Semester 1 · Core
Linear Algebra & Calculus for ML
https://epochschool.com/subjects/linear-algebra-calculus-for-ml
The mathematics every model is built from: vectors and matrices as geometry, solving linear systems, projections, eigenvalues and the SVD, then calculus from single-variable optimisation to gradients, Jacobians and the chain rule.
Every idea is derived, then computed in NumPy.
- Prerequisites
- Recommended: Helpful background. You can start without it if you are willing to fill the gaps.
What you’ll be able to do
- LO1Reason about vectors geometrically using dot products, norms, angles and projections.
- LO2Interpret matrices as linear maps and use rank, span, column space and null space to describe them.
- LO3Solve linear systems with Gaussian elimination and LU decomposition, and judge numerical conditioning.
- LO4Use orthogonality, eigen-decomposition, quadratic forms and the SVD to analyse and compress data.
- LO5Differentiate and optimise functions of one variable, including Taylor approximations.
- LO6Compute gradients, Jacobians and Hessians of multivariable functions and apply the chain rule to model losses.
Chapters
- 01Vectors as data and geometry
- 02Matrices as linear maps
- 03Solving linear systems
- 04Orthogonality and projections
- 05Eigenvalues and quadratic forms
- 06The singular value decomposition
- 07Calculus of one variable, for optimisation
- 08Gradients, Jacobians and the chain rule
Graded labs
- L1
Finding similar documents with vectors
After chapter 1 · about 7 hours · Word-count matrix of 30 short news items in five topics plus one blank item · CC0-1.0 (authored for this course) · Runs on a CPU
- L2
LU decomposition from scratch
After chapter 3 · about 7 hours · Random Gaussian matrices, hand-written singular matrices and Hilbert matrices · Generated for this course; no third-party data · Runs on a CPU
- L3
Eigenvectors and a tiny PageRank
After chapter 5 · about 7 hours · Synthetic directed link graphs and matrices with known eigenvalues · CC0-1.0 (authored for this lab) · Runs on a CPU
- L4
Compressing images with the SVD
After chapter 6 · about 7 hours · Sample photographs china.jpg and flower.jpg · CC BY 2.0 (creativecommons.org/licenses/by/2.0). china.jpg by danielbuechele (flickr.com/photos/danielbuechele/6061409035); flower.jpg by vultilion (flickr.com/photos/vultilion/6056698931); both retrieved by Robert Layton for scikit-learn. · Runs on a CPU
- L5
Gradients by hand and by finite differences
After chapter 8 · about 7 hours · Synthetic regression and binary classification data · CC0-1.0 (authored for this lab) · Runs on a CPU
Before you start
Recommended
Helpful background. You can start without it if you are willing to fill the gaps.
Where it leads
Neural Networks & Deep Learning
Optimisation & Training at Scale
Sequence Models & Transformers
Responsible AI, Ethics & Governance
Image Formation and Classical Computer Vision
Probabilistic ML & Bayesian Methods
Reinforcement Learning Foundations
Capstone Project
How it’s taught
You read short sections written for the page. Each ends with a check, and in-browser exercises let you practise. Graded labs run on your own cloud lab machine, CPU-friendly.
No videos. No live classes. No AI tutor.