Not to pile on, but if linear algebra is really a part of the day-to-day job and not some manager’s mistaken idea of a proxy for more general talent, then you’re hiring specialists and the pool will not be that large. People who remember all their math and enjoy it and can also code, are also very employable at all the AI companies and departments, including at Meta.
And how do you know if someone’s eligible for security clearance without applying for it? (Other than the obvious “be a US citizen, don’t be a spy” part.)
> if linear algebra is really a part of the day-to-day job [...] then you’re hiring specialists
It kind of bothers me that the parent and other readers here are passing off knowing linear algebra as some kind of esoteric skill. Linear algebra is a year 2 course in a undergraduate eduation. There are polished libraries to make it fast.
Unless you mean enough knowledge to be writing linear algebra libraries, there is no need to consider this skill a high hurdle.
It's not so much that it's esoteric, it's that it's not something most people use every day, and skills decay over time. I mean, Differential Equations (Diff-e-screw) was a year 2 class for me, and I assume I'd fail it if I took it today.
But most people that have any exposure to it can pick it back up fairly rapidly. And most people that have a reasonable exposure to math in general could probably come up to speed (a little less) rapidly.
> Linear algebra is a year 2 course in a undergraduate eduation.
From what I’ve seen, the year 2 course is great for graphics programming, game development, that sort of thing. It’s not enough for the tasks that require more serious linear algebra, when you’re working with systems of linear equations, large matrices, etc. These “big” linear algebra problems come up a lot in fields like physics simulation, finance, and machine learning / AI.
I’ve done some hobby work in graphics and game development, and I’ve done some professional work in physics simulation. The kind of linear algebra you use in physics simulation is a different beast.
I would expect the type you are talking about to be described as something more like scientific computing or HPC or something, right? Numerical methods.
Huh, interesting. What did they cover? I guess I thought you were talking about stuff like sparse iterative solvers (Krylov subspace, that sort of stuff). But those are computational tools mostly, I guess, right?
The math department at my college had three linear algebra courses.
“Intro to linear algebra.” 200-level. Vectors are (x,y,z), more or less. Class includes math, engineering, science, and business majors. 200-level makes it nominally a second-year course but lots of first-year students will take it. Required course for many different majors.
“Applied linear algebra.” 300-level. Vectors are finite. Eigenvalues, linear transformations, determinants, matrix algebra, factorization. Touches on numerical methods but doesn’t spend much time on them. Students were mostly math, with some physics and electrical engineers mixed in.
“Advanced linear algebra.” Series of two 400-level / 500-level courses. Almost exclusively math majors and math grad students. Algebraic topology, tensor spaces, exterior algebra, spectral theory, differential forms.
There were also numerical methods courses—one in the math department and one in the CS department.
I don't think it's esoteric, I just don't think it's used much in real-life, day-to-day software engineering as practiced by most professionals. I didn't mean to imply it's a high hurdle, just that IMO a minority of actual SWE's are going to bust out the proverbial slide rule, and anecdotally it seems like they have a lot of options.
That it's a year-2 undergraduate course for some people argues more for forgetting than remembering it, if you're not using it regularly.
Linear algebra may well be year 2 in a math B.S. program, and you’ll encounter it in physics and quite a few engineering fields, too. Maybe a bit of linear algebra in CS. And a lot of graduates who go do something else for a while will not remember too much linear algebra.
I can easily imagine that an overly aggressive linear algebra requirement will eliminate many excellent candidates.
I got a CS degree from a fairly high ranked state university.
Linear algebra wasn't a requirement. I took it as an elective just for my own curiosity. I have a feeling loads of programmers really don't know anything about linear algebra, and probably a large number are like me and learned it due to interest in game development.
The upstream comment mentioned Linear Algebra as a base requirement for applied programmers in their domain; satellites, remote sensing, communications, navigation, etc.
You can assume they're interested in esoterics like those who can grasp the spherical harmonic equations used to model the daily magnetic flux epoch models to control sats via mag torque, those who can do a multivariate 512 dimensional SVD reduction against pipelined multi spectral data to create sharpened images, create fuel optimal paths in constrained resource starved environments while dodging projected debris paths, .. you know, all that jazz.
How many years do you expect most working professionals to remember the content of each of their undergrad courses - unless they use it on a regular basis?
In Australia Linear Algebra was straight out of high school first year university basic STEM common core math course work for Engineering, Physics, Chemistry, Medical, Biology, etc. streams.
I’ve seen it put after calculus for whatever reason, usually. Surprisingly, even for engineering students, calculus often takes up the first year of classes in the US.
In Australia, and a number of European countries, Calculus takes up the last two years of high school in the advanced stream (for anybody intending to go to university and take Law, Engineering, Medicine, Physics, Chem, etc).
Interestingly in serious university mathematics when looking at the foundations of mathematics, Linear Algebra is a functional prerequisite of multivariate calculus and anything higher dimensional as LA provides a literal basis for abstract spaces and local approximations to continuous functions, etc.
At the place I went, they designed the curriculum around students that came in without it. But I guess testing out gives room for a gen-ed.
