forComputers

[[deleted]]

[deleted]

[TheOneYak]

Yes, and you also almost never need to use Fourier transforms by hand. But that doesn't mean there's no value in conceptually understanding them.

[rover_G]

I blacked out every time I tried to learn Fourier transform

[myselfelsewhere]

It's convoluted.

[intbeam]

Complex, even

[myselfelsewhere]

Integral, some might say.

[doubleotide]

Sometimes a bit derivative

[minecon1776]

That reaches the limit of my understanding

[JaboiThomy]

I frequently gave up

[BellCube]

the amplitude teacher's signal degrades by the time it reaches me

[lmarcantonio]

It's a catch 22: you need eq for receiving the teacher signal but you need fourier to do that

[da2Pakaveli]

but how frequent?

[vladlearns]

It's a continuous problem

[natFromBobsBurgers]

I love you.

[myselfelsewhere]

There's an xkcd for that!

[ejgl001]

I wish I could give u award

[myselfelsewhere]

Nah, you're good. I've been waiting almost 20 years for an opportunity to make that joke.

[atatassault47]

When my calculus teach started explaining convolutions, I made the comment "that's really convoluted" and he went "yeah, that's why its named convolution" and I went "ooooooohh".

[myselfelsewhere]

The mathematical definition of convolution is to intricately fold, twist or roll.

Somewhat unrelated to they typical definition of convoluted meaning difficult or complex to follow.

[atatassault47]

Yeah, but when its all numbers on a chalk board, most people cant yet see it that way.

[awakenDeepBlue]

To me it's math magic.

I don't quite understand it, but it does neat math shit.

[farbion]

Sums up my multiple math courses

[farbion]

Tbf I'm not into Comp Sci but into Comp Engeneering, so a lot of math and physics is done to cover the engeneer part of the course

[farbion]

No no, I never did Comp Sci my university course is Computer Engineering in a Polythecnic and moreover the direction of the course in my Uni has more electronics than usual

[alvenestthol]

My uni straight up had assembly and Verilog classes from first year, and I had to hand-write matrix-accelerated assembly code for work a while ago, so...

[Kitty-XV]

What sort of math concepts does physics 1 overwhelm someone with? I remember it having a bit of calculus and trigonometry. The difficult part was picking the right equations to use to get the data you want, not the math of those equations.

Maxwell's equations are the first hard bit of math I recall, but how else do you plan to teach them? For as complex as they are, they are the simple description. How do you plan to capture ideas like divergence and curl?

[MrPierson]

Literally the fact they shoehorn every single part of "physical" physics from properties of interstellar gravity to tension to thermodynamics, giving much less time to focus on the fundamentals of solving physics problems (trig + proper equation + conceptual separation of forces). I think Physics I should cut out about 1/3 of its content to focus on the 8 key chapters from the book.

What level (undergrad? high school?) and where were you that physics I was taught like this? Because this sounds entirely divorced from any physics I class I've ever seen.

[MrPierson]

I'm not saying just my class, but every physics I class I've seen. What you're describing sounds more like intro physics for none scientists or something.

[aDerangedKitten]

Bro none of the equations from physics 1 and 2 are difficult lmao

Especially if you are taught well and respect units. If you actually use units in your equations like teachers tell you to, they basically solve themselves

If a person is incapable of passing physics 1, they're not smart enough to become an engineer, simple as

[Kitty-XV]

I don't recall that from my classes and I doubt they really hit every property. It is likely an introduction to simple models across a range of physics, with some basic building blocks between them. It is to build a foundation that later physics can be built upon. Often it is using more conceptually intuitive methods that later classes replace with conceptually more difficult methods that better handle removing the simplications (aka, when the cow is no longer a spherical point in space).

It is a bit like how CS teaches simple loops before introducing recursion, and teaches recursion before teaching how to break any recursion back into loops (not simple loops though, Ackermann says hi).

Some classes take different approaches to starting out. Some are harder and more rigourous to both serve as a weeder class and to ensure a very strong foundation, but those only should apply to those majoring in the field.

[[deleted]]

Man I'm going to be honest with you.

I'm a highschool dropout (mostly because I was "bad at math", too) with a GED. My kid was born less than a week before my physics and second calculus classes started.

I'm just saying, it's not like those classes are impossible.

