A Software Engineer’s Adventures in Learning Mathematics • Hacker News Board

Re: A Software Engineer’s Adventures in Learning Mathematics

#121

Post by aethertap » Wed, Feb 04, 2015, 4:50 PM UTC

I am doing this too, with Macdonald's "Linear and Geometric Algebra" and "Vector and Geometric Calculus" along with "Networks, Crowds, and Markets" and "Chaos and Nonlinear Dynamics." It's slow going, but very enjoyable.

The most interesting side effect I've noticed from doing this is a dramatic improvement in my ability to focus. I had been suffering from a general scatterbrained, distracted feeling for a while before I started. I think it was due to the way I consume content online, trying to follow too many interests at once. I set aside about an hour a night to work on these math courses and within a couple of weeks I noticed that my focus was greatly improved. For that reason alone I'm counting this project as a major win, regardless of whether I master these topics or not. Having something to study seems to be extremely valuable for general mental health, at least for me.

Re: A Software Engineer’s Adventures in Learning Mathematics

#122

Post by mcguire » Wed, Feb 04, 2015, 4:51 PM UTC

"Get your fundamentals on lock so that you can start getting into the ill advanced shit. This is universally applicable. — Earl Sweatshirt"

"ill advanced shit"? I know, I know, it's a quote and probably intended to be funny. Heck, it might be.

But I swear, if I start hearing people say that without an awful lot of irony, I'm going to be kicking people in the testicles.

Re: A Software Engineer’s Adventures in Learning Mathematics

#123

Post by jonathantm » Wed, Feb 04, 2015, 4:55 PM UTC

mcguire wrote: post #122

" Get your fundamentals on lock so that you can start getting into the ill advanced shit. This is universally applicable. — Earl Sweatshirt " "ill advanced shit"? I know, I know, it's a quote and probably intended to be funny. Heck, it might be. But I swear, if I start hearing people say that without an awful lot of irony, I'm going to be kicking people in the testicles.

Dude... have you listened to Earl? He can put out a tape every 4 fours and STILL have shit on lockdown.

Yo.

Re: A Software Engineer’s Adventures in Learning Mathematics

#124

Post by otakucode » Wed, Feb 04, 2015, 4:55 PM UTC

When I pick up a book and start to learn something new (which is pretty much what I do in my free time), I usually do it with an IDE at hand. I try to implement as much of what I learn in code. If I can teach the computer how to do it, then I am sure I really understand it, and it often helps me find holes in my understanding.

I have significant trouble with doing this with mathematics, though. Programming languages (at least the ones I know) just don't seem to be good for expressing things like identities and invariants. Anyone have any suggestions on how to handle such things?

Re: A Software Engineer’s Adventures in Learning Mathematics

#125

Post by mcguire » Wed, Feb 04, 2015, 4:55 PM UTC

danso wrote: post #82

decasteve wrote: post #48

This topic comes up every so often. I think my previous comment applies here [1]: I started a Math degree after 16 years of programming without any Math beyond high school (the highest being high school calculus). Most of my work as a software developer didn't require any "higher" Maths. Once I began studying math, including Modern Algebra, Analysis, Graph Theory, Category Theory, etc., I realized I understood many t…

> The biggest misconception is that in Math there is one "correct" answer. Well written...and I'd argue the same is for both Computer Science and software engineering in general. When teaching beginners, it still astonishes/annoys me how many students tell me, "My program didn't work"...as if there was just one reason why it didn't work, as opposed to hundreds of possible reasons.

The first sign of programming maturity is the realization that it might be working just by accident. On that one case.

Re: A Software Engineer’s Adventures in Learning Mathematics

#126

Post by calebm » Wed, Feb 04, 2015, 4:56 PM UTC

I can personally strongly recommend the book, "Who is Fourier?" for learning math: http://www.amazon.com/Who-Fourier-Mathematical-Adventure-Edi.... It is the best math book I have ever read.

