Good morning!

Trying to (re?)learn some maths. Having some fun implementing matrix multiplication in the REPL.

I'm unsure if I ever really encountered matrix multiplication in my education. I still don't know exactly what I can model onto it.

Which maths do you get good use of in your programming ventures?

My girlfriend thinks you have to be good at math to learn to program. I say no. Some aspects, like abstract thinking, might benefit you, but you don't need anything beyond the very basics (addition, subtraction, multiplication and division) for some things. I mean, you can get by even with addition and subtraction, depending on the situation. Maybe I'm wrong, though! Maybe I'm missing out on a lot of efficiency or more advanced programming that I could be doing, because I've neglected to educate myself in this field. What do you say?

Recently I had some use for matrix multiplication in particular when implementing a Linear Programming algorithm (Simplex), for a configuration optimizer I was working with. Less recently (like 30 years ago) I employed matrix multiplication when implementing 3D bezier curves in a PostScript application. So with some decades apart, I guess I have had use for it. 😃 Not that I learnt matrix multiplication in school. I only have senior high school schooling. To me these kind of things is something I study either because I need it for something or because I get curious about it.

I should add that I was not the main developer in the Simplex implementation. I didn't know Clojure well enough to be able to pull it off. It was my main Clojure mentor who created most of the thing. I mentioned it in this thread, trying to encourage him to publish it, because it's a wonderful thing: https://clojureverse.org/t/writing-a-new-parser-for-the-prolin-library-using-instaparse/7028 But I needed to study the math involved quite a bit to be able to contribute in any meaningful way.

morning~

morning!

@reefersleep funny that you’d talk about this topic - I am a math major… 👉👈

… and I struggle to recall from my memory instances where “hard math” is critical to CS in a sufficiently “practical” context lol

(not that there aren’t application…

… it’s just that most are rather “niche”)

(but it could be because (pure)-math itself is already sufficiently niche that anything it touches also become niche by association XD)

graphics application and statistics are the only relevant domains that immediately come to my mind

but if you insist on some example, here’s a “generic” one: • background: the 6 main area of pure maths are: number theory, algebra, geometry, analysis, discrete math; (foundations) • Some Graph algorithms/Graph Theory are fully pure math, but also rather CS’y. The line/difference b/w them can get blurry. • Foundation of math is heavily intertwined with CS. Logic - not “just” ordinary logic, but logic as a formal system, meta-logic, and non-standard logic systems are all important to Programming language theory. And then there’s Category Theory (just ask the static typing ppl - but don’t blame me if you get trapped in a lecture room for hours lol)…

… and if you are willing to go full hardcore, there’s Homotopy Type Theory (applying a combination of Algebraic Topology + Foundation of math)

… (example of non-standard logic: modal logic and temporal logic. Some academic research blah blah blah trying to reason rigorously about concurrency issue in your program, preferably in an automated manner blah blah blah lol)

You're mentioning both things that I know I don't know and things that I didn't know existed 😅

• number theory is “easy (to think of applications)” - crypto. Enough said 🙀

(concrete example: zk-snark and zero knowledge proof. Homomorphic encryption - uses some commutative algebra too)

• Algebra and geometry can be hard to think of examples. Some that I heard during my times in universities: Persistent homology, Information Geometry - both in ML/AI

• analysis: well, to be pedantic (because the entrance requirement to study analysis is to be pedantic) - technically every time you solve a differential equation with computer or that kinds of thing, some numerical algorithms are used which is backed up by pure math

--

but what do I really think? well, a bit tired today, but I can think of two points: • “Just programming” doesn’t require much math. But if you do a certain kind of “software engineering” where you need to invent a whole new class of technology, then math may give you the background to find a solution/design/algorithm faster • Pure mathematics have grown exponentially in the last 2 centuries. But since high school only get you to “early modern age”, and even undergrad degree doesn’t get you fully updated, most people don’t know how vast the frontier is

My wife is also a math major :-D

good+morning!

Very thick math book for reference/inspiration/when you have lots of $$ to spare (both are picked for illustrating the “exponential growth” aspect I mentioned above): https://press.princeton.edu/books/hardcover/9780691118802/the-princeton-companion-to-mathematics https://link.springer.com/book/10.1007/978-3-642-56478-9

I think most of what you've mentioned is well beyond the scope I imagined getting into. But who knows, one thing might lead to another 🙂

Right now, I'm sussing out basic geometry, the aforementioned matrices (with no idea what to use them for), and maybe I should revisit some very basic equational axioms to ensure a solid foundation

Using geometry for graphics/art is very interesting to me, and whatever equations and matrices and whatnot that can aid that are, by nature of usefulness, also interesting. I think I'd have to have an unnaturally long life to really consider getting into pure mathematics - I've seen things that are interesting in their own right, but without an immediate application and without immortality, the interest/time ratio isn't good enough.

At least for now!