mathematics self-study Articles

Tag Archive for: mathematics self-study

The Many Faces of Topology

December 6, 2024

Abstract Topology as a branch of mathematics is a bracket that encompasses many different parts of mathematics. It is sometimes even difficult to see…

Yardsticks to Metric Tensor Fields

August 27, 2022

1 Comment

I asked myself why different scientists understand the same thing seemingly differently, especially the concept of a metric tensor. If we ask a topologist,…

10 Math Things We All Learnt Wrong At School

April 21, 2021

10 Comments

Some of these could even lead to heavy debates within the scientific community, so maybe I should say: from my point of view. So before you get excited…

How to Solve Second-Order Partial Derivatives

May 19, 2020

1 Comment

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…

The Analytic Continuation of the Lerch and the Zeta Functions

April 27, 2020

0 Comments

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

A Path to Fractional Integral Representations of Some Special Functions

March 23, 2020

9 Comments

Introduction This bit is what new thing you can learn reading this:) As for original content, I only have hope that the method of using the sets $$C_N^n:…

A Numerical Insight for the Fundamental Theorem of Calculus

November 8, 2018

9 Comments

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…

The 10 Commandments of Index Expressions and Tensor Calculus

July 28, 2018

16 Comments

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…

What is the Homopolar Generator: An Analytical Example

November 27, 2017

8 Comments

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? The mathematical point of view.

June 18, 2017

58 Comments

Tensor Key pointsThe author begins by questioning the nature of numbers and their deeper significance. Numbers can represent various mathematical…

Learn How to Solve the Cubic Equation for Dummies

October 1, 2016

5 Comments

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

July 22, 2016

31 Comments

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

Some Misconceptions on Indefinite Integrals

July 3, 2016

40 Comments

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

June 30, 2016

7 Comments

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 Students Self Studying Mathematics

May 27, 2016

49 Comments

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

In High School and Want to Do Advanced Mathematics?

April 7, 2016

21 Comments

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…