Math for AI
Understand AI computations with linear algebra, and reason about uncertainty with probability and statistics.
Before you start: basic algebra and introductory NumPy. Calculus is not required.
Linear algebra
Jon Krohn — Linear Algebra for Machine Learning
Study the sections matching the five topics below and complete their short exercises.
Python notebooks
Run the linear algebra examples, then submit the four notebooks listed below.
| Topic | What to learn |
|---|---|
| Vectors and tensors | Shapes, addition, scaling, norms, dot products, distance, and cosine similarity |
| Matrices | Operations, multiplication, transpose, identity/diagonal/symmetric matrices, transformations, and compatible shapes |
| Linear systems | Ax = b, inverse, rank, independence, pseudoinverse, and exact versus least-squares solutions |
| SVD and PCA | Eigenvectors/eigenvalues, eigendecomposition, SVD, low-rank approximation, and PCA |
| AI computations | Samples/features, batches, weight matrices, embeddings, attention shapes, broadcasting, and dimension errors |
Practise with NumPy and small hand calculations. Focus on understanding and application; formal proofs, abstract vector-space theory, change of basis, Gram–Schmidt, detailed subspace theory, large hand calculations, and decomposition derivations are outside scope.
Submit four small notebooks:
- Vectors, norms, dot products, and similarity.
- Matrix transformations and shape compatibility.
- Linear systems and least squares.
- SVD, low-rank approximation, and PCA.
Include an AI tensor-shape exercise and repair a dimension error. These are verification exercises, not an integrated project.
Probability & statistics
Khan Academy Statistics and Probability
Complete Units 1–5 and 7–12. Pass every required unit test with at least 80%.
| Units | Focus |
|---|---|
| 1–5 | Categorical data, charts, summary statistics, normal distributions, correlation, and regression |
| 7–9 | Probability rules, counting, permutations/combinations, and random variables |
| 10–12 | Sampling distributions, confidence intervals, and one-sample significance tests |
Skip Unit 6 (Study Design), including its quizzes and test. It is also excluded from Academy verification. Units 13–16 belong to the Advanced Statistical Inference elective.
Finish this module
- Submit your four runnable notebooks, short calculations, and shape/debugging answers. Explain the operations and diagnose a relevant failure.
- Submit statistics unit-test results showing at least 80% on every required unit.
- Submit an interpretation exercise on sampling distributions, confidence intervals, and a one-sample significance test. Pass the Academy verification covering only Units 1–5 and 7–12; the full-course challenge is not the final assessment.
- Revise gaps after feedback.
Linear algebra’s source estimate is 14–18 hours, pending pilot. Statistics workload remains pending pilot; allow time for practice and review.
Next: Data Foundations.
