mathematics self-study Articles



How to Solve Second-Order Partial Derivatives

Introduction A frequent concern among students is how to carry out higher order partial derivatives where a change of variables and the chain rule are…
lerch and zeta functions

The Analytic Continuation of the Lerch and the Zeta Functions

Introduction In this brief Insight article the analytic continuations of the Lerch Transcendent and Riemann Zeta Functions are achieved via the Euler's…
Integral Representations of Some Special Functions

A Path to Fractional Integral Representations of Some Special Functions

0. Introduction As for the reference material I have used the text Special Functions by Askey, Andrews, and Roy which covers much of the theorems here…
Calculus Therom

A Numerical Insight for the Fundamental Theorem of Calculus

The purpose of this article is not to provide some rigorous statement, neither a rigorous clever proof of the fundamental theorem of calculus. It is rather…
tensor calculus

The 10 Commandments of Index Expressions and Tensor Calculus

Having more than 10 years of experience in teaching vector and tensor calculus and special and general relativity, I have noted that many people have the…
Maxwell equations

What is the Homopolar Generator: An Analytical Example

Introduction It is surprising that the homopolar generator, invented in one of Faraday's ingenious experiments in 1831, still seems to create confusion…

What Is a Tensor in Mathematics?

Let me start with a counter-question. What is a number? Before you laugh, there is more to this question than one might think. A number can be something…

Learn How to Solve the Cubic Equation for Dummies

Everybody learns the "quadratic formula" for solving equations of the form [itex]A x^2 + B x + C = 0[/itex], even though you don't really need such a formula,…

Omissions in Mathematics Education: Gauge Integration

The current (pure) mathematics curriculum at the university is well established. Most of the choices made are sensible. But still, there are some important…

Some Misconceptions on Indefinite Integrals

Integration is an incredibly useful technique taught in all calculus classes. Nevertheless, there are certain paradoxes involved with integration that…

Exploring the Relationship Between Group Theory and Geometry

There is a very deep link between group theory and geometry. Sadly, this link is not emphasized a lot in most courses of group theory, even though it is…

5 Problems with Self Studying Mathetmatics

For several years already I have been trying to help people who have been self-studying math. I did this completely free with no compensation for me. I…

In High School and Want to Do Advanced Mathematics?

This insight is written for high school students who don't feel very challenged by their high school courses. Or maybe those high school students who want…

How to Self-Study Basic High School Mathematics

  IntroductionWe often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study…

A Guide to Self Study Calculus

  We often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study and in what order.…

The Essential Guide to Self Study Mathematics

  How to self-study mathematics? People self-study mathematics for a lot of reasons. Either out of pure interest, because they want to get ahead,…