Self Learning Mathematics

9 Sep

The theme of this  blog has always been self learning – we started at self learning actuarial studies, have dabbled in self learning predictive modelling and now we are looking at self (re) learning mathematics, in order for a deeper push into predictive modelling and statistics.

I was reminded of the self-learning angle the other day when I stumbled across this blog:

http://latinandgreekselftaught.blogspot.com.au/2011/05/teaching-yourself-latin-and-greek.html

which charts the adventures of a gentleman self-re-learning the Latin and Ancient Greek he learnt up to the point he left tertiary education now that his time in the workforce has ended.

We have in common that there is an element of dishonesty in calling this ‘self-learning’ – this blogger above left tertiary education with an enviable grasp of the languages, helped by lecturers at uni and probably his high school teachers. He wasn’t going to stumble because the ablative case was too weird to understand, or become disheartened by deponent verbs.

In my case, I am re-learning some material that I have seen before and some other material that I haven’t seen before, and next year hope to take Linear Algebra, Abstract Algebra and Number Theory courses as non-award subjects to make sure that I have learned that material correctly.

Compared to the blogger, at least I have the advantage that where I have seen the material, it is only four or five years rather than 35 or 40 years since I worked with it. At the same time, half the motivation is to study some branches of mathematics that I think I should have studied before taking somewhat more advanced studies – Linear Algebra especially, which is obviously a foundation of statistics and spectral analysis.

My current foray into re-learning linear algebra is being supported by Serge Lang’s Introduction to Undergraduate Linear Algebra, which seems to have a terrible reputation among Amazon reviewers and commenters on places like math stack exchange. I think the reason is that the pace is fairly brisk. 

For my own part, I find the brevity a little bit refreshing, even when I am looking at stuff I have never seen before (or at least have no memory of seeing before!) The best part, is the portability which allows me to put it in a coat pocket, and take wherever I am going (some not true of the calculus text I used, by Anton Bivens Davis). Despite its brevity, it also seems to get to material which is advanced enough for my purposes – just short of the lecture notes for the course I plan to do next year, without the distracting ‘matrix operation’ notation and covering just about all of the same topics within the subject.

I also mentioned before that I had taken some more advanced studies in statistics and spectral analysis than my command of Linear Algebra ought to have allowed – it is certainly pleasurable to have various puzzles and obstacles of past studies resolved, although frustrating in the sense that I could have done better at the time with just a smidgen more Linear Algebra knowledge at my fingertips.

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