Books

Reading and exercise sets organized by textbook. The first entry is Course 1’s own booklet; the rest are its deeper-reading companions, with the exercise sets worked by hand. One shelf follows the booklet: the mathematics and theory books whose exercise sets are worked here.

Each book lists a Minimum: the bare-minimum chapters to read for the course that uses it. Specific worked problems are filled in here as I complete them (marked ✓ done where a chapter set is finished); the course pages link here rather than listing exercises themselves. Worked proofs are done by hand on paper first, then typeset.

The Course 1 Booklet

  • Abridged Math Foundations for Signal Processing, Machine Learning, and Artificial Intelligence
    • Minimum — the whole booklet: 51 lessons in 7 parts, 192 pages (PDF). 218 exercises across 51 lessons — 109 tagged [Proof], 109 tagged [Hand]. Numbered lesson.exercise, matching the booklet’s section numbers and the Course 1 anchors. ✓ done: Part I — Lesson 1 (1.1–1.4), Lesson 2 (2.1–2.4), Lesson 3 (3.1–3.4), Lesson 4 (4.1–4.4), Lesson 5 (5.1–5.5), Lesson 6 (6.1–6.4), Lesson 7 (7.1–7.4); Part II — Lesson 8 (8.1–8.4), Lesson 9 (9.1–9.4), Lesson 10 (10.1–10.4), Lesson 11 (11.1–11.4), Lesson 12 (12.1–12.4), Lesson 13 (13.1–13.4); Part III — Lesson 14 (14.1–14.9). Problems added as worked.

Mathematics & Theory

The nine books behind the theory foundation. Eight are ordered by dependency: linear algebra → numerical linear algebra → real analysis → measure & integration → probability → complex analysis → distribution theory and Fourier transforms → functional analysis. The ninth, Dunn & Parberry, sits outside that chain as the applied 3D mathematics serving Course 4. The reading lists here are deliberately minimal: the applied books of the other two shelves re-develop the applications in full, so each math book is cut to the sections the DSP, image, and audio work actually spends. One more subject from the dependency plan — a dedicated stochastic-processes text — will be added once a book with workable problem sets is chosen.