Re: A Software Engineer’s Adventures in Learning Mathematics

#127

Post by gtani » Wed, Feb 04, 2015, 4:57 PM UTC

I read this the first time posted (didn't get any comments), very poignant, especially the part about relearning trig/geometry, precalc. There's boundless resources for learning now but you don't get little endorphin/epinephrine releases like you do when your gcc/clang/VS compile succeeds, it's still mostly notebooks, whiteboards, pencils and 4-color pens (tho i've seen lots of cool JS animations, ipython notebooks, and libs in R, matlab/octave and now julia)

- a few universities have put (many/most) of lecture notes and student notes up: http://www.maths.cam.ac.uk/studentreps/res/notes.html as well as study guides: http://www.maths.cam.ac.uk/undergrad/studyskills/text.pdf

- books about how to think like a mathematician: Keith Devlin, Kolmogorov/Alexandrov et al did 2 Dover books, and Houston: http://www.amazon.com/How-Think-Like-Mathematician-Undergrad... and http://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199... and Ellenberg: http://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/15942...

- Concrete Math by Patashkin, Knuth et al; Streetfighting Math by Mahajan and his newer, freely available: http://mitpress.mit.edu/books/art-insight-science-and-engine...

- this machine learning/data science list: http://www.reddit.com/r/MachineLearning/comments/1jeawf/mach...

- Cal newport blog: http://calnewport.com/blog/2012/10/26/mastering-linear-algeb...

- besides Dover, Schaum Outlines are a good cheap resource abundantly available in used bookstores(tho there are in fact some type-ridden ones also)

____________

the best advice general advice i've seen is the same as what they tell you in college: form study groups and make commitments to regular discussion. Stronger students strengthen their understanding by tutoring others at the whiteboard. There's lots of machine learning and data sciencey meetups and informal groups springing up e.g.http://machine-learning.meetup.com/

Re: A Software Engineer’s Adventures in Learning Mathematics

#128

Post by randcraw » Wed, Feb 04, 2015, 4:59 PM UTC

jxm262 wrote: post #62

I don't mean to go off track here, but as someone who's been casually interested in math, I'm wondering which branches of math are the most applicable to software development. I've taken Discrete Mathematics, Stats, and Calc in college, but now I've been working in the field for a few years and want to try learning a bit more. I've been thinking of trying some courses on Cryptography, but it would be a major shift fr…

Probability, convex and nonlinear optimization, linear algebra, and statistics are clear wins in many problem spaces, especially machine learning, AI, and computer vision. Ordinary and partial differential equations and numerical methods are heavily used in process modeling and HPC for problems in science and engineering. Geometry, curvature, and matrix theory are heavily used in computer graphics to model shape and movement, as well as computer vision. Number and group theory are the basis of crypto, I believe. In general, calculus and its variations are used to represent and describe solution techniques theoretically before mapping them to discrete solutions using numerical methods.

Re: A Software Engineer’s Adventures in Learning Mathematics

#129

Post by mcguire » Wed, Feb 04, 2015, 5:01 PM UTC

bitL wrote: post #80

What I understood after studying CS for over 10 years at a few universities regularly ranked highly at ACM ICPC is that math is unnecessarily obfuscated to most people. There is even an excellent book "Concrete Mathematics" from Stanford that tries to bring fun back to math instead of drying people with some formal stuff without explaining how people over the centuries got to that structure. I honestly believe math l…

You mean Concrete Mathematics, by Ron Graham^, Don Knuth^^, and Oren Patashnik?[1]

I thought it was just an advertisement for Computer Concrete Roman (Knuth's other font family) and the Zapf(?) Euler math fonts.

^ Yes, that Ron Graham.

^^ Yes, that Don Knuth.

^^^ I don't recognize Patashnik. Sorry.

[1] http://www.amazon.com/Concrete-Mathematics-Foundation-Comput...

Re: A Software Engineer’s Adventures in Learning Mathematics

#130

Post by mcguire » Wed, Feb 04, 2015, 5:05 PM UTC

j2kun wrote: post #114

bitL wrote: post #80

What I understood after studying CS for over 10 years at a few universities regularly ranked highly at ACM ICPC is that math is unnecessarily obfuscated to most people. There is even an excellent book "Concrete Mathematics" from Stanford that tries to bring fun back to math instead of drying people with some formal stuff without explaining how people over the centuries got to that structure. I honestly believe math l…

For your analogy with Turing machines, do you have a better mathematical model of a computer? Nobody works directly with the TM model when they're doing theoretical CS anyway, they just describe the algorithm and everyone understands that if you really really wanted to you could work it down to a TM. The same is true of mathematics. It might be hard to get everything precise, but that's not the point of mathematics.…

And, of course, the point of the oracles is for proofs of non-existence.