Math Foundations Roadmap
You don’t need a math degree. You need enough math to understand why algorithms work and when they break. Learn just-in-time — study each topic when the ML concept you’re learning requires it.
1. Linear Algebra
The language of data. Every dataset is a matrix, every model parameter is a vector.
- Vectors and Matrices — what they are, operations, intuition
- Matrix Multiplication — why it’s the core operation in ML
- Dot Product — similarity, projections, the building block
- Eigenvalues and Eigenvectors — PCA, spectral methods, why they matter
- Matrix Decomposition — SVD, factorization, dimensionality reduction
2. Calculus
How models learn. Gradient descent is just calculus applied iteratively.
- Derivatives — rate of change, slopes, the basis of optimization
- Partial Derivatives — multivariable functions, one variable at a time
- Chain Rule — backpropagation is literally the chain rule
- Gradient — direction of steepest ascent, vector of partials
- Gradient Descent — the optimization loop that trains every model
3. Probability & Statistics
How we reason under uncertainty. Every prediction has a confidence.
- Probability Basics — events, conditional probability, Bayes’ theorem
- Distributions — normal, uniform, Bernoulli, Poisson — when each appears
- Expectation and Variance — summarizing distributions with numbers
- Bayes Theorem — updating beliefs with evidence, foundation of many models
- Maximum Likelihood Estimation — fitting models to data, why loss functions look the way they do
4. Information Theory
The math behind decision trees, cross-entropy loss, and language models.
- Entropy — measuring uncertainty/surprise in a distribution
- Cross-Entropy and KL Divergence — comparing distributions, loss functions
When to go deeper
Most ML requires linear algebra + calculus at an intuitive level. Go deeper into probability for Bayesian methods, information theory for NLP, and optimization theory for research.
Links
- Python for ML Roadmap — next step after building math intuition
- AI-ML Glossary