Course 3 of 7 · Beginner

Mathsfor reading and building models.

Each idea is drawn first, then computed by hand, then used on a model.

Start with 0.1 The Maths Inside One PredictionSee the syllabus
6modules
26lessons planned
26ready to study now
1free video

Who Maths is for and what you will learn

This track is for you if

  • You last did maths at school and want back in without starting over.
  • Machine learning notation stops you reading documentation and papers.
  • You want to know what gradient descent is doing, not just call it.

By the end you can

  • Follow the maths behind a model's training loop.
  • Find a derivative and a gradient, and say what it means.
  • Use vectors, dot products and matrices to describe data.
  • Read machine learning notation aloud in words.

Before you start

School algebra. Each lesson rebuilds what it needs before using it.

Every open lesson is free to read. The opening modules are a free sample: a free account opens all of their material. Pro adds it for the rest of the course.

The syllabus6 modules, each ending in its own finish line.

Every lesson is listed, including the ones still in production, so you can see where the track goes. Open lessons have their parts and key terms free to read, and their quiz free with an account.

  1. Module 0 · 1 lesson · videos in production

    Why Maths Matters

    Builds to: One More Prediction, Traced
    1. 0.1The Maths Inside One PredictionSee every branch of this track at work inside one prediction and one training step, so each later video has a place to land.
    Finish lineModule quiz · 10Project: One More Prediction, TracedInterview questionsModule overview: notebooks, common mistakes, cheat sheet
  2. Module 1 · 3 lessons · videos in production

    Functions, Logarithms and Notation

    Builds to: Reading Ridge and Lasso
    1. 1.1Functions and Their GraphsRead a function as a rule from input to output, and recognise the shapes ML keeps using.
    2. 1.2Exponents and LogarithmsKnow why logs appear everywhere in ML: they turn products into sums, and huge ranges into small ones.
    3. 1.3Reading ML NotationRead the formulas in ML papers and docs without stalling.
    Finish lineModule quiz · 15Project: Reading Ridge and LassoInterview questionsModule overview: notebooks, cheat sheet
  3. Module 2 · 5 lessons · videos in production

    Vectors

    Builds to: Nearest Cars, Raw and Standardised
    1. 2.1VectorsSee a row of data as a point and as an arrow, in any number of dimensions.
    2. 2.2Vector Arithmetic and NormsAdd, scale and measure vectors, and know that "length" has more than one definition.
    3. 2.3The Dot Product, Angle and ProjectionCompute a dot product and read it as alignment, and project one vector onto another.
    4. 2.4Lines, Planes and HyperplanesRead `wᵀx + b = 0` as a boundary in any dimension: which side a point is on, and how far away it is.
    5. 2.5Shapes and Distance in d DimensionsWrite the shapes that appear as decision regions and constraints, and see why distance behaves differently as the dimension grows.
    Finish lineModule quiz · 15Project: Nearest Cars, Raw and StandardisedInterview questionsModule overview: notebooks, cheat sheet
  4. Module 3 · 7 lessons · videos in production

    Matrices

    Builds to: PCA by Hand on the Lot
    1. 3.1Matrices, the Matrix–Vector Product and the TransposeSee a dataset as a matrix, and a linear model's predictions as one matrix–vector product.
    2. 3.2Matrix Multiplication as TransformationRead a matrix as something that moves space: rotate, stretch, shear, project.
    3. 3.3Identity, Inverse and Singular MatricesUse the inverse as the transformation that undoes another, and know when it cannot exist.
    4. 3.4Linear Systems, Rank and Least SquaresSolve `Ax = b` exactly when it can be solved, and in the least-squares sense when it cannot. Derive the normal equations.
    5. 3.5Eigenvalues and EigenvectorsFind the directions a matrix only stretches, and read the eigenvalues as how much.
    6. 3.6Singular Value DecompositionFactor any matrix into rotate–stretch–rotate, and keep only the largest parts.
    7. 3.7The Covariance MatrixBuild the covariance matrix from a centred data matrix and read its entries and its shape.
    Finish lineModule quiz · 15Project: PCA by Hand on the LotInterview questionsModule overview: notebooks, cheat sheet
  5. Module 4 · 9 lessons

