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Is linear algebra or calculus more important for machine learning?

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Ive been staring at this Coursera specialization for three hours and I feel like my brain is actually melting. Im trying to pull off a career pivot because my current logistics contract here in Bend is ending in early October, so I basically have twelve weeks to get my act together and learn enough to at least sound competent in a junior ML role. But man, the math is just hitting me like a wall. Every time I think Im making progress, I hit a wall of notation that makes no sense and it makes me want to throw my laptop out the window.

Ive spent the last week digging through different subreddits and blogs trying to figure out where to actually focus my energy because I dont have time to get a whole math degree in three months. I read on one site that linear algebra is the absolute most important thing because its basically the language of ML—you know, vectors, matrices, tensors, all that. They make it sound like if you dont understand transformations and dot products, youll never get how data actually moves through a model. But then I find these other threads where people are screaming that calculus is the real MVP because you cant do any optimization or even understand how backpropagation works without a deep grasp of derivatives.

Its super frustrating because my time is so limited and I feel like Im wasting it switching between different Khan Academy playlists and never really mastering either. One day Im doing matrix multiplication and the next Im trying to remember how the chain rule works for multivariable stuff. Here is what I keep seeing:

  • Some people say you only need applied math and not the theory stuff
  • Others say youre just a script kiddie if you dont know the underlying calculus
  • Most tutorials just gloss over the hard parts anyway which doesnt help me when the code actually breaks and I dont know why

I guess what Im really trying to figure out is which one is the actual gatekeeper for building things. Like, if I have to prioritize one for the next month to actually understand what Im coding in Scikit-learn or PyTorch, which one is going to give me the most bang for my buck? Is it the linear algebra that handles the data structure or the calculus that handles the learning part? Is one more foundational than the other or am I just screwed if I dont know both perfectly?


3 Answers
12

Late to the party, but which libraries are you targeting? Wellesley-Cambridge Press Linear Algebra and Learning from Data 1st Edition is a decent resource, though I need your stack first.


10

Unfortunately, Ive had issues with those high-priced certificates where you pay way more than what the info is actually worth. Its not as good as expected when you realize most of it is free online. If youre on a budget and tight on time, prioritize linear algebra because thats what shows up in the code errors every single day.

  • Linear algebra is the literal backbone. If you dont understand matrix dimensions and dot products, your models in Meta PyTorch Deep Learning Library wont even compile.
  • Calculus is mostly for understanding how the machine learns, but you can get by with just the basics of derivatives for now.
  • Grab a used copy of Pearson Linear Algebra and Its Applications 5th Edition for like twenty bucks on eBay instead of a monthly sub.
  • Stick to the free Khan Academy Multivariable Calculus videos for the chain rule stuff. You can definitely pull this off before October, just dont let the notation scare you... it eventually clicks once you see it in the code.


1

I felt that brain melt too when I first started. Im still not 100 percent sure which is the true gatekeeper. I think I read that calculus is for the training logic, but IIRC, linear algebra is what you use daily. Both have decent free resources online so dont spend much yet. Are you looking at engineering roles or more like data analyst stuff in Bend specifically?


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