Catalog
Prerequisite Course
Calculus Foundations
Single-variable calculus for ML practitioners who know algebra and trigonometry. Covers the derivative as a limit, differentiation rules (power, product, quotient, chain), exponentials and logarithms, optimization and gradient descent, and integration with the Fundamental Theorem. Every concept is anchored to its role in training neural networks.
Readings
1
Derivatives: Rate of Change and the Limit
The difference quotient, the limit definition of the derivative, the power rule, and an introduction to partial derivatives as gradients in ML.
15 min
2
Differentiation Rules
Constant, sum, product, and quotient rules; derivatives of sin and cos; higher derivatives and concavity; L2 regularization and MSE gradients.
14 min
3
The Chain Rule
Composed functions, the chain rule in prime and Leibniz notation, chains of three or more functions, and the direct connection to backpropagation.
15 min
4
Exponentials, Logarithms, and Their Derivatives
The natural exponential e^x and its self-derivative, ln x, chain-rule combinations, derivation of the sigmoid derivative σ(x)(1−σ(x)), and cross-entropy loss.
15 min
5
Optimization and Linear Approximation
Critical points, the second derivative test, local vs global minima, the first-order Taylor approximation, and gradient descent derived from the linear approximation.
16 min
6
Integration and the Fundamental Theorem
Area under a curve, Riemann sums, antiderivatives, the Fundamental Theorem of Calculus, key antiderivative rules, and integration in ML: PDFs, expected values, entropy, KL divergence.
15 min
Quizzes
Derivatives and Differentiation Rules
8 questions · 70% to pass
Optimization, Linear Approximation, and Integration
8 questions · 70% to pass
Labs
Derivatives in Practice
Implement finite differences, verify differentiation rules numerically, visualize the secant-to-tangent convergence, and explore the sigmoid derivative with PyTorch autograd.
45 min
Gradient Descent from Scratch
Implement gradient descent for 1D and 2D functions, run learning rate experiments, fit a linear regression by hand, and confirm the result matches torch.optim.SGD.
50 min
Integration and Probability
Build a trapezoidal integrator, verify the Fundamental Theorem, confirm Gaussian normalization and the 68–95–99.7 rule, estimate π via Monte Carlo, and compute KL divergence numerically.
40 min
Practice