mathematics self-study Articles

Tag Archive for: mathematics self-study

complex numbers

Fixing Things Which Can Go Wrong With Complex Numbers

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Abstract This article will build on the hints about treating the complex numbers as a branched surface, briefly described and pictured in section 4.2…

Groups, The Path from a Simple Concept to Mysterious Results

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Introduction The concept of a group is as simple as it gets: a set with a binary operation like addition and a couple of natural laws like the requirement…
topology

The Many Faces of Topology

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

Yardsticks to Metric Tensor Fields

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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

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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…
calculus

How to Solve Second-Order Partial Derivatives

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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

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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

The Orin Fractional Calculus

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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

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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

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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

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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.

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Introduction 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…
cubicfunction

Learn How to Solve the Cubic Equation for Dummies

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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

Why the Gauge (Henstock-Kurzweil) Integral Matters

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The gauge integral (Henstock–Kurzweil) The current (pure) mathematics curriculum at the university is well-established. Most of the choices made are…
integralmisconceptions

Integration Paradoxes: Indefinite Integrals and Constants

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

Klein’s Erlangen Program: Groups Define Geometry

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Klein's Erlangen program: groups and geometry There is a very deep link between group theory and geometry. Sadly, this link is not emphasized in most…
selfstudy

Why Self-Studying Mathematics Often Fails and How to Persist

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For several years I have helped students who were self-studying mathematics. I did this free, without compensation, because I found it an enriching experience.…
highschoolmath

College-Level Math Options for High School Students

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This insight is written for high school students who don't feel very challenged by their high school courses or who want a taste of what university mathematics…
studymath

Math Self-Study Roadmap: Topics & Book Recommendations

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Introduction We often get questions here from people self-studying mathematics. One common question is: what mathematics should I study, and in what…
studymath2

How to Self-Study Calculus: Topics, Order & Book Guide

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We often get questions here from people self-studying mathematics. One common question is: "What mathematics should I study and in what order?" To…
studymath1

The Essential Guide to Self Study Mathematics

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  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,…