

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This is a sequel to my posts on self-studying mathematics. I…

### The Case for Learning Complex Math

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

### Complex and Irrational Exponents for the Layman

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This Insight is part of our "Young Authors" series, where talented…

### What Are Eigenvectors and Eigenvalues?

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Two important concepts in Linear Algebra are eigenvectors…

### Things Which Can Go Wrong with Complex Numbers

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

### The Millennium Prize Problems: Part I

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

### Partial Fractions Decomposition

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Partial fractions decomposition is an algebraic technique that can…