University course on vectors, matrices, partial derivatives, gradient vectors, directional derivatives, and multivariable optimization.
Neural networks optimize scalar loss functions with respect to millions or billions of parameters simultaneously. MIT 18.02SC Part 2 (Partial Derivatives) teaches the exact mathematical machinery of partial differentiation, gradient vectors pointing in directions of steepest ascent, the multivariable chain rule, and Hessian second-derivative matrices.
Course status is tracked independently from roadmap topic checkboxes so you can mark external courses without altering your topic mastery percentage.
Phase 1 Modules 1.2 & 1.4 (Multivariable Gradients & Optimization)
100% free MIT OpenCourseWare Scholar course with full video lectures, notes, and problem sets.
Status: Verified (2026-11-09)
Review these foundations before starting so you get the most out of this material:
In Phase 1: Mathematics for AI
Focus heavily on Part 2 (Partial Derivatives, Gradient Vectors, Chain Rule, and Max-Min Optimization Problems) alongside Modules 1.2 and 1.4.
Derivatives, the chain rule, partial derivatives, gradients, Jacobians, Hessians, and the mathematical mechanics of gradient descent.
SGD, mini-batching, Momentum, RMSProp, Adam, learning-rate schedules, numerical stability, log-sum-exp, finite-difference gradient checking, and computational graphs.
Comprehensive MIT OpenCourseWare Scholar course covering differentiation, the chain rule, optimization of single-variable functions, and integration.
A university-level linear algebra course covering vector spaces, matrices, linear systems, eigenvalues, and related topics.
Mathematical foundations of machine learning, including linear algebra, vector calculus, probability, and optimization.