Become an AI Expertv2.1
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On-ramp from zero (Path A)Novice track, module A2

Just-enough math

Track: Novice (Path A, the on-ramp from zero) Time: about 20 guided hours, run alongside A1. Longer if you are starting from arithmetic. Goal: Understand what a model is doing when it trains. Not prove theorems. Principles: Principle 3 (learning is gradient descent through the chain rule). Lab 01 shows it.

How much is enough

The vetted stories split cleanly. For engineering roles, a staff ML engineer at a FAANG company says he mostly uses algebra plus intro statistics day to day. The highest-voted answer (124 points) in the 2026 "what actually worked" thread says learn just enough, then fill gaps when a project demands it. For research roles the answer is different: deep math matters, and the one person who went from no schooling past 6th grade to studying ML at ETH Zurich did it by re-learning math from arithmetic up with Khan Academy mastery challenges and textbooks.

This module targets the engineering level. Module A7 track C tells you how to go further if you choose research.

Learn

  1. Linear algebra, as intuition. Vectors, matrices, matrix multiplication as transformation, dot products as similarity. This is what embeddings and attention are.
    • 3Blue1Brown, "Essence of Linear Algebra" (about 3 hours of video). Watch each episode, then write the idea in your own words.
  2. Calculus, just gradients. What a derivative is, the chain rule, what a gradient is and why we step against it.
    • 3Blue1Brown, "Essence of Calculus" episodes 1 to 4, then the neural network series (4 videos).
  3. Probability and statistics, the parts models use. Probability distributions, expectation, conditional probability, Bayes' rule, mean/variance, the normal distribution, sampling. Then the applied ML stats: bias/variance, overfitting, p-values at the "what does it mean" level, and metrics (precision, recall, F1, ROC-AUC).
    • Khan Academy "Statistics and probability" units on probability and distributions.
    • StatQuest (Josh Starmer) videos on bias/variance, ROC, and confusion matrices.
  4. If you need to go from zero. Khan Academy from pre-algebra up, using mastery challenges, before any of the above. Budget 3 to 6 months. One Redditor did exactly this to pass a university entrance exam at 29.
  5. Reference book to keep open. "Mathematics for Machine Learning" (Deisenroth, Faisal, Ong), free PDF. Do not read it cover to cover. Open it when a later module uses a term you do not know.

Build

Project A2: gradient descent by hand. In a notebook with only NumPy:

  • Fit a straight line to 50 noisy points by computing the gradient of mean squared error yourself and stepping
  • Plot the loss curve and the fitted line
  • Then fit a 2-feature logistic regression the same way
  • Write one paragraph explaining what the learning rate did when you set it 10x too high

Done when: you can draw, on paper, what gradient descent is doing and why the loss curve bends.

Runnable reference: labs/lab01_gradient_descent.py does exactly this (line fit, logistic fit, and a divergence at 15x learning rate) with assertions. Run it, read it, then write yours without looking.

Skip for now

  • Full calculus or linear algebra courses before touching a project.
  • Measure theory, information theory, convex optimization. Only Track C needs these.
  • Proving anything.

Checkpoint

  1. Multiply a 2x3 matrix by a 3x1 vector on paper. What shape comes out and why?
  2. What is a gradient? Why do we subtract it?
  3. Your model scores 99% accuracy on a dataset where 99% of rows are one class. What is wrong, and which metric would you use instead?
  4. Explain bias vs variance using a story about fitting a curve.

Sources

Follow-ups

When you finish this module, paste one of these into your assistant. In Claude Code write /aiexpert-tutor before it; in Codex write $aiexpert-tutor.

  1. Ask me to explain a derivative, a dot product and a conditional probability in plain words, then correct me.
  2. Give me three gradient-descent problems to work by hand and check my steps.
  3. Ask questions until we find the math gap behind my A2 build.

Free to use: code MIT, writing CC BY 4.0, third-party media under its owners’ terms. Licence and terms.