Start here: notation and Python
The language and the tools that every other track uses: how to study so that you remember, how to read math notation, NumPy, the functions of ML (exp, log, sigmoid, softmax), and short first looks at vectors, derivatives, probability and proofs.
For people who want to learn machine learning but whose school math or Python is rusty. You need arithmetic, basic algebra (solve 2x + 3 = 7) and a web browser; the notebooks run in Colab, so you install nothing. If you already read Σ-notation and NumPy with ease, skim the summaries and do the quizzes.
Quick recap
The key takeaways of all lessons on one page
All interactive figures
Every figure of the track on one page
Videos and books
The best free courses
Glossary
Every technical term of the track with a short definition
Concept map
How the lessons of this track connect to each other and to other tracks.
Keeps every lesson page and figure of this track in this browser, so you can read it without internet.
How to learn here
Active learning, spaced repetition, and how to use the figures, quizzes, cards and notebooks of this site.
The language of math, and its code
Sets, functions, indices, sums and products, Greek letters, and the same ideas as NumPy arrays.
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02
Reading math notation: sets, functions, indices, sums and productsThe symbols that every ML paper and every later lesson uses, each with a small example. Sets and intervals, functions and composition, indices such as x_i and x^(i), Σ and Π with their rules, max versus argmax, and the Greek letters of ML.
55 min
5 figures
Beginner -
03
Python and NumPy for math: arrays, broadcasting, plots and random numbersThe Python you need for this site, and NumPy arrays as the code form of vectors, matrices and Σ-sums. Shapes, indexing, axes, broadcasting, * versus @, plots, seeded random numbers and float surprises.
70 min
5 figures
Beginner
Functions you meet in ML
Lines, powers, exp and log, then the sigmoid, softmax and log-sum-exp that turn scores into probabilities.
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04
Functions you meet in ML: lines, powers, exp and logThe graphs and rules of the functions that every ML formula uses. Lines and slope, moving and scaling graphs, powers, the exponential and its inverse the logarithm, the log rules with their reasons, log-scale plots, and why ML works with log-likelihoods.
55 min
5 figures
Beginner -
05
From scores to probabilities: sigmoid, softmax and log-sum-expHow a model turns real-valued scores (logits) into probabilities. The sigmoid and its inverse the logit, the softmax and its shift invariance, temperature, the log-sum-exp as a smooth maximum, and the max trick that keeps all of them from overflowing.
55 min
4 figures
Intermediate
First looks at the main tracks
Gentle tours of vectors, rates of change and chance, each a bridge to its full track.
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06
A gentle tour of vectors: arrows, lists, length and the dot productA vector is an arrow and a list of numbers at the same time. Addition, scaling, length, distance, the dot product and its angle, cosine similarity, and a linear model as a dot product.
55 min
4 figures
Beginner -
07
Rates of change: slope, derivative and the gradientThe derivative is the slope of a curve at one point, the limit of secant slopes. The gradient collects the slopes of a function of many variables; it points uphill, and gradient descent steps the other way.
65 min
5 figures
Intermediate -
08
Chance and data: probability, mean, variance and the normal curveProbability as long-run frequency and its basic rules; the mean, median, variance and standard deviation of data (with n or n − 1); histograms and densities; the normal curve, z-scores and the 68–95–99.7 rule; and why averages become normal (the central limit theorem).
60 min
5 figures
Beginner
Reading and writing proofs
Direct proof, contradiction, induction and counterexamples, so that the theorems in later tracks are readable.