  • Linear Algebra Done Right — Axler
    • Minimum — read Ch. 1–3, 5–7 (vector spaces, linear maps; eigenvalues and invariant subspaces; inner product spaces; the spectral theorem, polar decomposition and the SVD), plus the determinant material of Ch. 9. ✓ done: Ch. 1: §1A (all), §1B (all), §1C (1, 3, 4, 19, 20, 23, 24); Ch. 2: §2A (1, 2, 3, 5, 7, 10, 11, 18, 20), §2B (1, 5, 10), §2C (1, 2, 10, 18, 19, 20).
  • Numerical Linear Algebra — Trefethen & Bau
    • Minimum — read Lectures 1–8 (matrix-vector products, orthogonality, norms, the SVD, projectors, QR, Gram–Schmidt), 10–12 (Householder triangularization, least squares, conditioning and condition numbers), and 18 (conditioning of least squares problems). The stability-proof and eigenvalue-algorithm lectures are cut — eigentheory is Axler’s, and the later coursework consumes factorizations and eigendecompositions as primitives. Problems added as worked.
  • Elementary Analysis — Ross
    • Minimum — read Ch. 1–6. ✓ done: Ch. 1: §1 (1.1, 1.6, 1.12), §2 (2.1, 2.8), §3 (3.3, 3.4, 3.5, 3.6), §4 (4.9, 4.14, 4.15, 4.16); Ch. 2: §8 (8.4, 8.5, 8.6, 8.9, 8.10), §9 (9.9, 9.10, 9.11, 9.12), §10 (10.2, 10.5, 10.6, 10.7, 10.8), §11 (11.1, 11.8), §12 (12.1, 12.10, 12.11), §13 (13.4, 13.5, 13.6, 13.14), §14 (14.9, 14.12); Ch. 3: §17 (17.4, 17.5, 17.6, 17.8).
  • Measure, Integration & Real Analysis — Axler
    • Minimum — read 1B (the case against the Riemann integral); 2A (skim), 2B–2D (measurable spaces and functions; measures; Lebesgue measure, skipping the Cantor material), selected 2E (convergence of measurable functions); 3A–3B (integration with respect to a measure and its limit theorems); 5A (skim), 5B, selected 5C (product measures, iterated integrals, integration on \(\mathbb{R}^n\)); the integration of complex-valued functions in 6B; 7A–7B (the \(\mathcal{L}^p\)/\(L^p\) spaces); 8A–8C (inner product spaces, orthogonality, orthonormal bases); and selected 11A with 11B–11C (Fourier series, the Poisson integral, and the Fourier transform on \(L^p\)). Problems added as worked.
  • Introduction to Probability — Bertsekas & Tsitsiklis
    • Minimum — read Ch. 1–7 (probability models, random variables, expectation, limit theorems, the Bernoulli and Poisson processes, Markov chains). Problems added as worked.
  • Complex Analysis — Bak & Newman
    • Minimum — read Ch. 1–4 (complex numbers; functions of \(z\); analytic functions and the Cauchy–Riemann equations; line integrals and entire functions), Ch. 6 (properties of analytic functions — the Cauchy integral formula and power series), and Ch. 9–11 (isolated singularities and Laurent expansions; the residue theorem; its applications to integrals and sums); skim Ch. 5 for Liouville’s theorem and the fundamental theorem of algebra. Ch. 7–8 and 12–13 (max-modulus, simply connected domains, contour techniques, conformal mapping) are cut — the residue calculus is what the z-transform and filter-stability work spends. Problems added as worked.
  • A Guide to Distribution Theory and Fourier Transforms — Strichartz
    • Minimum — read Ch. 1–4 (distributions, the Dirac delta, distributional derivatives, convolution, the Fourier transform of tempered distributions), §§6.1, 6.3, 6.6 (the support of a distribution; distributions with point support; approximation by test functions), and §§7.1, 7.3, 7.5, 7.8 (the Riemann–Lebesgue lemma; the Poisson summation formula behind the Dirac comb and the sampling theorem; the Heisenberg uncertainty principle; Haar functions and wavelets). Problems added as worked.
  • Introductory Functional Analysis with Applications — Kreyszig
    • Minimum — read §§2.2, 2.6–2.8, 2.10 (normed and Banach spaces; linear operators, bounded and continuous operators, linear functionals; normed spaces of operators and the dual space), §§3.8–3.10 (Riesz representation on Hilbert space; the Hilbert-adjoint; self-adjoint, unitary, and normal operators), §4.8 (strong and weak convergence), §§5.1, 5.3 (the Banach fixed-point theorem; its application to differential equations, for control), §§6.1, 6.4, 6.5 (approximation in normed spaces; Chebyshev polynomials; approximation in Hilbert space), and selected §§7.2–7.4 (spectral theory of bounded linear operators). The metric-space, Hilbert-space, and \(L^p\) foundations come from Axler’s MIRA above, so Kreyszig is read only for what it adds on top. Problems added as worked.
  • 3D Math Primer for Graphics and Game Development — Dunn & Parberry
    • Minimum — read Ch. 1–10. Ch. 1–2 and 4 (Cartesian coordinate systems; vectors; introduction to matrices) are fast review after Axler — read them for the coordinate and handedness conventions, not the algebra. The load-bearing chapters are 3 (multiple and nested coordinate spaces, basis vectors), 5 (matrices as linear transformations — rotation, scale, orthographic projection, reflection, shearing, composition), 6 (determinants, inverses, orthogonal matrices, \(4 \times 4\) homogeneous matrices and perspective projection), 8 (orientation in three dimensions — Euler angles, axis-angle and exponential map, quaternions, and the conversions between them), 9 (geometric primitives — lines and rays, spheres, bounding boxes, planes, triangles, polygons), and 10 (mathematical topics from 3D graphics — viewing, polygon meshes, texture mapping, the standard local lighting model, light sources, bump mapping, the real-time graphics pipeline); Ch. 7 (polar and spherical coordinates) is short and pays for itself at image-based lighting. Ch. 11–12 (linear kinematics and calculus; linear and rotational dynamics) and Ch. 13 (curves in 3D — Hermite, Bézier, splines) are cut: no Course 4 lab needs a physics integrator or spline interpolation. Worked as the standalone 3D-math set serving Course 4. Problems added as worked.