mathematics self-study Articles

Tag Archive for: mathematics self-study

complex numbers

Fixing Things Which Can Go Wrong With Complex Numbers

/
0 Comments
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

/
9 Comments
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

/
0 Comments
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

/
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
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

/
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

The Orin Fractional Calculus

/
8 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

Fundamental Theorem of Calculus: An Intuitive Numerical View

/
9 Comments
The fundamental theorem of calculus states that integration and differentiation are reverse operations of one another. This article gives an intuitive,…
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

Tensors Explained: Scalars, Vectors, Matrices & Math

/
58 Comments
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

/
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

The Gauge Integral: Why Henstock–Kurzweil Deserves a Course

/
31 Comments
The gauge integral, also called the Henstock–Kurzweil integral, is a modification of the Riemann integral that replaces a single fixed tolerance with…
integralmisconceptions

The Calculus Paradox: Why ∫1/x dx Can Equal 1 = 0

/
40 Comments
The paradox where integration seems to prove 1 = 0 arises from treating an indefinite integral as a single function instead of a set of antiderivatives.…
groupsandgeometry

Klein’s Erlangen Program: How Groups Define Geometry

/
7 Comments
Felix Klein's Erlangen program defines a geometry as a set paired with a group of transformations that preserve "sameness" of figures on that set. Different…
selfstudy

Why Math Self-Study Projects Fail (And How to Avoid It)

/
49 Comments
Most self-study math projects fail for a handful of predictable reasons: mismatched help, rushing through material, discouragement from slow visible progress,…
highschoolmath

University Math for High Schoolers: Where to Start

/
21 Comments
High school students who want a taste of university-level mathematics before they graduate can start now with subjects like abstract algebra, linear algebra,…
studymath

Self-Study High School Math: Best Books & Order to Learn

/
5 Comments
To self-study high school mathematics in a logical sequence, most learners should progress through basic algebra, then synthetic geometry, then trigonometry,…
studymath2

How to Self-Study Calculus: Topics and Book Guide

/
25 Comments
To self-study calculus, work through four core areas in order: differentiation, integration, sequences and series, then multivariable calculus. Each builds…
studymath1

How to Self-Study Mathematics: A Step-by-Step Guide

/
12 Comments
Self-studying mathematics is achievable for most learners willing to commit to daily, consistent practice rather than occasional cramming. Success depends…