I'm surprised by the excitement at every piece of teaching material or set of course notes posted here. Free textbooks and PDF notes have been around for years, especially for mathematical topics.
This PDF won't do the work for you, and you can't skim-read this kind of material. To properly understand an area of mathematics then you need to put a significant amount of time and effort into working through the text, and a set of condensed notes is probably not as good as a well written textbook with careful examples and exercises (and with fewer errors).
I'm not making a judgement about the quality of this document, I guess I'm saying that if you really wanted to learn this material you would have started already.
>> if you really wanted to learn this material, then you would have started already
This is pretty much the only statement i have an objection or reaction to.
I simply don't understand the basis for assertions along these lines. These sorts of fatalistic proclamations are made not-infrequently in the context of programming and development as well.
Its as if we feel that the only ones worthy of pursuing a given discipline are those who realized their passion and interest early in life. Why the exclusivity? This is just knowledge, after all.
I agree with your sentiment. Sometimes we get articles on (say) the Fourier transform, with its own intuitive take on how and why it works, some visualisation and some maths. I think these articles are great. I can understand how they would spark the interest of someone who is not familiar with the maths, whatever their age.
That's not the case here. I don't think that anyone who has upvoted this has read any significant part of the document, simply because it would take months if not years to go through. It's like me posting a several-hundred page set of homemade notes on cell biology and saying "Notes to take you to medical school level biology".
Fair. I happen to agree that the document is probably not going to be of much use to anyone who hasn't already studied the material.
I do, however, firmly believe that anyone - no matter their age - may find interest and cause to learn math, even if starting with high school calculus.
This kind of mathematics is at a level that requires a certain amount of self-motivation, passion, desire, whatever you want to call it, to learn. It's probably something you're born with, which is why not many people pursue graduate studies in mathematics and those who do are mostly people with a real love for it. It's unlikely that at some point in your adult life you're going to suddenly develop the necessary burning desire to motivate such study on the basis of a set of notes someone posted on the internet.
>> It's unlikely that at some point in your adult life you're going to suddenly develop the necessary burning desire to motivate such study
While it's true that adults are not likely to re-enroll in University to study mathematics, that doesn't necessarily mean the desire isn't there.
For instance, a "burning" desire may be sufficient to motivate a 22 year old to study mathematics, however that same desire in a 44 year old might not overcome the pressures, realities and obligations of life, work & family.
> For instance, a "burning" desire may be sufficient to motivate a 22 year old to study mathematics, however that same desire in a 44 year old might not overcome the pressures, realities and obligations of life, work & family.
You'd be surprised at how many there are.
I'm mid-30s and I've recently finished a maths degree via distance learning (Open University in the UK). During the time I've been studying I've moved house, got married, had increased work pressures, become a father and I am helping bootstrap a startup in what little free time is left from all of that.
At the various tutorials, revision day schools and exams during my studies I met lots of others who were in similar positions. It's more common than you think.
So you're actually proving the point: you weren't born with this burning desire, you didn't learn it in college or high school or (as burning desire would indicate) when you were twelve - you waited until now, and were perfectly capable of learning it once your motivations changed.
As they do, as time passes. Anybody out of their 20s will know that.
I had a desire to study it since I was young. I excelled at both Comp Sci and Maths during school[1]. Studied both all the way prior to University and then had to pick one (I didn't want to do a joint degree as I wanted to study one in depth rather than two partially).
A Comp Sci degree was going to be a bigger advantage for the kind of job I was looking for and so that won. The desire to study Maths has always been there, it's just taken a while since leaving University until I was in a position where I had the time/money to study it in my spare time.
[1] First computer was a ZX81 when I was just 5 years' old.
Almost complete agreement here. There seems to be a 'shortcut mentality' among some hackers - the idea being that if you are faced with a difficult subject, begin with the assumption that standard learning material is padded with lots of useless filler material, and hence conclude you can save time by going for the more summarised stuff.
I think this is not generally a bad strategy in many subjects (business comes to mind), but mathematics is different. There really is no 'royal road' to any subset of it. There are shortcuts, sometimes, but every shortcut you take (with the exception of clever mathematical tricks, which count as solid learning here) deprives you of the opportunity to make a small but significant improvement to your logical problem-solving apparatus.
And that is probably a greater waste of time than anything else: shallow learning. Again, this is possibly not a bad strategy in many subjects, but again mathematics is not one of those.
and hence conclude you can save time by going for the more summarised stuff.
I think this is not generally a bad strategy in many subjects (business comes to mind), but mathematics is different.
I agree, math books tend to be on the terse side as they are - you wouldn't want the material to be even more terse, because you'll end up spending more time grasping it without the help the additional text may provide.
probably not as good as a well written textbook with careful examples and exercises
Name one. While I agree that this document (probably) won't compensate for a more complete education, including textbooks, the truth of the matter is that most textbooks (even many highly regarded ones) are horrible for learning on one's own. Rigorous and sound, yes, but many are bad for pedagogy, and even worse for self-teaching. A good majority are muddled and unclear to the layman, with not a very good "big picture" or "here's why it's done this way" approach. Just look at the K&R C article from the other day.
Gilbert Strang's Linear Algebra textbook is designed to be useful to the self-learner, and I think the latest edition was revised after MIT's OCW was a thing, so actually references all the material online, IIRC.
I've read some of it and it's quite good. His lectures are great too.
I woke up one day 4 years ago and realised that I wanted to learn mathematics. I realised I had always wanted to learn Mathematics - only I had never before understood what it actually was. I now have a MSc in mathematics and I am getting to the point where I am able to bring that knowledge to bear on my satellite interests, mathematical physics and my own ideas for GAI.
It is documents like this which have helped me get to here and will take me to where I want to be.
People can change; most won't. While I, like you, take issue with the fatalistic statement of "you would have started already" (how young a person would the GP say this to? 30? 25? 18?), there is a grain of truth to it. Most people, even if they want to, won't get much out of this. Not that I'd like to discourage anyone.
This PDF won't do the work for you, and you can't skim-read this kind of material. To properly understand an area of mathematics then you need to put a significant amount of time and effort into working through the text, and a set of condensed notes is probably not as good as a well written textbook with careful examples and exercises (and with fewer errors).
I'm not making a judgement about the quality of this document, I guess I'm saying that if you really wanted to learn this material you would have started already.