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.