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Comment by _cbsz | Hacker News Reader

I run screaming from courses that cover mathematical background I don't have (e.g., machine learning because of linear algebra) because it's impossible to keep up without having terminology and definitions memorized.

Recently got annoyed with the overuse of math in http://www.eecs.umich.edu/courses/eecs461/lecture/Lecture8.p... . The lecture covers numerical integration in an embedded system. If you know dx/dt = f(x,u) (where u is the input), the completely obvious approximation by computer is to execute x += dt * f(x, u) at intervals of dt seconds. Said lecture takes ages to get to this point, unnecessarily puts things in matrices, and never puts the point so concisely. IMO, it's easy to use linear algebra to belabor simple points.

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You know the missing mathematical background isn't actually that hard to learn. And once you learn it, you may notice important details you're currently missing.

For instance the lecture you got annoyed with was covering how to correctly model a second degree differential equation. So you know that d^2x/dx^2 = f(x, u). This is a different and more complicated problem than a first order differential equation. They handled it by turning it into a system of first order differential equations. And then demonstrated how the obvious way to do it lead to numerical instability, creating a physically incorrect result. And then they had to do more complex stuff to avoid the numerical instability.

The underlying concepts share a lot with a simple first order equation. But the generality is letting you tackle and deal with issues that a simple model can't. Plus the technique described can be expanded in a straightforward way to model a combination of interacting things.

But you froze up at the idea of linear algebra and didn't even realize that they were dealing with a much more complicated problem than you thought.

It could be easier to understand if instead using z-Transform they shown that you could do better numerical second order integration if you take few previous points into account instead of just one as in naive method of integrating twice with forward Euler integration.

Of course purpose of this lecture was probably not to make you understand what you are actually doing while numerically integrating, just to teach you how to put this stuff into simulink that has z-Transform as one of it's primitive building blocks.

I did just fine, thank you. Matrix form is not necessary to tell me that we need to approximate both x and dx/dt in order to use our knowledge of d^2x/dt^2. It is not particularly difficult to remember that the second derivative is the first derivative of the first derivative.

I run screaming from courses that cover mathematical background I don't have

I had the opposite attitude when it came prerequisites in college. For example, I had no problem taking a course that required linear algebra, or signal analysis, or data structures (none of which I had taken; eg, I took Data Structures II before I). You pick up the missing pieces as you go. I actually had more fun that way - "Signal Analysis" was much more interesting when I already knew the applications!

BTW, I didn't do this on purpose. I was trying to get these classes in to fit my schedule.

I was always annoyed during college how math notations occluded what was actually happening.

I always had to translate math to common sense. Translate derivatives to speeds of gain, gradients to slopes, vectors to movements and so on. Only then I could understand why given theorem actually might be true (and useful). I could often spot some error in lecture during this process. Unfortunately my peers were most of the times not able to do the same (at least not in real-time).

I think much more general understanding could be achieved if my teachers could stand back from math notation and do some hand-waving more often.

It's weird - I find it a lot easier to understand theory when I'm presented with an opportunity to use said theory. Linar algebra isn't terribly hard to get started on, and seeing it used will reinforce your understanding.

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