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A Software Engineer’s Adventures in Learning Mathematics

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Re: A Software Engineer’s Adventures in Learning Mathematics

#191

Post by brational »

rntz wrote: post #184
qmalxp wrote: post #117

Earlier quoted context omitted.

Re: 4). As a pure mathematician, I would argue Calculus and Linear Algebra are the father and mother of pure math as well (okay maybe not logic).

Number theory. Set theory. Category theory. Combinatorics. Graph theory. Linear algebra certainly has applications in some of the above. But I don't think that calculus & linear algebra can be fairly described as "father & mother" to these areas. (Am I wrong? I could be missing some connections; I'm not a mathematician.)

Not wrong - the poster above you probably means pure math in the analysis sense - real analysis, topology, functional analysis, algebraic topology. All of which are abstractions/generalizations (zoom out, if you will) from the real life world of 2 and 3 dimensional calculus/LA to N or infinitely many dimensions.

Re: A Software Engineer’s Adventures in Learning Mathematics

#192

Post by nkurz »

graycat wrote: post #174
graycat wrote: post #172

Earlier quoted context omitted.

Part II -- More Specific After freshman calculus, it would be good to start with abstract algebra . There you will get handy with (relatively simple versions of, and, thus, a good place to start -- and, I have to say, put you ahead of a surprisingly large fraction of the best chaired professors of computer science) theorems, proofs, sets, axioms, groups (once I published a paper in multi-variate, distribution-free st…

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.

Re: A Software Engineer’s Adventures in Learning Mathematics

#193

Post by kirse »

decasteve wrote: post #160
[deleted] wrote: post #150

Earlier quoted context omitted.

[deleted]

I had a couple of things in mind. One was means. That you can solve a problem by restating another way, in a way that it's almost indistinguishable from the original. e.g. solving a problem in linear algebra that also solves a problem in graph theory. solving a group theoretic problem that gives you an answer in topology. solving a problem using category theory that gives you a combinatorial answer, using quaternion…

Thanks! I had deleted under the assumption it would just get lost in the pile of comments.

Re: A Software Engineer’s Adventures in Learning Mathematics

#195

Post by Chronic31 »

jackpirate wrote: post #11
sz4kerto wrote: post #7

Earlier quoted context omitted.

Most of us (engineers of any kind) learn quite lot of maths during uni, and most of us forget 90% of that as it's not needed in most jobs, which is a shame. The thing I have needed all the time is statistics and prob. theory, that keeps coming up literally everywhere. Calculus - not so much. If you need something, you can always re-learn it quickly. (For example, I learned quite a lot of linear algebra, but haven't u…

As a machine learning guy, I can't imagine doing stats without calculus and linear algebra :)

From sklearn import svm

Done

Re: A Software Engineer’s Adventures in Learning Mathematics

#196

Post by grecy »

It's interesting someone who studied Software Engineering didn't get a solid math education at university.

I studied Software Engineering, and am a certified engineer. I sat next to the Aerospace, Chemical and Mechanical engineers for all 4 years of "Engineering Math". (They did crazy physics and chem that I didn't)

How can you call yourself a "Software Engineer" without having studied a huge amount of math?

Re: A Software Engineer’s Adventures in Learning Mathematics

#197

Post by Yhippa »

vdnkh wrote: post #103
brational wrote: post #97

Earlier quoted context omitted.

>I think it's dishonest to call yourself a Software Engineer and not have an engineering degree. Definitely semantics. For example, I have a BS/MS in applied math from a good engineering school university. I am a software engineer mainly working with ECEs, physics, and other math guys, who are all "software engineers". I see where you're coming from about being a SW eng without knowing a lot of math - but there are o…

Right, an engineering degree is a guarantee that you know the important points of what it means to be an engineer. Ethics, engineering process, math, etc. When you get an engineering degree from a certified university, you are an engineer. It's a guarantee that (at one point, at least), you possessed the set of skills and knowledge determined by a board of professionals to be necessary for a career of engineering. Ot…

I think one thing that's understated is the amount of time we spend in ethics classes. I felt that there was always a semester where I was in some form of ethics or engineering history class.

Re: A Software Engineer’s Adventures in Learning Mathematics

#198

Post by gsastry »

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…

Did you start an accredited Math degree? If so, how did that work for you, and how did you get into the program?

Re: A Software Engineer’s Adventures in Learning Mathematics

#199

Post by csirac2 »

Pyret wrote: post #52
csirac2 wrote: post #26

Mary L Boas "Mathematical Methods in the Physical Sciences" [1] has absolutely been my favorite and most-used maths text in the 9 years since graduating uni. It's like a reference manual of just about all the non-CS (i.e. continuous/non-discrete) mathematical techniques required in my career. Highly accessible. It's a little too terse in places but I prefer this style of presentation over the insane long-form verbiag…

Note the OP chose typical why-books for math majors(Axler/Macdonald). Boas' is a how-book for physicists.

That's an important distinction, thanks.

Re: A Software Engineer’s Adventures in Learning Mathematics

#200

Post by bigger_cheese »

sz4kerto wrote: post #7
bndr wrote: post #3

I always thought that being an Engineer assumes you have knowledge of mathematics. The way this word is being used in Software ist kind of strange. "I built a blog in php, I'm a Software Engineer" - this feels kind of awkward to me.

Most of us (engineers of any kind) learn quite lot of maths during uni, and most of us forget 90% of that as it's not needed in most jobs, which is a shame. The thing I have needed all the time is statistics and prob. theory, that keeps coming up literally everywhere. Calculus - not so much. If you need something, you can always re-learn it quickly. (For example, I learned quite a lot of linear algebra, but haven't u…

I find my self surprised just how often Linear Algebra pops up. A few years ago I was doing some work with Splines, trying to smooth some noisy plant data and I had to relearn matrix decomposition (LU factorisation). Every year or so since I've been ambushed by some other "stealth" aplication of linear algebra in something you'd otherwise think would not be applicable. Nowadays my old beat up linear algebra text book from uni sits right beside "C in a nutshell" and the printed GDB manual on my shelf at work.
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