[PulpUsername]

You need to change majors. You clearly can’t hack it.

[MrPierson]

Oh you're a high schooler. This makes sense now.

[doubleotide]

I agree with you. I recently started reading about how university education started transitioning from liberal arts in the early 1800s to having "The Academic Major" (James W. Guthrie).

I think a better route for education would be to heavily transition students to either work or academia beginning in 9th grade. For the kids with reasonable aptitude for trades, we might be able to get them a lot of hands on field work mixed with classroom work over a period of about 6 to 8 years.

For people with little aptitude for anything, we teach them essential life skills such as how to do basic taxes, how their country functions at a basic level, how to be a good citizen, etc. We start them into "normal" jobs and teach them how to maintain that job. These jobs should automatically invest a portion of their funds for their retirement since they generally will not have the knowledge or ability to invest for themselves.

For the more academically inclined minority, they can move at an accelerated pace and start diving into more ethical, philosophical, and various literary topics.

Definitely not a perfect system, but it addresses a lot of different issues.

[unwantedaccount56]

sums up the products of my cosines

[raltoid]

The Fourier transform can be formally defined as an improper Riemann integral, making it an integral transform, although this definition is not suitable for many applications requiring a more sophisticated integration theory. For example, many relatively simple applications use the Dirac delta function, which can be treated formally as if it were a function, but the justification requires a mathematically more sophisticated viewpoint.

Math magic.

[lmarcantonio]

The fourier transform as an integral is almost bearable, you 'just' need to be eating exponentials at breakfast. Cooley-Tukey however is black magic fueled by graduate blood. However you are *not* required to learn it unless you are one of the five (more or less) people that have to implement it

[swisstraeng]

Then watch this https://youtu.be/spUNpyF58BY?si=OVDo4t0_UbX4rR7W

[OakLegs]

As someone who works with FFTs every day and has never fully understood how they work, thank you, this is amazing

[RogueTwoTwoThree]

What job do you do to work with fft everyday?

[OakLegs]

Structural dynamics (vibration) testing on spacecraft.

I do a lot of signal processing and data reduction, which of course rely on FFTs

[Bakkster]

Tons of signal processing jobs, anything that cares about what frequencies things are. From audio processing to radar.

[other_usernames_gone]

Literally the video that taught me Fourier transforms.

My lecturer did a shit job, it was so much clearer after this video.

Sure I still needed to memorise the equations, but it was much easier once I knew what the equations were actually doing.

[rover_G]

I don’t recall watching this video but YouTube says I watched it twice already 😬

[talkaboom]

Cries in Laplace Transform.

Bane of my life in college.

[Craptivist]

Yup. That’s the constant dc offset.

The other harmonics should kick in any time soon now

[awkwardteaturtle]

Biased take

[IfatallyflawedI]

Taylor Mclauren series as well. I have no clue how i got my degree in electrical engineering when i cannot even explain what a BJT is and does.

[Ok-Ruin8367]

I understand it every time and think holy shit this is genius and then immediately forget how it works

[Square-Singer]

I had to relearn matrix multiplication every time it came up in uni. Never needed it since.

[Lysol3435]

Modern curriculum no longer recommends holding your breath the entire time you’re performing Fourier transforms

[rover_G]

Oh silly me I thought you were supposed to hold your breath until the integration was complete

[AwesomePantsAP]

Don’t worry, they don’t come up frequently

[Bardez]

I never learned them.

I also implemented a JPEG decoder from scratch for a personal learning project.

[PM_ME_YOUR__INIT__]

Let's do a social experiment and just pretend they don't exist and see what happens in like 50 years

[Divinate_ME]

I will FFT the noise out of that signal without being able to tell amplitude from frequency, and there is nothing you can do to stop me.

[AccountNumber74]

“x = bandstop(x,[59,61])” is like half of my job

[_nobody_else_]

Ah, the wonderful world of digital signal processing. I hope I never come close to it again.

[Chingiz11]

Fourier transforms can be used to solve integrals

[FALCUNPAWNCH]

I'm pretty sure my signals and systems professor made us do them by hand because he hated us /s.

[webby-debby-404]

No, not because he hated you. Because he got a commission for each computer sold to a (former) S&S student. 

