Lessons

Weekly lessons published as I complete them. The lesson titles and plan summaries were generated with AI assistance. All lesson notes, exercises, coding projects, and proofs are written entirely by me — no AI-generated content — since the goal is to learn or re-learn the material and that can only be achieved by producing my own work. All proofs are done by hand on paper first; the handwritten proofs are then converted into LaTeX using AI (OpenAI or Claude) so I can focus on the mathematics and let the AI handle the typesetting.

See the full syllabus for the complete 36-week plan.

Phase 0 · Weeks 1–4 — Foundations: GPU + Linear Algebra + Analysis

• Week 1 — Vector Spaces and GPU Data Representation
• Week 2 — Linear Maps, Transformations, and Program Structure
• Week 3 — Matrix Multiplication and Linear Systems
• Week 4 — Eigenvalues, Eigenvectors, and Diagonalization

Phase 1 · Weeks 5–8 — Probability + Functional Thinking

• Week 5 — Probability Spaces and Normed Vector Spaces
• Week 6 — Random Variables and Linear Operators
• Week 7 — Covariance, Inner Products, and Numerical Stability
• Week 8 — Spectral Decomposition and Principal Component Analysis

Phase 2 · Weeks 9–12 — Geometry + Graphics Math

• Week 9 — Coordinate Systems and Geometric Transformations
• Week 10 — Curves, Surfaces, and Curvature
• Week 11 — Surface Normals and Illumination Models
• Week 12 — Topological Concepts in Geometric Spaces

Phase 3 · Weeks 13–16 — GPU Algorithms + Numerical Stability

• Week 13 — Parallel Reduction Algorithms and Floating-Point Error
• Week 14 — Prefix Sums and Parallel Scan Algorithms
• Week 15 — Sorting Networks and Parallel Sorting Algorithms
• Week 16 — Optimized Matrix Multiplication and Memory Hierarchy

Phase 4 · Weeks 17–20 — Signals + Fourier + Complex Analysis

• Week 17 — Discrete Convolution and Linear Time-Invariant Systems
• Week 18 — Discrete Fourier Transform and Frequency Analysis
• Week 19 — Sampling Theory and Aliasing
• Week 20 — Monte Carlo Methods in Rendering

Phase 5 · Weeks 21–24 — Probability Deep Dive

• Week 21 — Law of Large Numbers and Modes of Convergence
• Week 22 — Variance Reduction Techniques in Simulation
• Week 23 — Markov Chains and Stochastic Processes
• Week 24 — Advanced Sampling Techniques for Rendering

Phase 6 · Weeks 25–28 — Optimization + Information Theory

• Week 25 — Convex Sets and Convex Functions
• Week 26 — Gradient-Based Optimization Methods
• Week 27 — Duality Theory and Constrained Optimization
• Week 28 — Entropy, Divergence, and Information Measures

Phase 7 · Weeks 29–32 — Abstract Algebra + Coding Theory

• Week 29 — Groups and Subgroup Structure
• Week 30 — Rings, Ideals, and Polynomial Arithmetic
• Week 31 — Finite Fields and Field Extensions
• Week 32 — Error Correcting Codes and Polynomial Methods

Phase 8 · Weeks 33–36 — Systems + Capstone

• Week 33 — GPU Profiling and Performance Analysis
• Week 34 — Integration of Graphics and Compute Pipelines
• Week 35 — Capstone System Implementation
• Week 36 — System Optimization and Final Presentation