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MATH ML 10110 of 10 free seats leftMathematics

Math for Machine Learning

Vectors, matrices, derivatives, probability, statistics and entropy: the maths behind every machine learning model, learned through figures you touch. Drag arrows, move the plane, roll a ball down a loss surface, count the people behind Bayes' rule one dot each, then put it all together in a tiny neural network. High-school maths is enough; no programming needed.

  • Intermediate
  • About 12 to 15 hours
  • 16 sections
  • 45 lessons
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Course outline

  1. Section 1

    How does a machine learn?

    • About this course

      Lesson · 5 min

    • Guessing a taxi fare

      Lesson · 20 min

    • Turning the knobs yourself

      Lesson · 25 min

  2. Section 2

    Vectors: data as arrows

    • Every row is an arrow

      Lesson · 20 min

    • Mixing two vectors

      Lesson · 15 min

    • Who is most like you?

      Lesson · 25 min

  3. Section 3

    The dot product

    • The shadow of an arrow

      Lesson · 20 min

    • Computing it from coordinates

      Lesson · 20 min

    • A model's score

      Lesson · 20 min

  4. Section 4

    Matrices move the plane

    • Editing a photo on a phone

      Lesson · 20 min

    • Where does one vector go?

      Lesson · 20 min

    • One move after another

      Lesson · 25 min

  5. Section 5

    A matrix for the whole table

    • The whole table at once

      Lesson · 20 min

    • How much do areas grow?

      Lesson · 20 min

    • Flattening and undoing

      Lesson · 25 min

  6. Section 6

    Directions that stay: eigenvectors and PCA

    • Directions that don't tilt

      Lesson · 20 min

    • Again and again, and the spread of data

      Lesson · 20 min

    • PCA on real penguins

      Lesson · 25 min

  7. Section 7

    Derivatives: the slope at a point

    • Speed right now

      Lesson · 20 min

    • The derivative as sensitivity

      Lesson · 25 min

    • Flat places and the loss

      Lesson · 20 min

  8. Section 8

    Gradients and the chain rule

    • Two knobs

      Lesson · 20 min

    • The chain rule

      Lesson · 25 min

    • Backpropagation

      Lesson · 15 min

  9. Section 9

    Gradient descent

    • One step downhill

      Lesson · 20 min

    • Narrow valleys, two valleys

      Lesson · 20 min

    • Mini-batches, epochs and when to stop

      Lesson · 20 min

  10. Section 10

    Probability and Bayes

    • A positive result

      Lesson · 25 min

    • Bayes' rule

      Lesson · 25 min

    • A spam filter

      Lesson · 20 min

  11. Section 11

    Distributions, expectation, variance

    • Many draws make a distribution

      Lesson · 20 min

    • Expectation and variance

      Lesson · 25 min

    • Averages of many

      Lesson · 25 min

  12. Section 12

    From data to model: likelihood and overfitting

    • Which model fits the data?

      Lesson · 25 min

    • Memorising or understanding?

      Lesson · 20 min

    • Calming the wiggles, judging on new data

      Lesson · 15 min

  13. Section 13

    Information: entropy and cross-entropy

    • How much surprise?

      Lesson · 25 min

    • From scores to probabilities

      Lesson · 20 min

    • What a wrong guess costs

      Lesson · 25 min

  14. Section 14

    Putting it together: a tiny neural network

    • When one straight line isn't enough

      Lesson · 20 min

    • Teaching the network

      Lesson · 25 min

    • Real penguins

      Lesson · 25 min

  15. Section 15

    Review the whole course

    • Revision notes

      Lesson · 30 min

  16. Section 16

    Final exam

    • Final exam

      Quiz · 30 min

    • After the exam

      Lesson · 5 min