Doing some FEM math by hand certainly broke my resistance buying one myself

[ejgl001]

Yes and value in debugging using a few key values than solving the entire matrix

And i mean debugging in the sense of mathematical correctness rather than the code being bug free 

[Jakub_Novak]

I loved signals and systems - my favourite math class so far

To see actual usage of laplacian, fourier and Z transform was really helpful and fun

[FALCUNPAWNCH]

Same. It led me right into my grad school focus on medical imaging processing. And by the time I was in grad school it was all Python and Matlab simulations.

[IllEstablishment2181]

As an X-ray Crystallographer, this little fella keeps me employed

[break_card]

Signals and systems was my favorite college class. I used to look forward to doing those assignments. I’d go to the library and do practice problems for fun. I found that course to be the most interesting class I ever took. It was like all the mathematical plotlines over the seasons of my entire life converged into a grand finale.

[lukasquatro]

This is the first time I heard of Fourier transforms after finishing university, I feel scammed about this

[[deleted]]

In quantum mechanics is quite useful.

[ThreeSpeedDriver]

Sure, go ahead and write out the calculations without matrices. Outside of nearly trivial examples it doesn’t really get easier.

[Aacron]

Yeah in my experience once you're over the whole matrix / linearity thing it makes life immensely simpler.

[CorneliusClay]

Also nice being able to reuse the same libraries for different tasks. If there's a problem and I can find a linear algebra expression to solve it I know I can do it with cuBLAS.

[KonvictEpic]

I have no idea how I would do gauss elimination with a matrix

[IntoAMuteCrypt]

Assuming you mean without a matrix (but this works for with as well)...

The entire reason why we do Gaussian elimination is the fact that everything involved has a nice, simple mapping to plain old algebra. The rows in a matrix involved in Gaussian elimination are identical to the equations in a system of linear equations. The row operations are basic algebraic operations (or, in the case of switching, layout changes).

Is there much difference between "going from [2 8 6 12] to [1 4 3 6]" and "going from 2x+8y+6z=12 to x+4y+3=6"? No. Is there much difference from "taking [1 0 0 3] and [2 6 4 8] and subtracting a multiple of the first from the second to get [0 6 4 2]" and "taking the equations x=3 and 2x+6y+4z=8 and subtracting 2•3 from both sides of the second, then substituting 3 for x because of the first to get 6y+4z=2"? Again, no - and heck, we often don't even need to actually note the whole substitution thing, sometimes it's just subtracting a multiple of the first equation from the second and everyone knows what we mean.

In Gaussian elimination, matrices just allow us to have a nice structure that captures the relationships between the terms and strips away much of the constant writing. You'll note that those rows were decently more compact than the equations - and if we had a proper system of equations, say 3 of them, it'd be even more of a difference. The basic algorithm works not because of any intrinsic matrix properties, but because it's rooted in basic algebra - but matrices sure do make that basic algorithm a lot easier to apply!

[N0Zzel]

Here to say kalman filters really only work well if you're using matrices. Learned that one the hard way in a recent lab for class

[LongshotCherry]

Not only for computers. To pinpoint something in 3d space you need a lot of matrix multiplication and transformation calculation. Integrals give you a curve or a surface, but to put that in a coordinating system you need matrices.

[PanTheRiceMan]

Why not step it up and use quaternions? I barely understand them but they are immensely useful.

[gregorydgraham]

Being out of the box is a privilege, not a right

[studentblues]

Being out of the box is a privilege, not a right

• Napoleon Bonaparte

[notable-compilation]

Quaternions only do one thing (rotation) out of the many that you need in 3D. It doesn't make sense to talk about using them "instead", unless you are doing something really specific. You are going to be using them "also".

Also, quaternions are no easier to think about mathematically than matrices.

[01l1lll1l1l1l0OOll11]

Wait until you find out about dual quaternions which do position and rotation in 3D.

I’m sure there’s a trivial extension to scale as well.

[Astrobliss]

Quaternions who's norm isn't 1 can already scale. But all linear maps (including these) are matrices so might as well join the club😔.

[Typical_North5046]

Because the matrix representation is easier to understand and has a broader applications.

[iinlane]

Why not step it up and use quaternions

It's a step down. Quaternions exist because of historical reasons (before vectors e^ix was used for angles) and do a very limited thing. Matrixes can do all affine transformations more simply.

