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

Re: A Software Engineer’s Adventures in Learning Mathematics

#201

Post by tokenrove » Thu, Feb 05, 2015, 12:29 AM UTC

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…

> Part of the reason I began studying math, is that I felt it was my limiting factor. The range of problems I could tackle as a programmer was limited by math. It turns out this was partly true.

I started studying math intensely (doing every exercise in books, etc) when I realized the same thing: math was a limiting factor for my programming ability. Michael Abrash hints about this in some article, and I sneered at it until I realized it was true.

I considered going back to do a math degree but the amount of hassle involved, as well as other life changes required, made that impossible.

I would like to know how it worked out for you. Are you glad you did a degree program? Do you feel you met people and made connections that were valuable, that couldn't be made by an autodidact?

Re: A Software Engineer’s Adventures in Learning Mathematics

#202

Post by tokenrove » Thu, Feb 05, 2015, 12:36 AM UTC

pakled_engineer wrote: post #144

IndianAstronaut wrote: post #108

Earlier quoted context omitted.

This is what drew me to CS over math. I enjoy describing things with code or pseudo code, not difficult to understand equations and math symbols. Also, it is much easier to see the practicality of an equation when presented in code form.

After I read SICP and HtDP I started retaking math I had forgotten but writing out the equations in Scheme to further grasp the language. At first doing Spivaks Calculus in this method took a long time but now I can write formulas and basic proofs just as fast in a programming language as I can with a pencil. I skimmed SICM (Structural Interpretation Of Classical Mechanics) just to get an idea of how they represented…

This is something I like doing. Something I keep meaning to do is take it further and write my proofs in a proof checking language, or at least write "unit tests" for my proofs with one (interleaved with the natural language proof with org-mode!), but they all seemed pretty unwieldy. Has anyone tried this with any success?

Re: A Software Engineer’s Adventures in Learning Mathematics

#203

Post by graycat » Thu, Feb 05, 2015, 1:02 AM UTC

nkurz wrote: post #192

graycat wrote: post #174

Earlier quoted context omitted.

Part III -- Statistics For statistics, that is a messy field. It has too many introductory texts that over simplify the subject and not enough well done intermediate or advanced texts. Also the subject has essentially a lie: They explain that a random variable has a distribution. Right, it does. Then they mention some common distributions, especially Gaussian, exponential, Poisson, multinomial, and uniform. Then the…

Fabulous write up. Do you somewhere besides here to publish it so it's easier for people to wander across in the future? I'd be interested to see what else you've written.

> Fabulous

All praise welcome!

> I'd be interested to see what else you've written.

For some more math, more technical,

https://news.ycombinator.com/item?id=8919311

Re: A Software Engineer’s Adventures in Learning Mathematics

#204

Post by seanmcdirmid » Thu, Feb 05, 2015, 1:17 AM UTC

eli_gottlieb wrote: post #154

seanmcdirmid wrote: post #28

Earlier quoted context omitted.

Depends on your school. UW CSE (a top 10 program) would be called rigorous but is not as theoretical (there is math, but nowhere near enough for a math minor).

I went and checked the undergrad curricula back at UMass Amherst where I went. I was incorrect: a generic Comp Sci program there stops three courses short of a math minor. The more theoretical concentrations - such as Theory of Computing, Machine Learning, or Programming Languages - teach enough theoretical content to come within one course of a math/stats minor, or even cross the line. So yes, if you take a Computer…

Minors are mostly meaningless on your degree; but the knowledge you get from the classes is worthwhile. I took some advanced math classes but kind of burned out on it towards the end of my degree (ironic since I went to grad school immediately after). What I did notice: CS classes are easy compared to advanced math classes...man, I struggled to eek out B's in the courses when CS classes were just easy A's.

If you want to do good at machine learning...electrical engineering is probably a better choice; the maths learned in EE overlap fairly well with what is needed to do ML. PL theory is quite niche, even for PL researchers.

Re: A Software Engineer’s Adventures in Learning Mathematics

#205

Post by decasteve » Thu, Feb 05, 2015, 1:20 AM UTC

tokenrove wrote: post #201

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…

> Part of the reason I began studying math, is that I felt it was my limiting factor. The range of problems I could tackle as a programmer was limited by math. It turns out this was partly true. I started studying math intensely (doing every exercise in books, etc) when I realized the same thing: math was a limiting factor for my programming ability. Michael Abrash hints about this in some article, and I sneered at i…

It was a big hassle and a big life change. But I've always had in the back of my mind that I wanted to do it and I'm glad I did. I put it off because the money I was making, and the places I was traveling, was too good to pass up at the time. So I saved money with the idea that I would get the chance to go to school.

