Learn ML / Stage 1
1 · Foundations
The maths that machine learning and computational modelling are built on.
By the end of this stage, you can…multiply matrices and explain what an eigenvector is, take partial derivatives and use the chain rule, work with probability distributions, expectation and variance, update a belief with Bayes' theorem, explain what a confidence interval and a p-value tell you, and explain how gradient descent finds a minimum.
What you will learn
- Linear algebra Essential
- Calculus Essential
- Probability Essential
- Statistics Essential
- Optimisation Essential
- School maths refresher If you need it
Resources per subject
proof-based you learn by proving results · practical you learn by computing and applying
Linear algebra Essential
- 3Blue1Brown, Essence of Linear AlgebraBuilds the geometric intuition in a few hours of video. Follow it with Gilbert Strang's MIT 18.06 for depth.★ recommended · practicalvideos
- Gilbert Strang, MIT 18.06: Linear Algebrapracticalvideos · notes · exercises
- Gilbert Strang, MIT 18.065: Matrix Methods in Data Analysis, Signal Processing, and Machine Learningpracticalvideos · notes
3 more options
- Gilbert Strang, Differential Equations and Linear Algebra (MathWorks)practicalvideos · exercises
- Adrian Banner, Princeton Universitypracticalvideos
- Mathematics for Machine Learning (Deisenroth, Faisal & Ong)free book
Calculus Essential
- 3Blue1Brown, Essence of CalculusThe ideas behind derivatives and the chain rule. For gradients and several variables, continue with Khan Academy's Multivariable Calculus.★ recommended · practicalsingle-variable · videos
- Khan Academy, Multivariable Calculuspracticalmultivariable · videos · exercises
- Denis Auroux, MIT 18.02: Multivariable Calculuspracticalmultivariable · videos · notes · exercises
9 more options
- Math Insight, Multivariable calculuspracticalmultivariable · videos · notes
- Jeffrey Chasnov, Vector Calculus for Engineers, HKUST (Coursera)practicalvector · videos · exercises · free to audit
- Khan Academy, Calculus 1practicalsingle-variable · videos · exercises
- Khan Academy, Calculus 2practicalsingle-variable · videos · exercises
- Robert Ghrist, Calculus: Single Variable Part 1, Functions (UPenn, Coursera)practicalsingle-variable · videos · exercises · free to audit
- Robert Ghrist, Part 2: Differentiationpracticalsingle-variable · free to audit
- Robert Ghrist, Part 3: Integrationpracticalsingle-variable · free to audit
- Robert Ghrist, Part 4: Applicationspracticalsingle-variable · free to audit
- Robert Ghrist, Part 5: Numerical methods, convergence, Taylor seriespracticalsingle-variable · free to audit
Probability Essential
- Jeremy Orloff, MIT 18.05: Introduction to Probability and StatisticsClear notes with exercises and solutions; covers probability, Bayesian updating and the basics of statistics together.★ recommended · practicalnotes · exercises
- Khan Academy, Statistics and probabilitypracticalvideos · exercises
- Introduction to Probability and Data, Duke University (Coursera)practicalvideos · exercises · free to audit
1 more option
- Arkady Etkin, Probability lecturespracticalvideos
Statistics Essential
- Philippe Rigollet, MIT 18.650: Statistics for ApplicationsAfter 18.05: estimation, hypothesis testing and regression, with the maths shown.★ recommended · practicalvideos · notes · exercises
- Jeremy Orloff, MIT 18.05: Introduction to Probability and Statisticspracticalnotes · exercises
- Frequentist vs Bayesian statistics (Broek)practicalexplainer on this site
2 more options
- Khan Academy, Statistics and probabilitypracticalvideos · exercises
- Mine Çetinkaya-Rundel, Linear Regression and Modeling, Duke University (Coursera)practicalvideos · exercises · free to audit
Optimisation Essential
- Convex Optimization (Boyd & Vandenberghe)The standard text; chapters 1 to 5 cover what ML needs, such as gradients, convexity and duality.★ recommended · free book · lecture slides
- NPTEL, Optimisationvideos · notes · exercises
School maths refresher If you need it
- Khan Academy, MathsFills gaps in school maths before you start the rest.★ recommended · practicalvideos · exercises
- ExamSolutions, A-level mathspracticalnotes · exercises