(Every time I write something like this I immediately feel defensive about being an impostor. Someone saying, "how can you not know that? You should know that. You must not be doing _real programming_.)
My current take is that the tech industry is so young that we are still struggling with proper definitions of titles and division of labor.
In my experience, after school I could do all the hard mathy/algo/data structure things, but I had no idea what REST even meant. So all startups instantly rejected me, while FAANG was very excited to have me. I felt like a huge imposter also, because if I were smart, how come I didn't know all the cool stuff that people at hackathons know.
When I graduated I had no clue how to correctly statistically validate a complex robotically collected set of bathymetric data or how to mathematically explain Universal Kriging. But I did know how to design and build the data collection workflow, web portal, processing software, and PDF generation. So I was ridiculously effective at my job, but any time I was near the other roboticists, I felt like an absolute fraud. They'd be writing algorithms and formulas on a whiteboard and it was all Greek to me.
You can make something, and
You can engineer something.
If what you are building is a complex distributed software system, if you are not aware of algorithms and the implications they have on the system, then you are not engineering, you are just making. And whatever it is you are making is going to fail a lot sooner that if you were aware of the algorithms and the implications.
A lot of people never touch algebra again.
Some of us end up touching it a lot.
This is a bit of a tricky thing, in that:
- A whole lot of practitioners have very limited continuous math and deep CS needs, so some of these requirements are artificial barriers to some extent for many jobs.
- But is it reasonable to give them CS degrees without at least basic competence?
- Plus, part of the point of a university education is to round-out students and expose them to many things...
Yes, when we truly understand "competence".
A lot of "math" as talked here, is not part of what make a programmer competent FOR programming.
It only make you competent for THAT segments of math.
That is something that many has a hard time understanding: Programming is NOT math. Equally as math is NOT programming.
If you are studying FOR programming/CS, math is ASIDE. Is not the focus.
Similarly, if you are FOR math, programming is ASIDE. Is not the focus.
Basic algebra is quite useful. It's reasonable to expect most programmers to be able to do simple algebra when it comes up. There's a whole lot of reasons:
- Analysis of algorithms and work done generally involves manipulating algebraic expressions and factoring.
- Reordering numeric expressions in code means understanding the composition of operations and invertibility.
- A whole lot of work can often be avoided by being able to derive an equivalent expression.
Yes, continuous math isn't "CS math" but it's a reasonable thing to expect a programmer to be competent in.
Similar, Perform music is too. And learn about accounting. Or law.
But IS still "aside". Sometimes, here in THIS function, I need to apply to algebra. But that is not the majority of the tasks, neither, learn algebra help me much about the whole endeavor (maybe only if I'm building an algebra library).
> but it's a reasonable thing to expect a programmer to be competent in.
Any person too?, maybe. I heard identical arguments in other fields. No joking, even in a law firm.
Curiously, by people that probably are better at THAT that the actual problem they have, in their niches, where -despite not be my job- I could have better idea...
Sorry-- I completely and totally disagree with you. The core things I learned about mathematical structure in algebra classes have informed my entire programming career: pure functions, commutativity and associativity, factoring and composition. Both discrete and continuous math are necessary to be a computer scientist. Yes, you may be able to do some things without them... but you're going to be limited.
> Any person too?, maybe. I heard identical arguments in other fields. No joking, even in a law firm.
Algebra is basically required for a secondary education at this point, let alone college. Yes, it has broad applicability. Even in law: we expect many lawyers to be competent at calculations that are best addressed with algebra.
Sure, but CS is still about "Computing", not algebra or calculus!
They also offer a lot of "math for non mathies" courses, which would have been a great place to teach quadratics.
Imagine if you had been given an exercise of such a low level nature for every single topic you might touch in IT in the future. You would have had to code a function to do UTF8 decoding, JPEG rendering, TCP/IP error correction, font rasterization, ray tracing, PEG parsing, an USB driver, data diffing, model training, etc.
Also, you don't learn much about programming by creating a function to factor a quadratic equation. You seldom learn about types, side effects, algo complexity, or even about collections, iteration, branching, memory, debugging, etc.
You just learn to badly translate a very specific, narrow problem to the language you use.
Actually, I have, because I've done a fair bit of embedded development and "toss this massive lib on" is not always a reasonable solution. Inferring the structure of plant in controls is often a polynomial factoring problem and it's not something that one tosses Singular or FLINT at on small hardware. But aside from that...
