51 of 51 written · a work in progress
Study
Notes on technical topics, built around interactive explanations and cited throughout. Pick a topic.
Physics Engines
How physics engines work on the inside: the math, contact optimization, XPBD, and GPU-scale simulation.
Linear Algebra
The language underneath everything else: linear maps, from vectors and elimination up to eigenvalues, the SVD, and numerical conditioning.
Convex Optimization
The optimization that runs inside contact solvers and policy updates: convex sets, quadratic programs, duality, cones, and how solvers descend.
Optimal Control
Computing controls for the systems a physics engine simulates: LQR, dynamic programming, iLQR, and MPC, and the Bellman bridge to reinforcement learning.
Probability & Information Theory
The probability behind RL and state estimation: expectation and Monte Carlo, entropy and KL divergence, the score-function gradient, and Bayesian filtering.
Lie Groups & Manifolds
The geometry of rotation and motion done right: SO(3)/SE(3), the exponential map, and optimization on curved spaces for orientation state and pose estimation.
Reinforcement Learning Theory
The math spine of RL: MDPs and value functions, the Bellman operators, policy gradients, and the trust-region and natural-gradient methods that stabilize them.
Matrix Calculus & Autodiff
How gradients are actually computed for learning and differentiable simulation: matrix calculus, forward vs reverse-mode AD, backprop, and differentiating through a physics step.