    Calculus and Optimisation

    Builds to: Linear Regression on the Lot, Three Ways
    1. 4.1Derivatives: Rate of Change and the TangentSay what a derivative measures, and read its sign and size off a graph.Free video
    2. 4.2Derivative Rules and the Chain RuleDifferentiate the functions ML uses, including functions of functions.Video in production
    3. 4.3Maxima, Minima and Setting the Derivative to ZeroFind where a function is lowest or highest, and know when that cannot be done by solving an equation.Video in production
    4. 4.4Partial Derivatives and the GradientDifferentiate a function of several variables, and read the gradient as the direction of steepest increase.Video in production
    5. 4.5Curvature: Second Derivatives, Taylor and NewtonUse the second derivative to see how a function bends, and step straight to the bottom of a local quadratic.Video in production
    6. 4.6Integrals as AreaRead an integral as accumulated area, enough for densities and AUC.Video in production
    7. 4.7Convexity, Local Minima and Saddle PointsTell a convex function from a non-convex one, and know what a zero gradient does and does not guarantee.Video in production
    8. 4.8The Chain Rule Through a ComputationCompute the gradient of a loss that is built from many steps, by passing derivatives backwards through a graph of operations.Video in production
    9. 4.9Constrained Optimisation and Lagrange MultipliersMinimise a function subject to a constraint, and read the multiplier.Video in production
    Finish lineModule quiz · 15Project: Linear Regression on the Lot, Three WaysInterview questionsModule overview: notebooks, cheat sheet
  6. Module 5 · 1 lesson · videos in production

    Numbers on a Computer

    Builds to: Naive Bayes from Products and from Sums of Logs
    1. 5.1Floating Point and Numerical StabilityKnow why a correct formula can give a wrong answer on a computer, and the standard fixes.
    Finish lineModule quiz · 10Project: Naive Bayes from Products and from Sums of LogsInterview questionsModule overview: notebooks, common mistakes, cheat sheet

How Maths is taughtone lesson, opened up.

Lessons in this track are built the same way. Here is Maths 4.1 as its outline lists it: what it builds on, its parts in order, and everything around it in its module.

Maths 4.1 Free video

Derivatives: Rate of Change and the Tangent

Say what a derivative measures, and read its sign and size off a graph.

The lesson, part by part
  1. Which way is down?
  2. Rate of change between two points
  3. Letting the gap shrink
  4. The derivative as a function
  5. Reading the sign and the size
  6. Checkpoint: the derivative so far
  7. The hero cars' error against the slope
  8. When a smaller h is worse
  9. Derivatives in Python
  10. Recap, challenge, and next: derivative rules

Key term · derivativethe slope of the tangent, the limit of Δy/Δxe.g. 2 for x² at 1

After the lesson
  • A 5-question quiz, marked the moment you answer
  • Practice at levels A to C, with values to check against
  • Where the idea is used in real work
  • Common mistakes: the error you will see, why, and the fix
In its module · 4. Calculus and Optimisation
  • 6 notebooks to run the examples yourself
  • 15 interview questions with model answers
  • The module project: Linear Regression on the Lot, Three Ways, set with no template
Watch it free See the module

What's inside a lessonin Maths, published so far.

Counted from this track's published lessons. A part still being written is left out until it is published.

  1. Learn

    The lesson

    Short parts, each with its key terms, and a free video where one is recorded.

    26 lessonsNo account
  2. Check yourself

    Quiz

    Multiple-choice questions on the lesson, marked the moment you answer.

    26 lessonsFree account
  3. Practise

    Assignments

    Exercises to do yourself, starting from the lesson's own challenge.

    26 lessonsPro
  4. Apply it

    Real-world applications

    Where each idea is used in real work, from data analysis to production models.

    24 lessonsPro
  5. Avoid

    Common mistakes, and the fix

    The error you will actually see, why it happens, and how to fix it.

    24 lessonsPro
  6. Prepare

    Interview questions

    Questions an interviewer asks about each module, with model answers.

    81 questionsPro
  7. Build

    Projects and notebooks

    Module projects, set as a problem with no template and checked by a notebook, and notebooks to run the examples yourself.

    6 projects, 22 notebooksPro

What you will build6 module projects, each set with no template.

Each project is a problem to solve on your own, then checked against test values or a notebook.

Start free, go further with Pro

Compare the plans

Pro

Pricing announced soon.

  • Every course, from Python to deep learning and generative AI
  • Practice problems for every lesson, levels A to C, with values to check
  • Self-checking notebooks that mark your answers as you go
  • Module projects, cheat sheets, common mistakes and interview answers
  • A certificate for every course you complete
  • Weekly live sessions with Gaurav
  • Everything in Free

Worked articles on Maths

All Maths resources

Where Maths is used

All AI applications

Questions about Maths

How much maths do I need for machine learning?

Linear algebra, a little calculus and some probability. This track covers the parts models actually use, just before the lessons that need them.

Do I need to finish this track before machine learning?

No. Each maths lesson is best taken just before the machine learning lesson that uses it. The learning path says which.

Other courses

See the machine learning path