Math for AI
Essential mathematical intuition for AI: linear algebra, vectors, matrices, eigenvalues, gradients, optimization, and probability distributions.
Course Syllabus & Units
Numbers
2 lessonsDot products and similarity
A **dot product** combines two vectors into one number that reflects how aligned they are. In AI, it often stands in for **similarity**—especially after vectors are normalized.
Scalars, vectors, and matrices
AI math starts with three picture-friendly ideas: - **Scalar:** one number (temperature = 72) - **Vector:** an ordered list of numbers (a point or arrow) - **Matrix:** a table of numbers (rows × columns)
Probability
2 lessonsBayes rule worked examples
Worked numeric examples of **Bayes’ rule**: updating beliefs when evidence arrives—pairing Course 04 probability with Course 06 uncertainty.
Probability basics for AI
**Probability** measures how strongly we should expect an outcome, from 0 (impossible) to 1 (certain). AI uses probabilities for classifications, sampling, and uncertainty.
Calculus
2 lessonsDerivatives and chain-rule intuition
A **derivative** measures how fast an output changes when an input nudges a little—slope. The **chain rule** says: when functions stack, slopes multiply along the path.
Gradient descent geometry
A geometric view of **gradient descent**: loss as a landscape, gradient as steepest uphill, steps downhill with a learning-rate stride.
Linalg
3 lessonsEigenvalues intuition
An **eigenvector** is a direction a linear map only stretches or shrinks—not turning aside. The **eigenvalue** is that stretch factor.
Linear maps and projections
A **linear map** transforms vectors in a structured way (stretch, rotate, shear). A **projection** flattens vectors onto a subspace—like casting a shadow.
Norms and distance
Ways to measure vector size (**norms**) and closeness (**distances**)—L1, L2, and cousins used in losses and nearest-neighbor search.