Calculus or Bust

So this is funny. To do anything technical with machine learning, you need advanced maths skills. Specifically:


  •     Linear algebra
  •     Multivariate calculus
  •     Probability and statistics

 

Great. So I'll learn those. What's involved in each? Breaking those down (thanks, Claude), we have:



1. For Linear Algebra:

  •     Matrices and matrix operations
  •     Vector spaces and subspaces
  •     Systems of linear equations
  •     Basics of calculus (limits, derivatives, integrals)
2. For Multivariate Calculus:
  •     Single variable calculus (derivatives, integrals, optimization)
  •     Partial derivatives
  •     Multiple integrals
  •     Vector calculus (grad, div, curl)
3. For Probability and Statistics:
  •     Sets and set theory
  •     Combinatorics
  •     Fundamentals of probability
  •     Discrete and continuous probability distributions
  •     Descriptive statistics (mean, variance, etc.)

 

Gulp. Okay. One at a time. I'll get there. Let's pick one of those prerequisites and break that down further. What do I need to know to learn single variable calculus?



2.1. For just Single Variable Calculus:

  •     Precalculus
  •     Limits
  •     Differentiation
  •     Integration
  •     Optimization

 

Okay, this is more than a YouTube video. But it makes sense to study Precalculus first, so no biggie.



2.1.1. For just Precalculus:

  •     Algebra
  •     Trigonometry
  •     Functions

 

Aha! Things one learns in school. Except I didn't go to school. I was home educated and we didn't do maths. The maths I did afterwards in college is long forgotten; I don't even know what topics it covered.

So, Precalculus. But... but... those sub-topics have dependencies too.

Fine, lets take another step back and start with a course in 'pre-Precalculus'. Great. First lesson: imaginary numbers. Simplify i to the power of 227. Simple, apparently, when you know the properties of exponents.

YouTube. Learn the properties of exponents. Got it. But in order to apply them I need to know basic long division, which... I never learned.

Today, dear reader, I learned how to long divide.

It's a long, hard road from here to multivariate calculus (and all the other essential maths areas). But I feel weirdly good having just learned a tiny piece of it. It's just a jigsaw puzzle. And jigsaws are satisfying as you make gradual progress.

Let's see where I'm up to a year from now.



 (Random calculus image pulled from the web - credit to openlab.citytech.cuny.edu.)


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