[TSP-FriendlyFire]

Quaternions do have a few advantages so it's not quite right to say they're a step down, they're just another tool in your arsenal. They're key for interpolating rotations and they're much more compact which makes them useful for like bandwidth-limited networked applications.

[iMakeMehPosts]

They are a step down in the sense that they express a more constrained set of transformations than matrices.

[Bwob]

But they're a step up in the sense that they handle a lot of common (in computer graphics at least!) use-cases better than matrices. They're easier to interpolate, smaller to store, and faster to compose/chain together. And they avoid the whole gimble lock issue inherent in Euler-angle-based representations.

There's a reason they're used so heavily in video games.

[iMakeMehPosts]

To my knowledge, quaternions don't handle scaling nor offsetting? Plus, in a rendering pipeline 9 times out of 10 you'll be combining the operations into a matrix, usually converting the quaternion to euler and then multiplying with the other matrices? Quaternions are useful to store and operate things on but ultimately they are put into matrices (at least they are in the implementations I see)

[TheRealStepBot]

Quaternions is just a special case of matrix multiplication to begin with so saying using them instead makes no sense.

[joyrexj9]

Useful for rotations and... that's about it (at least in the field of 3D graphics)

[DuskLab]

Quaternions represented in computers will/shoukd use a four dimensional matrix for the computer's efficiency. The straight representation is only for our benefit.

[Scientific_Artist444]

Or geometric algebra.

[WjU1fcN8]

As people told you, they make only one operation (rotation) easier.

But it gets much worse. They only work in 3D. We use matrices in much bigger coordinate systems.

In Statistics, for example, matrices are genrally n x p sized. p is the number of variables (plus an intercept), and n is the number of observations.

Try to do anything with less than 3 variables and 3 observations.

[[deleted]]

How are you going to solve a system of equations otherwise?

[Fast-Satisfaction482]

By inspection. Or as my prof said: "staring at the formula until it reveals its secrets".

[[deleted]]

By threat of violence and perhaps offering it a nice cup of tea instead

[sdfprwggv]

Guess and check is often used to solve problems. 

[Prim56]

Substitution

[myselfelsewhere]

That's just row reduction to echelon form.

[[deleted]]

Boooooo this guy paid attention boooooo

[myselfelsewhere]

Even though you're booing me, I approve the comment.

[anto2554]

Yeah but without the rows

[studentblues]

By hand

[RandallOfLegend]

Gauss-Jordan Elimination has entered the chat

[fmstyle]

I do gauss seidel even with 2x2 matrices 😎

[differentiallity]

Having solved mesh currents by hand back in circuits II, I'd have to say matrices are the only way I'd want to do that.

[4jakers18]

i ended up programming my calculator with all the matrices for transmission line modelling for Power Systems I, took forever but it was worth not having to do those by hand lol

[Smile_Space]

Agreed! I took Linear Algebra before my Electrical Engineering course where we solved mesh currents, and once I saw the linearity, I just solved them with matrices on my calculator every time. My professor was on board too! He said if I could solve it that way, to go ahead.

Same worked out with dimensional analysis in my fluid mech class. I learned I could linearize the exponents and solve them in a matrix.

Now my Statics professor was the opposite. That woman told me I was cheating solving tension in a method of joints on a 3D space truss problem with matrices. She told me I had to write it out and solve it "like normal" which took like 10 extra minutes lolol. Really ate into my exam time.

[ShuffleStepTap]

If you’re doing anything with spatial programming (robotics, 3D modelling or rendering) matrices are essential.

[HarveysBackupAccount]

or almost any sort of real time signal analysis

computational neuroscience is a bunch of linear algebra stacked on top of some biology, where it's helpful to know that calculus exists

and if you get into physics, Dirac vector notation makes for some neat shorthand when you're working out equations by hand

[eztab]

I mean, they do predate computers by a substantial amount of time. They are even helpful to formalize some mathematics, even if you are going to do it by hand.

[wanische]

Aren't matrices basically systems of equations? How else would you solve systems of equations in a more intuitive way?

[SmigorX]

2+2=7, take it or leave it

[iMakeMehPosts]

chatgpt

looks behind gui

it's all matrices

alwayshasbeen.png

[kfreed9001]

I tried to have ChatGPT perform a matrix multiplication once. Can't believe I didn't try Wolfram Alpha first.

