### 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…

### Solving Nonhomogeneous Linear ODEs using Annihilators

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My previous Insights article, Solving Homogeneous Linear ODEs…

### Solving Homogeneous Linear ODEs using Annihilators

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In this Insights article we'll look at a limited class of ordinary…

### Trials and Tribulations of a Physicist who Became a Math Geek

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

### Matrix Representations of Linear Transformations

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Let X and Y be finite-dimensional vector spaces. Let ##T:X\to…

### How to Self-Study Basic High School Mathematics

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How to self-study basic high school mathematics We…

### How to Self-Study Calculus

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We often get questions here from people self-studying…