The foundations that matter.
WHAT LINEAR ALGEBRA PROVIDES
The language of the field: vectors, matrices, and transformations.
WHAT TO UNDERSTAND
Matrix multiplication and what it represents Dot products and similarity Eigenvectors, conceptually Decompositions, conceptually
WHAT PROBABILITY PROVIDES
Reasoning about uncertainty.
WHAT TO UNDERSTAND
Distributions and their parameters Conditional probability Expectation and variance Bayes' rule Independence, and why it is usually assumed and usually false
WHAT STATISTICS PROVIDES
Reasoning from samples to populations.
WHAT TO UNDERSTAND
Sampling and its error Confidence and uncertainty Hypothesis testing and its limits Correlation and why it is not causation
WHAT CALCULUS PROVIDES
Understanding of how models are optimised.
WHAT TO UNDERSTAND
Derivatives as rates of change The chain rule, which is what backpropagation applies Gradients and descent
HOW MUCH IS ENOUGH
Enough to read explanations and reason about behaviour.
WHAT IS NOT NECESSARY
Deriving everything from first principles, for applied work.
WHAT TO DO IF THE FOUNDATIONS ARE MISSING
Build them, rather than working around them.