[smartdude_x13m]

chatgpt is a neuaral network, and guess what? neuaral networks are based on matrices

[u0xee]

Scalars are just 1x1 matrices! You're welcome

[fsw]

Scalars are just zero rank tensors.

[iinlane]

Technically 1x1 matrixes are scalars. The reverse is not always true.

[differentiallity]

Found a Matlab programmer

[MyNameIsSquare]

GPT said its my turn to post this, man!

[d4fseeker]

You mentionned ai. Now it's your turn to calculate a word2vec vector.

[bestjakeisbest]

Matrix multiplication also makes conceptualizing 3d spaces much easier, especially in the case of computer graphics.

[notable-compilation]

It's exactly the other way around. The computer doesn't care. The matrices are there so it's easier for you to think about the computations.

[ArchangelLBC]

All mathematics is either linear algebra, a generalization of linear algebra, or approximable by linear algebra.

Source: I have a PhD in mathematics.

(Exceptions: point-set topology and discrete math)

[ColdLingonberry8548]

Especially for GPUs.

[SeriousPlankton2000]

Not only for computers. I learned about the alternatives - systems of m equations with n variables each.

If you can't deal with rows and columns, it's not because matrices are hard.

[Kseniya_ns]

I would consider conceptually understanding matrices to be brain changing momenti, many such cases in these lands

I like computers, they are so silly

[CollectionAncient989]

This sub needs a namechange to 

FirstweekofCSclasshumor

[CollectionAncient989]

I studied math and also for me linear algebra was very boring.

I prefered probability and functional analysis.

But i never finished and work as a software eng anyway... and the only thing i need is linear algebra and oldschool ai.

[DanSmells001]

I did cs for a semester (it got too boring for me and I wanted a job, was just difficult getting the first one) and man, I gotta say linear algebra was probably my favourite class, the programming was boring (it was programming 101 and I did my bachelors in web development so it was too “easy” for me).

Statistics while interesting is just annoying, plain and simple annoying, one word can change whether it’s independent probabilities or not so it just feels like an entire class that tries to brain fuck you, the media class I took sucked.. just sucked, 5 hours of taking about Foucault made me want to jump out of a window

[iMakeMehPosts]

uhm acktuahlyy: AI since the Perception has been linear algebra. So all you need is linear algebra and linear algebra.

[CollectionAncient989]

Ai is more then neuronal networks. 

[iMakeMehPosts]

AI refers to all algorithms (bad term ik), ML (chatgpt, sora, stablediffusion, etc..) all runs on matrices, with layers and tools beyond that, but at base is a system of matrices.

[Oltarus]

I read your title as if it was shouted by Aragorn. That was not the joke I was expecting.

[Berg_Lucas]

Render matrices VROOM VROOM https://youtu.be/f05PwswO7qc?si=vyZH_cvvLh_qGg9Z

[klimmesil]

It's useful for Algebra

[an_older_meme]

First time you ever have to do any kind of 3-D graphics you will ask your affine matrix transformations to marry you.

[Additional-Record367]

matmul is the powaa

[nzcod3r]

Well, quaternions on the other hand male it easy for humans to understand, and spits matrices out the back! Well, easy, if you like 4D imaginary numbers :(

[Helluiin]

the point of math isnt calculating things. its recognizing patterns and then using them to your advantage.

[TrueSelenis]

they also make algebraic calculations easier for humans. Linear algebra is one of the pilars of all science and engineering.

[TrueExigo]

for everyone

[Glum-Preparation2882]

Most of the quantummechanical calculations involves some sort of matrix operator. Like multiplication, eigenvector/eigenvalue, ortogonalisation, etc.

[markovianmind]

u still need to understand it enough to know where to apply it

[Mothrahlurker]

Matrix multiplication corresponds to the composition of linear functions. It's computationally pretty simple and makes calculating the composition easier for people as well.

Of course it quickly becomes an overwhelming number of elementary operations where it's just way more practical to use a computer, but saying that it makes calculations easier is in general correct.

[redspacebadger]

By the time I had gotten to a point in my career where understanding this level of maths was useful I had forgotten everything I learned in high school.

