Mathematical Theorems – Sci-advent – Day 6


Maths Theorems Graph

Mathematical theorem network built from Walter Rudin’s Principles of Mathematical Analysis.

Scientific knowledge is built by building up on hypotheses and theories, repeatedly check them against observations of the natural world and continue to refine those explanations based on new ideas and observations. In the case of mathematics, that knowledge is organised in an incredibly structured manner. Starting up with properties of natural numbers, called axioms, and slowly working our way up, reaching the real numbers, calculus, and… well beyond. To prove new theorems, mathematicians make use of old theorems, creating a network of interconnected results—a mathematical house of cards.

Andy Reagan has recently published a blog post entitled “What’s the most important theorem?” where following Walter Rudin’s Principles of Mathematical Analysis, he displays them as nodes in a network.


Structured Documents in LaTeX

The LaTeX logo, typeset with LaTeX

Continuing with the brief introduction to LaTeX that I posted recently, in this video I discuss the use of LaTeX to produce a document that has a structure similar to that of a book for example. The idea is to build a master file that controls the flow of the document and separates each “Chapter” in separate files. This provides the author with a lot of flexibility in terms of organising content and makes large documents far more manageable than when using a single LaTeX file.

Enjoy and any feedback, comments or suggestions are more than welcome.

Using LaTeX to write mathematics

I have been meaning to do something like this for a long time and finally got the courage to do it. A lot of times I get completely horrified by the way in which some documents that contain mathematical notations are mangled (quite literally) by using MS Word. It helps sometimes that some people have access to MathType but still…

LaTeXSo, in this video I intend to provide some help to those that are interested in using LaTeX to include mathematics and  produce their documents. LaTeX is freely available for various platforms. You can obtain MikTeX for  Windows here, and MacTeX for Mac here. There are a great variety of editors to choose from; in this video I recommend TeXmaker, which I believe provides quite a lot of help to those of us that still are attached to the pointing and clicking of MS Word.

Let me know what you think! Any feedback is always welcome.