mathematics self-study Articles

Articles for: mathematics self-study

definition differences

Yardsticks to Metric Tensor Fields

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,…
blackboard

10 Math Things We All Learnt Wrong At School

10 Comments
/
The title is admittedly clickbait. Or a joke. Or a provocation. It depends on with whom you speak, or who reads it with which expectation. Well, I cannot…
calculus

How to Solve Second-Order Partial Derivatives

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…
lerch and zeta functions

The Analytic Continuation of the Lerch and the Zeta Functions

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…
Integral Representations of Some Special Functions

A Path to Fractional Integral Representations of Some Special Functions

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:…
Calculus Therom

A Numerical Insight for the Fundamental Theorem of Calculus

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…
tensor calculus

The 10 Commandments of Index Expressions and Tensor Calculus

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…
Maxwell equations

What is the Homopolar Generator: An Analytical Example

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…
whatisatensor

What Is a Tensor? The mathematical point of view.

58 Comments
/
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…
cubicfunction

Learn How to Solve the Cubic Equation for Dummies

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,…
omissionguage

Omissions in Mathematics Education: Gauge Integration

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

Some Misconceptions on Indefinite Integrals

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

Exploring the Relationship Between Group Theory and Geometry

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…
selfstudy

5 Problems with Students Self Studying Mathematics

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.…
highschoolmath

In High School and Want to Do Advanced Mathematics?

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…
studymath

How to Self-Study Basic High School Mathematics

5 Comments
/
  IntroductionWe often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study…
studymath2

A Guide to Self Study Calculus

26 Comments
/
  We often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study and in what order.…
studymath1

The Essential Guide to Self Study Mathematics

13 Comments
/
  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,…