Factoring a quadratic by hand is something I expect a CS major to know how to do, because they might very well be doing algebraic manipulation to develop solutions to real world problems.
And someone who knows how to factor a quadratic by hand knows a number of formulaic (suboptimal) steps to perform it-- the exact kind of things that's easiest to translate to code before you have gotten into that mindset of explicit thinking.
So--- declare and manipulate variables to do the quadratic formula. OK, what if we want to confine ourselves to integers, what can we do? Can we loop and search solutions in some meaningful way like a human would?
It's a completely reasonable space to explore as an early programming problem for someone who's familiar with it.
I'm teaching a secondary student to program right now. In his core math class he's doing a lot of trig. In turn, we're doing a whole lot of exercises like "make these dots chase the other dot using atan2 and sin/cos".
Can't argue there :)
> Factoring a quadratic by hand is something I expect a CS major to know how to do
Agreed, I'm more concern about teaching programming while asking such a task. Once you have solid foundation, you can have valuable insights by doing this exercise about float based maths, moving variables around, naming things, translating maths to code. But before that, I think it would hinder learning.
> And someone who knows how to factor a quadratic by hand knows a number of formulaic (suboptimal) steps to perform it-- the exact kind of things that's easiest to translate to code before you have gotten into that mindset of explicit thinking.
I disagree, because it takes 2 abstracts things and mix them together. It's a harsh first step. As a teacher, I get better results when I map coding to some concrete reality first. Later on, yes, you can mix.
> I'm teaching a secondary student to program right now. In his core math class he's doing a lot of trig. In turn, we're doing a whole lot of exercises like "make these dots chase the other dot using atan2 and sin/cos".
This is what I'm talking about. I have terrible results with those for anybody who doesn't really love maths. But creating small games and analysis the text of their favorite song are instant hits.
He def doesn't love math. But he just finished the swarm thing and it's awesome.
A quick search tells me that factoring quadratic equations is covered around grade 8 or 9. I'm guessing that the instructor assumed that everyone would have enough math to know how to do this or quickly refresh their memory so they could focus on the programming aspects and not the problem solving.
It is not totally unreasonable to expect students in an intro to CS course to have some basic competency in algebra (university dependent). Giving them a problem in a domain they're already familiar with (or that where familiarity can be expected) lets them, in theory, focus on the algorithm/data structure side without having to also be taught the domain. Most of the exercises in a first CS course are solved with libraries (standard in some languages, or 3rd party in others). That doesn't mean it's not useful for developing the knowledge the course is aiming for.
Do you also think we shouldn't teach arithmetic and should only teach using calculators? (You may, actually, I know people who think that way.)
Besides, most intro to CS courses also include basic algorithm analysis (that may not be true for the non-major version of the course) which means the course will require the use of at least arithmetic, probably some algebra, and some basic calculus. So why not write programs that make use of math when you're already assuming the students are competent in basic math?
At least at the universities I was familiar with, a non-major first CS/programming course was generally targeted to STEM, but not CS, majors, so again familiarity with algebra would be a reasonable assumption (at GT, these were taken by the various engineering majors and used Matlab as the language of instruction, I think they previously offered Fortran).
I feel like I'd be more on board if you said something like "compute an integral", etc. Factoring is just.... a single equation.
I've been a successful software engineer for over ten years, yet without looking it up, I don't even know what "factoring a quadratic equation" means, let alone how to do it.
Code refactoring and factoring in algebra are related in the sense that they aren't meant to change the system (that is, its meaning or behavior), but instead are meant to change its appearance. In particular, in the above, if you can factor it out you end up with the two roots (what I termed r_1 and r_2) of the equation, which are useful for various other things.
This is hard to understand because it doesn't make sense. Quadratic polynomials (or more generally, algebraic expressions) are factored. Equations are not factored.
x^2 + 2x - 3 = 0 = (x+3)(x-1)
This is not factoring?
The idea that you might not know how to do it as someone working in a STEM related field wouldn’t come to me.
I think this very much depends on what you end up specializing in. I bet a lot of the code we write every day has a dependency buried somewhere where all sorts of equations end up getting factored.
Both statements can be true, but neither negates the utility of the activity.
If you are going into a Math heavy domain, you are going to use a programming language to solve math problems, and hence involves learning Math.
This the same problem, with whiteboard leetcode style problems in interviews. Most people fail to understand why they have to put in months to years of practice into a domain to which doesn't concern with their everyday work.
On the other hand there is tremendous shortage of people with skills for real world problems and applications.