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Mathematics for the viKid

I didn't start to appreciate mathematics until after University. It started with book by Professor Ian Stewart called The Foundations of Mathematics. It was a short white book that looked very complicated. Yet I was determined to figure out just what math was.

How did math work?

Why was it so effective at describing natural phenomenon?

I can't remember too much of that book anymore. It is lost somewhere in my collection, but the one thing I do remember clearly was the slow realisation of just how important set theory is.

(please see my article Understanding Deeply for a quick introduction)


In the following sections below I will try and explain to you, the reader, what I have learned from all my mathematical exploits. I am nothing but a two-bit amateur with high ambitions. I was never really very smart or gifted in this subject. I just love it. So please if you find any mistakes, let me know and I will do my best to correct them. I will try new and novel approaches to explain each subject wherever I can. Emphasis will be on achieving intuitive understanding rather than any kind of formal explanation. I am very much still learning all these subjects and don't even have a degree in Math. So please forgive any errors.

What is Mathematics

To the vikid, mathematics is really just a disciplined process of thought. Mathematics is thought and it is a bridge between different kinds of thought and reality. Being a discipline, an abstraction as such, it is limited. It is not suitable for discussions on the language of love for example. Yet, we must embrace this limitation and know its boundaries, often pushing them further out where we can. The language of love is similarly limited, yet we would not want to give it up for being so. The mind is multi-dimensional and the language of math is in its purest sense a infinitely complex bridge connecting connecting vastly differing disciplines of thought. This is its greatest gift. Through the mastery of math, we can start mastering the first dimension of reality and this is ultimately what Mathematics is.

Set Theory, Sets & Structures

Set Theory is the Machine Language of mathematics. It's a very low level language, close to the machine, so to speak. In set theory with define really primitive operations on even more primitive types data. Set theory in a way isn't as illuminating as high level mathematics but in another way, it is the light that makes all of math possible. In fact, there is a philosophy called formalism which says that mathematics is a game of symbols with no intrinsic meaning

Abstract Algebra

To me, Algebra is a branch of Mathematics that deals with symbols and the rules for manipulating those symbols. It really is the foundation of all Mathematics because it sets up and sets out the written language of math. Without algebra we would have no powerful method of communicating our Mathematical ideas (to humans or computers) and progress would essentially ground to a halt.


Connections and Curvature


Differential Geometry

Differential Forms

Measure Theory


Hilbert Spaces

Quantum Mechanics

Integration on Manifolds

Lie Groups and Lie Algebras

Discrete Mathematics

Homeotopic Type Theory

Homotopy type theory is a new branch of mathematics that combines homotopy theory and type theory. Homotopy type theory also brings new ideas into the very foundation of mathematics.


Math on Computers



Sources, Links and Reading Lists


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