Abridged Math Foundations for Signal Processing, Machine Learning, and Artificial Intelligence — Course 1 Booklet

Self-contained booklet, 337 pages, 70 lessons in 9 parts. The text of Course 1 — Math Foundations for Signal Processing, Machine Learning, and Artificial Intelligence, read cover to cover: download the PDF.

This is the worked exercise set for that booklet. Every lesson closes on an exercise block tagged [Proof] (prove a statement) or [Hand] (compute a small example by hand); a \(\star\) marks the harder proofs. 294 exercises across 70 lessons — 147 [Proof], 147 [Hand].

Numbering. Exercises are numbered lesson.exercise: Exercise 5.4 is the fourth exercise of Lesson 5. Lessons are numbered continuously 1–70 across the nine parts, matching the booklet’s own section numbers and the anchors on the Course 1 page.

Solutions are worked by hand on paper first, then typeset. Sets appear here as they are completed.

Parts

• Part I — The Linear Algebra Core — Lessons 1–7, 29 exercises. ✓ done: Lessons 1–7 (all 29) — the whole of Part I;
• Part II — Eigenstructure, the Spectral Theorem, the DFT, and the SVD — Lessons 8–13, 24 exercises. ✓ done: Lessons 8–13 (all 24) — the whole of Part II;
• Part III — The Probability Core — Lessons 14–17, 21 exercises. ✓ done: Lessons 14–15 (13 of 21);
• Part IV — Random Vectors, Limit Theorems, and Stochastic Processes — Lessons 18–23, 24 exercises
• Part V — The Signals-and-Systems Core — Lessons 24–30, 28 exercises
• Part VI — The Analysis Behind the Transforms — Lessons 31–43, 60 exercises
• Part VII — Convex Optimization and Information Theory for ML, Signals, and Sensors — Lessons 44–51, 32 exercises
• Part VIII — Neural Networks and Deep Learning — Lessons 52–62, 44 exercises
• Part IX — The Mathematics of Real-Time Rendering — Lessons 63–70, 32 exercises