I dunno. The vibe in high school’s hardest math class and college’s easiest math class is kinda different. Might be worth doing both, haha. Easy A, too.
I generally think it should be taught along calc 3 (advanced integration and differential equations), as there's decent conceptual overlap and basic calculus helps weed out those who might not be ready for a more rigorous course.
Also to clarify wrt calculus, it is very common for university-track students to take AP calculus in high school, which allows them to take an examination that most universities accept to prove mastery of the equivalent to calc 1 or calc 1+2 depending on the examination.
Here in the US I was: calc 2 (year 1), calc 3, linear methods (year 2), discrete math, theory of computation (year 3). The downside being that the math and comp. sci courses had no overlap, so I've basically forgotten the first 1.5 years. Might have been better off at a state college.
And wow, coming in from the other end of the scale to even the bias...
Did an internship in biotech then spent the next ten years working the only 2-3 blue collar jobs I could land while applying to thousands of jobs per year and writing hundreds of cover letters per year: retail, call centers, IT, software development, comp sci, secretarial, and other random fields I have certifications in. All told, zero interviews. Spent my spare time working on open-source projects and tutoring programming and data science.
Suffered a horrible work-related injury near the end of the decade and had to quit, but just as my savings were about to expire I managed to find a government contracting job for 80K/year, which is nearly 3x my previous salary. I suffer incredible pain at work due to my injury, and spend all my spare time recuperating and exercising, and spend all my money on healthcare and moonshots to no avail. I've wound down all my hobbies. I thought I'd start socializing once I could afford it, but I'm in too much pain.
Competence in government really doesn't reflect my experience in landing a job. What a silver lining. When I can barely walk I can just not show up and nobody would even notice. So career-wise I don't think I'm going anywhere. Life-wise I'm limping on, I guess.
At my university, the quickest you would be able to take it was the second year because Calc 1 and Calc 2 were considered pre-reqs. Assuming you're a normal student doing only Fall/Spring semester, you can't take Calc 1 and 2 simultaneously.
Unless you had AP Calc in high school and managed to get the university to accept it. I think quiet a few ABET schools don't accept AP Calc as a full replacement for Calc 1 if your an engineering major.
Agreed - If you got a Computer Science degree from an engineering school, you probably had to take Linear Algebra as one of your required classes. Also, Linear Algebra is not that hard to learn.
And you’re going to remember that at a job interview 10 years later after never dealing with it after class? Uh, no.
I took through calc 3 + discrete math, but didn’t have to take the full linear algebra course for the BS in CS. I’m sure I could refresh myself on calculus, but almost no one is regularly maintaining their more advanced math knowledge in this field.
The bigger risk I think is that most engineers took it in the first couple years, didn’t realize they were applying it in all their other classes, and forgot about it.
Why is this down-voted? I was going to add most people have already seen some sort of linear algebra even in high school. Determinants, Gaussian elimination, etc.
It's unclear what "linear algebra" means to GP, though. I agree writing linear algebra libraries is next level, since that involves numerical code and knowing FP math well.
The number of American (and most other countries too) students who interacted with Gaussian elimination or Determinants in High School can fairly safely be rounded down to zero.
Isn’t linear algebra heavily used in machine learning and computer graphics (not just know it, but be able to wield it proficiently)? So ya, the talent probably exists, but they hit the “these engineers are making half a million a year to do something else” problem.
Yes, exactly, I would (naïvely) assume it's common among e.g. ML specialists, who are in high demand and thus hard to recruit. I'm sure there are a lot, but if I had to extrapolate from experience ("OK, who's good at math, hands up?") I would say it's less than 20% of coder genpop.
There is a lot of published research work in ML that had huge impact without explicitly touching linear algebra.
Given that is the case, to answer your question: yes, linear algebra is the foundation of ML. No, a lot of impactful day-to-day ML engineering can be done without touching linear algebra.
This is how assembly is the basis of compilation and programming. But you probably are going to get a whole lot of work done without ever using it.
It's generally a nice flex when applicants can code assembly, and usually a yellow-flag when the company suggests they require knowledge of assembly.
To me, my eyebrows raise when an industry person mentions linear algebra. I'm just saying the odds are really low that you actually use it.
> People who remember all their math and enjoy it and can also code, are also very employable at all the AI companies and departments, including at Meta.
That's either a wishful thinking or a stretch of definitions, IMHO.
What about the opposite? My math is getting super rusty but it doesn't matter because all I do is push protos around. Yet I seem to be pretty employable.
> And how do you know if someone’s eligible for security clearance without applying for it?
The short answer is "You can't, not with 100% certainty.".
Based on my experience from decades ago, the long answer is "Anyone who's a US citizen and doesn't lie about their drug use and debts can get a Secret clearance.". Things MIGHT have significantly changed since my clearance lapsed way back when, but I doubt it.
Actually, after engaging my brain a bit more fully, I realize that one can be eligible for a security clearance but fail to actually be granted one.
That is, eligibility concerns whether or not the State Department will consider your application, not whether or not they will grant the clearance after performing their background and lifestyle investigation.
And how do you know if someone’s eligible for security clearance without applying for it? (Other than the obvious “be a US citizen, don’t be a spy” part.)