Abridged Math Foundations for Signals and Systems — Course 1 Booklet

Self-contained booklet, 185 pages, 60 lessons in 8 parts. The text of Course 1 — Mathematical & Theoretical Foundations, read cover to cover: download the PDF.

This is the worked exercise set for that booklet. Every non-capstone 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. 205 exercises across 53 lessons — 90 [Proof], 115 [Hand]. The seven capstone lessons (8, 15, 20, 27, 35, 52, 60) carry projects rather than exercises and are not part of this set.

Numbering. Exercises are numbered lesson.exercise: Exercise 5.4 is the fourth exercise of Lesson 5. Lessons are numbered continuously 1–60 across the eight 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 1–8, 29 exercises. ✓ done: Lessons 1–7 (all 29) — the whole of Part I; Lesson 8 is Capstone I, a project.
• Part II — Eigenstructure, the Spectral Theorem, the DFT, and the SVD — Lessons 9–15, 24 exercises. ✓ done: Lessons 9–13 (all 20).
• Part III — The Probability Core — Lessons 16–20, 17 exercises
• Part IV — Random Vectors, Limit Theorems, and Stochastic Processes — Lessons 21–27, 24 exercises
• Part V — The Signals-and-Systems Core — Lessons 28–35, 28 exercises
• Part VI — Applied Signal Processing — Lessons 36–44, 27 exercises
• Part VII — The Analysis Behind the Transforms — Lessons 45–52, 28 exercises
• Part VIII — Convex Optimization and Information Theory for ML, Signals, and Sensors — Lessons 53–60, 28 exercises