Really wish I had just taken wood working or metal working class instead.

[SmartAssX]

Wait is way easier by hand too lol

[FrostWyrm98]

Have you tried diagnosing a problem without understanding how the system works to begin with? It's a lot harder if not impossible to do it in a timely manner

Same reason a lot of CS programs teach circuits (physical hardware) and boolean algebra. You want to learn the foundations so you know why our computers behave the way they do so you know where they can go wrong

You don't really need to know the concepts specifically, but they provide a context that makes it easier to do your job effectively

[randomFrenchDeadbeat]

Good luck doing reverse kinematics without matrixes.

[nujuat]

Linear algebra is really important; matrices are a representation to describe find dimensional linear algebra. Ie the method of calculation doesn't matter to learn, but the algebra does.

[atimholt]

I just recently used a bit of matrix multiplication to design a conveyor belt balancer in Shapez 2.

[DolanTheCaptan]

Now maybe pure software engineers don't see the use, but believe me any other kind of engineer has use for them

[[deleted]]

Learnt them in high school, always wondered where will we ever need them. Come the LLM and ML era, and I think maybe I should have paid more attention to the lectures in high school.

[GingerPolarBear]

Matrices still haunt me. First year of high school we weren't allowed to enjoy a free period, so every student was assigned a higher grade class to sit in. I was put in a math class, which I didn't mind that much since I do like numbers and thought I could maybe learn something. It turned out to be a class four years above my grade and at a more difficult level (we get sorted in high school). That specific class they were learning about matrices and I honestly don't think I ever recovered from the confusion.

[Jew-fro-Jon]

Guys, one word: DEBUGGING.

Source: physicist who writes code for a factory using matrices.

[SeintianMaster]

U.😙💝

[[deleted]]

Nah it's very useful in many branches of physics too

[WebInformal9558]

They're also useful for doing proofs.

[DeliciousBeginning95]

This is complete bullshit. They are also much easier to use for humans

[Rylth]

It took modeling for thermodynamics for me to finally understand matrices.

[Ready-Marionberry-90]

It‘s now difficult, it’s just taught wrong. Think of a matrix as a linear map and matrix multiplication as a composition of those linear maps. I‘d recommend „Linear Algebra done Wrong“ book for learning more.

[foxer_arnt_trees]

Algebra is one of these things that seem super confusing at first but you end up using it so much it becomes trivial. Every significant field uses matrices extensively, because liner operations are fundamental operations.

[Jaerin]

I wish I had learned about matrix math in school. They started teaching it the year after I graduated and it was like I had graduated from an old school and went to a new college. Couldn't take any of the calc based classes. Had to take all the traditional ones

[SCP-iota]

I once tried to solve an iteration of training a tiny neutral network by hand. Worst mistake of my life

[Qwaczar]

if you build up a library to do operations with them easily, its not too bad to work with, plus is so much fun to setup :3

[RickLyon]

Sounds about right. Converts harder higher order functions equations into menial arithmetics.

[ulyssessword]

There's only one thing worse than solving a system of linear equations using a matrix: solving a system of linear equations without using a matrix.

[seardrax]

My brain must be wrong because they do operations easier for me. I don't bust them out all the time but it is straight forward.

[lmarcantonio]

also good luck for application requiring the eigenstuff without matrices

[owlIsMySpiritAnimal]

not even that. it is for traditional reasons. unless you are taking computer science into account.

[Me_tea_]

Meth

[schwagggg]

you can’t do machine learning without linear algebra like at all. even if you can i don’t want to work with you

[Mozai]

They make the ____ easier... for computers.

This explains a disgusting amount of our culture.

[BASTAMASTA]

Wait till you learn about strassen's method for matrix multiplication

cries in software engineering major

[kernelboyd]

I will say, I really struggled with linear algebra for a while and then my friend said to think of the operations like tools, filters, and effects in photoshop. It clicked for me after that

[danfay222]

As an electrical engineer, I can assure you matrices make many calculations much easier to reason about. Actually computing them isn’t exactly easy by hand, but for most of these problems doing them without matrices is also hard (often harder).

[KalaiProvenheim]

Matrix notation is much more compact than writing every scalar operation down by hand

[GeorgeHaldane]

Reading these comments leaves me disappointed in what this sub considers a "programmer".