The mathematical prerequisites for the rest of the book.
Part I is taught in three levels rather than as three separate courses. The probability and statistics material is deliberately interleaved — you learn enough probability to read real data, spend time with real data, then go back for the distributions that let you model it, then finish the statistics toolkit. This is the pedagogical arc Allen Downey’s Think Stats gets right and most courses get wrong.
Linear algebra runs as an independent track alongside. It’s orthogonal to the prob ↔ stats arc — needed throughout the book, but not gated by either.
1The curriculum map¶
┌─ Level 1 — Foundations ───────────────┐
│ │
│ probability/part0 What is a │
│ distribution? │
│ probability/part1 Bernoulli │
│ ↓ │
│ statistics/ch01 EDA │
│ (real data) │
│ statistics/ch02 Histograms │
│ (shape question) │
└───────────────────────────────────────┘
↓
┌─ Level 2 — Distributions ─────────────┐
│ │
│ probability/part2 Binomial │
│ probability/part3 Poisson │
│ probability/part4 Normal │
│ probability/part5 CLT │
│ probability/part6 Sensor model │
│ │
│ (we now have the shapes needed to │
│ answer the Ch 2 question) │
└───────────────────────────────────────┘
↓
┌─ Level 3 — Inference ─────────────────┐
│ │
│ statistics/ch03–ch14 │
│ PMF → CDF → modeling → PDF → │
│ relationships → estimation → │
│ hypothesis testing → least squares →│
│ regression → time series → │
│ survival → analytic methods │
└───────────────────────────────────────┘
┌─ Linear Algebra (independent track) ─────┐
│ │
│ part1 Vectors and dot product │
│ part2 Norms and similarity │
│ part3 Orthogonality and projection │
│ part4 Linear transforms │
│ │
│ Read in parallel to any level above. │
└──────────────────────────────────────────┘2Why interleaved?¶
A normal probability-then-statistics course teaches distributions first, in the abstract, and then drops real data on you in a separate course. Students arrive at real data armed with formulas they can’t connect to anything concrete, and arrive at distributions not knowing what they’re for.
The interleaved path flips this:
Level 1 builds the minimum probability needed to understand “a random variable has an outcome” (parts 0–1), then dives straight into real survey data (stats ch01–02). By the end of histograms the reader has a concrete question — “what mathematical shape matches this histogram?” — that cries out for an answer.
Level 2 provides the answer: the family of standard distributions (binomial, Poisson, normal, CLT), each introduced with the exact shape question it solves.
Level 3 returns to the data with the distributions in hand, and builds the full statistical-inference toolkit: PMF, CDF, PDF, estimation, hypothesis testing, regression, time series, survival.
Every chapter after Level 1 has a motivating question that came out of the chapter before. Nothing is introduced “because it’s on the syllabus.”
3How to read this section¶
Sequential (recommended). Follow the levels top to bottom. Linear algebra can be read in any parallel order.
Already know probability? Skip Level 1’s probability pieces, skim Level 2, read Level 3 in full.
Already know statistics? Use Part I as a refresher. Level 1 is a fast read; Level 2 is a review of distribution families; Level 3 has the nontrivial material.
Need something specific? Every chapter lists prerequisites at the top. Jump in, backfill from earlier levels as needed.
4Folder layout¶
math/
├── README.md ← this file (curriculum map)
├── probability/ ← Levels 1, 2 (and Level 3 background)
├── statistics/ ← Levels 1, 3 (skip ch02 if taught linearly
│ — it's in Level 1 above)
└── linear_algebra/ ← independent trackThe files themselves never moved — the levels are an organization overlay
on top of the same chapter files. The myst.yml TOC renders the three
levels; this README is the reference for readers who want to understand
why the order is the way it is.