Lessons

Master the mathematical skeleton of reinforcement learning. Learn how the agent-environment loop formalizes decision-making, why the Markov property is the key assumption, and how Bellman expectation equations link policies to value functions.

When you know the full MDP model, dynamic programming finds the optimal policy exactly. Learn the Bellman optimality equation, the contraction argument that guarantees convergence, and the concrete difference between policy iteration and value iteration — with a value-iteration code walkthrough.

When grids fail in high dimensions, random sampling saves you. Understand why PRM builds reusable roadmaps, how RRT grows a tree toward the goal, what probabilistic completeness really means, and how RRT* achieves asymptotic optimality.

Discretise C-space into a grid, then search it intelligently. Understand Dijkstra's optimality guarantee, how A* accelerates it with admissible heuristics ($f=g+h$), why consistency matters, and where greedy search goes wrong.

Understand why every motion planner secretly works in configuration space: how robots become points, obstacles inflate, and why high-dimensional C-spaces make naive search intractable.

Trace the full perceive-plan-act loop on a mobile robot: AMCL localization feeds a global costmap, a global planner (A*/NavFn) sets the course, and DWA or TEB local planners execute it — with recovery behaviors when things go wrong.

The chicken-and-egg problem of robot autonomy: to localise you need a map; to build a map you need a pose. Covers front-end matching, back-end pose-graph optimisation, loop closure, and visual vs LiDAR SLAM systems.

How LiDAR fires pulses and measures time-of-flight to build a 3D point cloud; data structures, voxel downsampling, ICP registration, ground segmentation, and an honest comparison with cameras for robot perception.

Fuse noisy sensors over time with provably optimal estimates. Covers the state and noise model, predict and update equations with the Kalman gain, why it's optimal for linear-Gaussian systems, and the Extended KF for nonlinear robots.

From photons to 3D geometry: the pinhole model, intrinsic matrix K, lens distortion, feature matching, stereo depth, and where CNNs help (and fail) in robot perception pipelines.

Decode the economics of the world's largest games segment: why mobile is half the market, how the F2P funnel converts attention into revenue, and the LTV > CPI math every mobile studio lives and dies by — including what Apple's 2021 privacy shift broke.

Most AI ROI claims are marketing, not measurement. This lesson builds a rigorous framework: how to set baselines and counterfactuals, why RCTs beat vendor case studies, the real cost components of AI deployment, and how to avoid the attribution traps that make bad investments look good on paper.

Vectors are more than arrows — they're the atoms of every ML model, physics engine, and signal processor alive. Build rock-solid intuition for linear combinations, span, independence, basis, and orthogonality, then verify it all in NumPy.

When there's no exact solution, project. When data is high-dimensional, compress. The SVD is the Swiss Army knife that does both — and more. Master orthogonal projection, the normal equations, the Singular Value Decomposition, low-rank approximation, and the pseudoinverse.

A matrix doesn't just hold numbers — it reshapes space. Master the geometric view of matrix-vector multiplication, the four fundamental subspaces, rank, the determinant as a volume-scaling factor, and invertibility — all grounded in NumPy.

Some vectors only get scaled by a matrix — they don't rotate at all. These eigenvectors reveal the skeleton of a linear transformation. Master the eigen-equation, the characteristic polynomial, diagonalization, and why eigenstructure powers PCA, PageRank, and stability analysis.

Connect joint velocities to end-effector velocity through the Jacobian matrix. Learn how to build J, spot singularities where det J = 0, invert J with the pseudoinverse for velocity control, and measure manipulability — with NumPy code for the 2-link arm.

Flip the FK problem: given a desired end-effector pose, find the joint angles that achieve it. Master analytical closed-form IK for the 2-link arm, the elbow-up/elbow-down duality, atan2 arithmetic, and the basics of numerical IK via the Jacobian.

Translate a list of joint angles into an end-effector pose. Learn the four Denavit-Hartenberg parameters, build per-link transforms, multiply them into T_0^n, and implement FK for a 2-link planar arm in NumPy.

Master how roboticists describe rigid-body pose. Build rotation matrices from scratch, pack them into 4x4 homogeneous transforms, and compose multiple frames with NumPy to track every link in a robot arm.

Understand no-download game distribution: how HTML5 and instant games work, why WeChat and Douyin mini-games dominate in China, how Xbox Cloud Gaming and GeForce Now operate, and what Google Stadia's 2023 shutdown taught the industry about cloud gaming unit economics.

Understand where the $180B+ games market actually sits — mobile vs console vs PC — who skims the value chain, how the major revenue models compare, and why a tiny fraction of players drives most F2P revenue.

How do you scale a database beyond one machine while keeping it reliable? This lesson covers every major replication topology, the quorum math behind leaderless systems, and partitioning strategies from range keys to consistent hashing — including how to avoid hot partitions and handle rebalancing.

Distributed systems break in ways single machines don't: nodes crash silently, messages vanish, and clocks lie. Learn the standard failure taxonomy, why a global clock is physically impossible, and how Lamport and vector clocks let you reason about causality without one.