The Maths You Actually Need

Most people who avoid machine learning maths were failed by a teacher, not by their own brain. This course teaches the genuine minimum: vectors, dot products, matrices, derivatives, probability, distributions, expectation, and logarithms. Every lesson connects to something a real model does — an attention score, a training step, a loss curve. No proofs, no exercises with the answers in the back, no pretending a definition is an explanation.

1. 1A vector is just a list7 minA vector is an ordered list of numbers, and in a model its direction carries the meaning, not its length.
2. 2What a dot product measures7 minA dot product scores how much two lists agree, but it also grows with their length, so normalise before you compare.
3. 3A matrix is a stack of questions8 minA matrix is a stack of questions, each row a dot product; without a bend between them, stacked layers collapse into one.
4. 4Slopes, and why training is walking downhill9 minA derivative says how the loss moves when you nudge one number; training just steps against it, over and over.
5. 5Probability is a degree of belief7 minA probability states a degree of belief; you judge it by calibration across many cases, never by one outcome.
6. 6Distributions, and why the normal one keeps showing up8 minThe normal shape comes from many small independent effects adding up, and most real quantities are not built that way.
7. 7Expectation and variance in plain terms8 minAn expectation is a weighted average that may never occur, and its noise falls with the square root of the sample size.
8. 8Logs, and why losses are logged8 minLogs turn products into sums and make confident mistakes expensive, which is exactly what training needs.