Volume 1 · Eight-week foundations
Mathematical Foundations for Machine Learning and AI
Algebra, mathematical notation, linear algebra, calculus, and NumPy — rebuilt carefully for experienced engineers who want to read papers, follow derivations, and implement models from scratch.
- 20
- chapters
- 10
- interactive labs
- 320+
- exercises & solutions
Who this is for
You already program professionally and understand algorithms and software architecture. What you want is mathematical fluency: the ability to open a paper and read every symbol, follow the derivation, and reproduce the result in code. This course treats you as an engineer, not a beginner — careful explanations, no hand-waving, and every concept connected to implementation.
What you'll be able to do
- Read ML and AI papers without stalling on notation
- Follow derivations and reproduce important equations
- Translate mathematics directly into correct NumPy
- Implement algorithms and reproduce experiments from scratch
- Spot hidden assumptions and dimension errors
- Understand why training works — gradients, losses, optimization
How the mathematics connects to ML
Linear algebra → architecture
A neural layer is Wx + b. Shapes, matrix products, and rank are the language of every model — from embeddings to attention.
Calculus → learning
Training is optimization. Derivatives measure sensitivity; the chain rule is backpropagation; gradients point the way downhill.
NumPy → implementation
Every equation becomes vectorized code. You'll translate summations, dot products, and gradients into correct, shape-checked NumPy.
The eight-week plan
Full curriculum →- Week 10%
Algebra and Mathematical Language
Reading and unpacking the symbols ML papers assume you know.
- Week 20%
Functions and NumPy Foundations
Models and losses are functions; NumPy is how we evaluate them.
- Week 30%
Vectors
The geometry and algebra of feature vectors and embeddings.
- Week 40%
Matrices and Linear Systems
Matrices as data, as operations, and as transformations of space.
- Week 50%
Vector Spaces and PCA Intuition
Directions, dimensions, variance, and dimensionality reduction.
- Week 60%
Limits and Derivatives
Rate of change as the foundation of all learning.
- Week 70%
Chain Rule and Gradients
How gradients are computed through composed functions.
- Week 80%
Optimization and Linear Regression
Assembling calculus, linear algebra, and NumPy into a learner.
The five parts
- Part 1Algebra and Mathematical Notation
- Part 2Functions and Graphs
- Part 3Core Linear Algebra
- Part 4Calculus
- Part 5NumPy Laboratory
How to use this course
Lessons
Each chapter builds from motivation and intuition to a formal definition, a worked example, an ML use case, runnable NumPy, and common mistakes.
Laboratories
Interactive visualizations for vectors, matrices, derivatives, gradient descent, and PCA — manipulate the math and watch it respond.
Exercises
Four difficulty levels from recall to research-thinking, with graduated hints and complete, gated solutions you reveal deliberately.
Everything ends in a capstone: reproducing linear regression from scratch, from the equations to a gradient-checked implementation and a short research report.