Videos and books

Every resource on this page is free to watch or read, from the author's or the publisher's own page. Each lesson of the track also ends with a Watch and read section that names the exact video or chapter for that lesson.

How to use it. This track is the start of the site, so pick resources that are short and visual first. A good default: watch one short video before a lesson, do the lesson and its notebook, then read one book section from the table at the end of this page. Do not try to finish a whole course before you start the lessons; use the courses as a second explanation when a lesson feels hard.

Video courses #

How to study #

• The Learning Scientists (videos and one-page guides). Short videos and printable guides on six study strategies: retrieval practice, spaced practice, interleaving, elaboration, concrete examples and dual coding. Pairs with lesson 01.
• Barbara Oakley and Terrence Sejnowski, Learning How to Learn (Coursera, free to audit). A short course on focused and diffuse thinking, chunking, procrastination and memory. Pairs with lesson 01.

For the picture #

• 3Blue1Brown, Essence of linear algebra (YouTube playlist, course page). Animated chapters on vectors, linear maps and the dot product. For this track, chapters 1 (vectors) and 9 (dot products) pair with lesson 06; the rest prepares the Linear Algebra track.
• 3Blue1Brown, Essence of calculus (YouTube playlist, course page). Chapters 1–2 (the derivative) pair with lesson 07; chapter 5 (Euler's number $e$) pairs with lesson 04.
• 3Blue1Brown, Neural networks (YouTube playlist). Chapter 2 shows gradient descent on a real network (lesson 07). Chapter 5 shows softmax with a temperature in a language model (lesson 05).

Python and NumPy #

• MIT 6.100L, Introduction to CS and Programming using Python (Ana Bell, 2022) (course, YouTube playlist). A full first course in Python for people who have never programmed. Take it before lesson 03 if variables, loops and functions are new to you.
• Corey Schafer, Python Programming Beginner Tutorials (YouTube playlist) and Matplotlib Tutorials (YouTube playlist). Short, practical videos on Python basics and on plotting. Pairs with lesson 03.

Statistics #

• StatQuest, Statistics Fundamentals (YouTube playlist). Short videos with clear pictures: histograms, the normal distribution, mean and variance, sampling. Pairs with lesson 08. The same channel explains logs (lesson 04), odds, the logit and softmax (lesson 05).

Proofs #

• MIT 6.042J, Mathematics for Computer Science (Leighton, 2010) (course, YouTube playlist). Lectures 1–3 cover proofs and induction. Pairs with lesson 09; the free book below is the course text.
• MIT 6.1200J, Mathematics for Computer Science (2024) (course). The newer version of the same course, with lecture videos on proofs, contradiction and induction.

Free books #

Mathematics for machine learning #

• Deisenroth, Faisal and Ong, Mathematics for Machine Learning (free PDF). The table of symbols and chapter 2 (lesson 02), §3.1–3.4 on norms, inner products and angles (lesson 06), §5.1–5.2 on derivatives and gradients (lesson 07), §8.3 on the negative log-likelihood (lesson 04). The standard next book after this track.
• Goodfellow, Bengio and Courville, Deep Learning (free online). The notation page (lesson 02) and §4.1 on overflow, underflow and the stable softmax (lesson 05).
• Boyd and Vandenberghe, Introduction to Applied Linear Algebra (VMLS) (free PDF). Chapters 1 and 3: vectors, inner products, norms, distances and angles, with many applications (lesson 06).
• Zhang, Lipton, Li and Smola, Dive into Deep Learning (free online). §4.1 on softmax regression and the cross-entropy loss, with code (lesson 05).

School math, refreshed #

• OpenStax, Algebra and Trigonometry 2e (free). Chapter 3 (functions), chapter 4 (linear functions) and chapter 6 (exponential and logarithmic functions), with many exercises and answers (lesson 04).
• OpenStax, Calculus Volume 1 (free). Chapter 3 (derivatives), §3.1–3.3 and §3.6 on the chain rule (lesson 07).
• OpenStax, Introductory Statistics 2e (free). Chapter 2 (descriptive statistics), chapter 3 (probability), chapters 6–7 (the normal distribution and the central limit theorem) (lesson 08).

Probability and data #

• Grinstead and Snell, Introduction to Probability (free PDF). Chapter 1 (simulation and frequencies), chapter 6 (expected value and variance), chapter 9 (the central limit theorem) (lesson 08).
• Allen Downey, Think Stats (free online). The ideas of lesson 08 with Python and real data.
• Jake VanderPlas, Python Data Science Handbook (free online). Chapter 2 (NumPy) and chapter 4 (matplotlib) (lesson 03).

Proofs #

• Richard Hammack, Book of Proof, 3rd edition (free PDF). The clearest first book on proofs: logic, direct proof, contrapositive, contradiction, counterexamples and induction, with many exercises (lesson 09).
• Lehman, Leighton and Meyer, Mathematics for Computer Science (free PDF). Chapter 1 (proofs), chapter 4 (sets and functions), chapter 5 (induction) and chapter 14 (sums). Pairs with lessons 02 and 09.

Short reads and tools #

• Nicky Case, How to Remember Anything Forever-ish: an interactive comic about the forgetting curve and spaced repetition (lesson 01).
• Andy Matuschak, How to write good prompts: how to write recall cards that work (lesson 01).
• Michael Nielsen, Augmenting Long-term Memory: a researcher's experience with spaced repetition for mathematics and papers (lesson 01).
• Stanford CS231n, Python Numpy Tutorial: Python, arrays, indexing, broadcasting and matplotlib on one page (lesson 03).
• NumPy documentation, the absolute basics for beginners and Broadcasting (lesson 03).
• Andrew Ng and Tengyu Ma, CS229 lecture notes: the $x^{(i)}$ notation for training data (lesson 02), logistic regression and softmax (lesson 05).
• Seeing Theory (Brown University): interactive chapters on chance, expectation, variance, distributions and the central limit theorem (lesson 08).

Which lesson pairs with what #