Although I’m proud of my education and work experience thus far, the most important thing I have come to realise is where the vast gaps in my education are. A little too late did I realise that the degree I really wanted was Computer Science, and instead I studied Software Engineering.
If you need someone to analyse a complex problem and break it down into it’s components, I can do that. If you need someone to manage a project and make sure your resources are optimised, I’m your man.
However, during my degree, we only breifly touched on mathematics and algorithms. If I recall correctly, we covered some basic boolean logic and very basically touched on sets. We didn’t really get into the nitty gritty stuff that I’ve seen CompSci graduates talk about.
However, I’m not the kind of person who would shrug “Oh well” and go about my business – I’m taking it upon myself to learn in my own time.
I don’t know how other people learn. Although I’ve done a little reading into it, I’m still trying to come to terms with how I learn. While trying to study mathematics, I’ve realised I have a tendency to explore various elements of a topic in depth – I tend to dive into the intricacies of a concept, then go back to the shallow level and move on to a new concept.
However, I’ve found that this is very difficult to do with mathematics. All of the higher level concepts rely on lower level concepts, and there is much cross referencing. I might be looking into Euler’s Totient function, which will lead me to the concept of coprimes, which will lead me to rings, which are contrasted to groups, which were referenced back in the totient function! What’s worse is all of these topics, especially the more abstractable rings and groups, extend past the real number systems, which I haven’t even considered yet.
I’ve found the best way to learn mathematics is to go broad and shallow, pick up the basic concept of all related concepts, then slowly work your way down. It results in a kind of net of understanding that isn’t complete, but allows a person to easily recognise holes, and more intuitively link concepts together.
Learning methods and methods of thinking are both subjects that fascinate me, and I’ll probably have a deeper look into it when I get some time. I think these topics have a vast impact one what kind of knowledge people can learn easily, and can account for people having a “knack” for something.