Math for AI

Evaluate functions, compare growth rates and read a loss curve without confusing inputs and outputs.

1. M1.1Inputs, outputs and domains
2. M1.2Reading a graph
3. M1.3Powers and exponentials
4. M1.4Logarithms
5. M1.5Summation notation
6. M1.6A loss landscape

Compute vector operations, lengths, angles and projections and explain what each measures.

1. M2.1Addition and scaling
2. M2.2Dot products
3. M2.3Norm and distance
4. M2.4Cosine similarity
5. M2.5Projection
6. M2.6Vectors in learning

Multiply matrices, track dimensions and interpret transformations, inverses, eigenvectors and SVD.

1. M3.1Matrix-vector products
2. M3.2Matrix multiplication
3. M3.3Transpose and orientation
4. M3.4Determinants and inverses
5. M3.5Eigenvectors
6. M3.6SVD and low rank

Calculate slopes, use the chain rule and distinguish derivatives from partial derivatives.

1. M4.1Secants and tangent slopes
2. M4.2Basic rules
3. M4.3Products and quotients
4. M4.4The chain rule
5. M4.5Partial derivatives
6. M4.6Numerical checks

Perform gradient descent updates and explain learning rate, stochastic gradients, momentum and Adam.

1. M5.1Gradients as directions
2. M5.2One descent update
3. M5.3Learning-rate stability
4. M5.4Stochastic gradients
5. M5.5Momentum
6. M5.6Adam and local geometry

Calculate conditional probabilities, Bayes updates, expectations, variance and softmax probabilities.

1. M6.1Events and distributions
2. M6.2Conditional probability
3. M6.3Bayes updates
4. M6.4Expectation and variance
5. M6.5Common distributions
6. M6.6Softmax

Connect likelihood, estimation and uncertainty to entropy, cross-entropy, KL divergence and perplexity.

1. M7.1Sampling and estimation
2. M7.2Likelihood
3. M7.3Bias and variance
4. M7.4Entropy
5. M7.5Cross-entropy and KL
6. M7.6Perplexity