I did try to learn math as an autodidact before I began the degree. The more abstract the math, the harder it was for me to self-study. It was inefficient at best. At worst, I'd hit a wall and not have anyone to reach out to.

Re: A Software Engineer’s Adventures in Learning Mathematics

#206

Post by brudgers » Thu, Feb 05, 2015, 1:35 AM UTC

j2kun wrote: post #156

brudgers wrote: post #152

Earlier quoted context omitted.

I already admitted it was beyond my ability...

Math aside, it's an amusing misuse of vocabulary.

It's not a misuse of vocabulary, it's a misspelling. As my typing speed trends toward my thinking speed, the mechanical action becomes more tied to phonemes. I've found myself increasingly typing "are" for "our" which is fairly classic. "One" for "won" not so much.

Re: A Software Engineer’s Adventures in Learning Mathematics

#207

Post by decasteve » Thu, Feb 05, 2015, 1:41 AM UTC

jordanb wrote: post #78

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…

I'm in a similar boat as you. I went up through Calculus in school and hated it. Around 5 years ago I developed a strong interest in learning relevant applied math and have been enjoying it since. Some things I'd add: 1) Math is fun! If you have the aptitude and disposition to enjoy writing software you'll love working out math problems. They're little nuggets of mental stimulation that you can work on with just some…

> 1) Math is fun!

It's fun because its incredibly rewarding! The elation of the "a-ha!" moment in math is second to none.

> 4) Calculus and Linear Algebra ...

Though I wouldn't get too caught up in the rigor of analysis or vector spaces right away. If you are self-studying, just spend enough time to feel confident computing and manipulating integrals, differentiation, and matrix math.

Then find a good intro to discrete math textbook covering a wide range of topics: number theory, graph theory, logic, set theory, etc, and learn how to write a "good" proof. This will open up a number of mathematical doors.

Re: A Software Engineer’s Adventures in Learning Mathematics

#208

Post by cosmoharrigan » Thu, Feb 05, 2015, 2:10 AM UTC

drcomputer wrote: post #148

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…

Thanks for writing this. Over the last 4 years I switched from studying computer science with applications in mathematics, to studying math and symbolic logic with applications in computation. I did this alone, without interacting with anyone in the field. I thought I was going insane because of how many direct 'abstract' connections there are from computer science to mathematics and back again. I know these abstract…

> meticulously constructed symbolic reasoning world (...) connect such disparate symbols together and maintain that connection strongly for long periods of time

Out of curiosity, could you give an example?

Re: A Software Engineer’s Adventures in Learning Mathematics

#209

Post by p1esk » Thu, Feb 05, 2015, 2:40 AM UTC

pspencer wrote: post #149

bkcooper wrote: post #98

Earlier quoted context omitted.

If you liked Axler, you might check out Abbott's Understanding Analysis, also in the Springer UTM series. I think it covers somewhat less than Rudin (e.g. looking at baby Rudin's contents, I'm pretty sure Abbott doesn't touch Lebesgue integration) but it's a pretty great introductory analysis book IMO.

As a math graduate student, I second the choice for Abbott's "Understanding Calculus". It's a wonderful beginning book for analysis. Walter Rudin's "Principle's of Mathematical Analysis" is an amazing book but it's difficult to start with. For a quick intro to Lebesgue integration you can read the beginning of Rudin's "Real and Complex Analysis" or Halsey Royden's "Real Analysis". I haven't read Axler's book. I liked…

I think "Understanding Analysis", and "Understanding Calculus" are different books, by different authors.

Re: A Software Engineer’s Adventures in Learning Mathematics

#210

Post by darkmighty » Thu, Feb 05, 2015, 4:30 AM UTC

decasteve wrote: post #207

jordanb wrote: post #78

Earlier quoted context omitted.

I'm in a similar boat as you. I went up through Calculus in school and hated it. Around 5 years ago I developed a strong interest in learning relevant applied math and have been enjoying it since. Some things I'd add: 1) Math is fun! If you have the aptitude and disposition to enjoy writing software you'll love working out math problems. They're little nuggets of mental stimulation that you can work on with just some…

> 1) Math is fun! It's fun because its incredibly rewarding! The elation of the "a-ha!" moment in math is second to none. > 4) Calculus and Linear Algebra ... Though I wouldn't get too caught up in the rigor of analysis or vector spaces right away. If you are self-studying, just spend enough time to feel confident computing and manipulating integrals, differentiation, and matrix math. Then find a good intro to discre…

A good way to learn is to look at really good examples. I would recommend looking at "Proofs from THE BOOK" for a few gems.