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Orientation: relearning math
Why exam math did not stick, the three-pass method, and a cold diagnostic that finds your real holes before you waste time on things you already know.
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Math Relearn · companion to your ML notebook
Mathematics, rebuilt for
machine learning.
You already met all of this once — for an exam, on a deadline, with a formula sheet. This is the second pass: same ideas, but built around why they exist, what they mean geometrically, and where they show up inside the models you actually train.
1 · Remember
Retrieve before you read. Cold questions first — the discomfort of half-remembering is the signal that tells your brain to keep it this time.
2 · Understand
Every formula gets a picture, a purpose and a "what breaks without it". Notation is treated as a language to be read, not a ritual to be copied.
3 · Implement
Each idea ends in NumPy / scikit-learn code you can run and break on purpose, so the abstraction lands in your hands, not just your notes.
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—Quiz accuracy
Why this site exists
Learning math to pass a test produces a very specific kind of knowledge: you can recognise a problem, recall the recipe, and get the mark — and then it evaporates, because it was stored as procedure with no purpose attached. Machine learning punishes that hard. In ML, math is not an entrance exam; it is the working language. A matrix is your dataset, a gradient is your training signal, a probability is your model's confidence, an entropy is your loss function.
So this notebook is organised the other way around: every topic starts from the problem it solves, moves to the picture in your head, and ends with the line of code where it becomes real. Goal: reach machine-learning fluency — and be genuinely ready for deep learning and agentic models afterwards, where this same math is used at larger scale.
The path
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Start here · Orientation
Find your holes with a cold diagnostic, then learn the three-pass method the whole site runs on.
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Core tools · notation, linear algebra, calculus
The two languages of ML: space (vectors, matrices, eigen, SVD) and change (derivatives, gradients, chain rule). This track is the heaviest — and the highest leverage.
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Uncertainty · probability, statistics, information
Data is noisy and samples are small. This track is how you make honest claims: Bayes, distributions, estimators, tests, entropy and why losses use log.
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Learning · optimization and the algorithms bridge
Where the previous tracks combine: how a model actually learns (gradient descent, regularization, Lagrange) and how classic algorithms are assembled from the math you now own.
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Mastery · roadmap to DL and agentic models
A checklist, an 8-week schedule, and the map of how every idea here reappears inside neural networks, transformers and agent loops.
Modules
01
Mathematical thinking & notation
Notation as a compression language: functions, parameters, summations, vectors, and the single equation f(x; θ) that every machine learning model is an instance of.
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02
Linear algebra: the shape of data
Vectors are data, matrices are transformations. Dot products, projections, norms, eigen and SVD — and why PCA, embeddings, recommendations and attention are all this one subject.
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03
Calculus: change, direction, chain
Derivatives as sensitivity, gradients as direction, the chain rule as backpropagation, Jacobians and Hessians — the machinery that makes "learning" a computable thing.
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Probability: reasoning under uncertainty
Conditional probability, Bayes, the distributions that keep reappearing, expectation and variance — ML as a machine for making well-calibrated bets on noisy data.
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Statistics: trusting your numbers
Estimators, bias–variance, confidence intervals, hypothesis tests, A/B tests and cross-validation — the discipline that separates "the model scored 0.93" from "the model is better".
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Information theory: why log-loss
Surprise, entropy, cross-entropy and KL divergence — derived from first principles, so that cross-entropy loss stops being a memorised formula and becomes an obvious one.
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Optimization: how models learn
Loss surfaces, convexity, gradient descent and its variants, momentum and Adam, regularization, and Lagrange multipliers — the engine room behind every trained model.
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Algorithms as math assemblies
Rebuild ordinary least squares, logistic regression, ridge/lasso, k-means, Naive Bayes, decision trees and SVM from the pieces you already own — and implement several from scratch.
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Roadmap: ML → DL → agentic models
The mastery checklist, an 8-week schedule with spaced review, and the explicit map of how this math reappears in neural networks, transformers, diffusion and agent loops.
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How a module is built
Pass 1 · Remembercold retrieval
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Pass 2 · Understandpicture + purpose
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Pass 3 · Implementcode you can break
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CheckpointMCQ + open questions
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Space itreview in 1 / 3 / 7 days
Progress and quiz scores sync across all your devices through your own server — no account —
with localStorage keeping an offline copy on each device.
Each module has a Mark done toggle; only tick it when you can explain the topic aloud without notes.
Companion, not duplicate
This site teaches the math. Your practice with actual models lives in the ML notebook next door: Machine Learning Relearn — from first principles to production. Modules here link across when an idea becomes an algorithm over there (for example, calculus → ML module 05 · Regression & gradient descent).
Extras
Fast lookup when you are coding: the notation & formula reference — common symbols, matrix identities, derivative rules, the distributions that show up in ML, and every loss function written out with the math that justifies it.