Archive for February, 2021

Mathematical Typesetting: A Great Way to Learn Mathematics

February 12th, 2021

Introducing LaTeX

For those of you who are unfamiliar with the idea, mathematical typesetting is the means by which mathematicians produce documents that contain complicated mathematical expressions. It’s not possible to typeset things like integral signs and summands in basic word processing systems: instead, the mathematician relies on a special typesetting language, which interprets commands as instructions to reproduce particular mathematical symbols and does so cleanly and elegantly.

LaTeX is the de facto typesetting language in modern use and is used by mathematicians and teachers around the world to write articles, create notes and print out question sheets. LaTeX usually seems quite peculiar to the uninitiated. It is not a WYSIWYG (what you see is what you get) processing system, like Microsoft Word, but rather a behind the signs document markup language: the resultant document appearance bears little resemblance to what the author actually types. Say you wanted to typeset an integral into your document. Then you would so by writing something like:

$$
\int_0^1 x^2=\frac{1}{3}.
$$

The language used consists of instructions to the typesetting system; the two dollar signs “$$” tells the typesetting system that an inline equation is about to be inserted: the “\int” command tells it that an integral sign needs to be produced and the follow-up “_0^1″ informs it what bounds should be used; the “x^2″ specifies the integrand; and the “\frac{1}{3}” tells it that a fraction, with numerator 1 and denominator 3, needs to be produced. The final “$$” tells it that it can stop worrying about producing mathematics, as the equation has been entirely specified.

LaTeX may seem odd at first, but it is a powerful program with a lot of features and the capability to reproduce nearly every mathematical symbol that is out there.

Why LaTeX is a great tool for learning mathematics

When I was an undergraduate mathematician, I never really got into the groove of learning my subject until I discovered LaTeX. I did what the vast majority of students do when they first go to university to study mathematics: I went to lectures, I took notes and I muddled my way through various question sheets. What I discovered was that I struggled in subjects where a full set of typeset lecture notes wasn’t provided by the lecturer. For some reason, reading my own notes that I took in class rarely helped the material to sink in. Even when I took the time to sit down and write them up properly, I still found them a difficult tool to learn with.

At the end of my first year, I’d figured out the problem. It turned out I learnt best when I had a proper set of typeset lecture notes sitting in front of me. The problem was, not all lecturers were forthcoming with their own notes, and in subjects where the lecturer decided that he wasn’t going to release them, I had to muddle through as best I could without. By the end of the first year, I decided I’d had enough, and took the problem into my own hands. I learned LaTeX and started to type up the notes for courses where they were missing. Immediately I experienced a massive upsurge in my performance as a mathematics undergraduate. My grades improved, my grasp of the material became more solid, and I enjoyed the subject much more.

Aside from the fact that I just enjoyed the actual process of typesetting itself, I attribute a large part of my eventual graduation with a first class degree to LaTeX and the notes I produced using it. LaTeX is a great tool for letting maths sink in and the major reason why is simple: when you get competent enough with it, it allows you to put all your focus and attention on understanding the material as you write it up.

This is in direct contrast to what happens when you write material up by hand. If you’re anything like me, you’re probably a bit of a perfectionist. So when it comes time to write up a definition, theorem or proof by hand, there’s a big part of your mental focus dedicated to not making a mistake. There is no feeling worse than getting to the end of your second side of notes and slipping up somewhere, putting down a “y” instead of an “x”, or something even worse. Sure, Tipp-Ex can solve the problem to a certain extent, but it is usually problematic to do so and distracts from the flow of your work. Because you’re on guard for this eventuality (and it inevitably happens, no matter how hard you try!), you can’t focus your attention fully on what is at hand, which is learning advanced mathematics.

LaTeX removes this problem, by allowing you to have as many drafts as you want. There are no distractions when working with LaTeX. In your head, you know that any error, no matter how egregious, can be fixed quickly, usually by just hitting backspace a couple of times. You can therefore focus fully on the task of understanding the mathematics, safe in the knowledge that if you make an error, you can undo it painlessly. This also makes LaTeX a great tool for revision, because if you’re reading through your notes and you stumble across something that is just catastrophically wrong, you can replace it in no time with something that makes sense.