Always use more than 1 text, always do the problems, & always keep up a steady pace. I haven't found anything else to be really important.
Ask HN: Independent Math Study
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Re: Ask HN: Independent Math Study
#22First make sure you have a solid operational foundation on the basics. Advanced topics will feel so much easier.
For that I can recommend Discrete Mathematics and its Applications by Kenneth H. Rosen.
Optionally supplemented by Student's Solutions Guide for more elaborate answers to exercises.
Do as many exercises as possible.
Re: Ask HN: Independent Math Study
#23Book recommendation: Princeton Companion to Mathematics
It's a good way to skim a lot of different mathematical topics for further exploration.
http://www.amazon.com/Princeton-Companion-Mathematics-Timoth...
Re: Ask HN: Independent Math Study
#24I self-studied math for 2 years. I just attended lectures without officially enrolling to the university. I also did about half of the homework problems given in these courses (My math-student friend was envious of me: I could choose the interesting questions out of the homework paper, and ditch the boring ones!)
Some of my studies I also did with books, video lectures, and articles I found on the internet.
Re: Ask HN: Independent Math Study
#25Earlier quoted context omitted.
I would claim that Calculus isn't that important for engineers / scientists / programmers either. Real Analysis is important if one needs to understand thing deeper. In the real world, problems can't be solved analytically... and many of the tools one learns in Calculus are kind of useless. I think Linear Algebra is much, much more important than Calculus. Linear Algebra is the arithmetic of higher mathematics, like…
>In the real world, problems can't be solved analytically... Your other suggestions notwithstanding, you and I live in a very different "real world" my fried.
real world
Tell that to physicists “renormalizing”† it over and over all days long…
† I almost forgot not everyone on HN may know what that is, http://en.wikipedia.org/wiki/Renormalization
Re: Ask HN: Independent Math Study
#26You could do a purely applied approach, look at some Data Mining books, like Witten/Franke and the Weka java framwork (there's quite a few good books, check amazon reviews, ) and the assortment of methods that are applied from basic logit/probits, through clustering, SVM, neural, evolutionary programming, .
Re: Ask HN: Independent Math Study
#27Earlier quoted context omitted.
> calculus isn't that important for mathematicians That's a joke, right?
No. Many pure math classes require no (or very little) calculus. Abstract algebra, number theory, combinatorics, and graph theory certainly fall into this category. Topology does, too, depending on which area you study and what you consider calculus. Sure, there are obviously fields that do rely heavily on calculus, as well as certain branches in the above fields, but my point was that it's nowhere near universally n…
This is terrible, wrongheaded advice. It's like Pablo Picasso, in the middle of his Blue Period, trying to convince younger painters that red isn't a useful color for serious artists.
If you want to study graph theory or combinatorics [1], then calculus will be pretty much useless to you, and you'll naturally go years without using it.
Calculus is also useless in some situations in abstract algebra (which are said to have combinatorial character). There are other parts of abstract algebra, e.g. Differential Galois Theory [2], in which calculus is pretty important.
Topology is similar. Elementary topology is part of the foundation supporting calculus, while algebraic topology is one of the tools that's useful when we try to do calculus (or solve differential equations) in non-Euclidean spaces.
Fields making heavy use of calculus include differential geometry, differential equations (ordinary or partial), dynamical systems or control theory. That subsumes most of physics. Fields underpinning (and largely inspired by) calculus include real and complex analysis, measure and integration theory (aka axiomatic probability theory). Also functional analysis, which is a generalization of linear algebra, which is the bookkeeping methodology of calculus in higher dimensions.
[1] The first sentence here says it all: http://en.wikipedia.org/wiki/Combinatorics
Re: Ask HN: Independent Math Study
#28Always use more than 1 text, always do the problems, & always keep up a steady pace. I haven't found anything else to be really important.
This is really good advice. Also, remember that it means nothing beyond what it says, all you really have to work from are the definitions and the theorems. :)
Re: Ask HN: Independent Math Study
#29You could try MIT's free courses!
Re: Ask HN: Independent Math Study
#30It's been ages since my last university math class (I was a I math major), so I can't point you to any reference material, but I can say the following. If you really want to improve your problem solving skills, I would highly recommend studying real analysis. What you get out of this will go a long way to making you a better problem solver. The reason why I say this is when you have to so something like prove why 1 i…
What's a good real analysis text these days? Is Spivak's calculus book still a common favorite?