2  How to Use This Book

This book sits in an awkward but valuable place. It is not a “data science workflow” guide and it is not a pure mathematics text. It is an attempt to make the mathematical centre of modern data science readable — and to keep that mathematics tied to modelling choices, evidence, and consequences.

If the structure ever feels sparse, the fix is not to add more theorems. The fix is to add more orientation: why this topic exists, what question it answers, what kinds of mistakes it prevents, and what kinds of work it enables.

2.1 What a holistic program includes (and what this book does)

A good undergraduate data science pathway typically mixes:

  • programming and data structures
  • databases and data management
  • data acquisition, cleaning, and reproducible workflows
  • visualization and communication
  • statistics, regression, and time-series thinking
  • machine learning and model evaluation
  • ethical and social context
  • applied projects (often work-integrated)

Mount Royal University’s B.Sc. in Data Science is a clear example: students are expected to learn programming, databases, data acquisition/processing, visualization, regression/time series, machine learning, and professional context alongside mathematics and statistics.

This book does one job in that larger ecosystem:

Make the mathematics of learning systems legible enough that you can use it in applied work without treating it as magic.

If you need practical workflow support, treat it as a companion layer:

  • version control, notebooks, and reports
  • data validation and provenance
  • experiment tracking
  • deployment and monitoring (MLOps)

Those topics matter, but they are not the central spine here.

2.2 Three reading paths

Not all readers want the same route. Choose a path and accept that you will jump around.

2.2.1 Path A: “Modelling first”

If you want the book to feel like applied mathematics:

  1. Chapter 1 (modelling language)
  2. Chapter 2 (generalisation and evaluation)
  3. Chapter 3 (optimisation as an algorithmic idea)
  4. Chapter 4 (representation geometry)
  5. Chapter 5 (uncertainty and prediction)

Then return for dynamics, information, and deep learning.

2.2.2 Path B: “Engineering/process data”

If you are thinking in terms of sensors, plants, experiments, and operational decisions (a vibe closer to UAlberta’s CH E 358 framing):

  1. Chapter 1 (what is the system, what is measured, what is hidden?)
  2. Chapter 4 (dimensionality reduction and representation)
  3. Chapter 2 (regression/classification as decision support)
  4. Chapter 6 (time, filtering, latent state)
  5. Chapter 3 (why training is an optimisation problem)

2.2.3 Path C: “ML/AI mathematics”

If you want the neural network story quickly:

  1. Chapter 1 (objectives and losses)
  2. Chapter 3 (gradients, descent, and computation)
  3. Chapter 4 (vectors, projections, embeddings)
  4. Chapter 8 (networks as composed functions)
  5. Chapter 7 (cross-entropy and objective geometry)

Then circle back for uncertainty and time.

2.3 A running set of examples

To keep the mathematics anchored, chapters reuse three kinds of examples:

  • Prediction from tabular data (demand, risk, yield): good for regression, loss functions, and uncertainty.
  • Classification as a decision (spam/fraud/diagnosis): good for evaluation, asymmetry, calibration, and cross-entropy.
  • Time and latent state (tracking, filtering, forecasting): good for sequences, estimation, and dynamical models.

When the prose feels thin, ask: which example would make this section feel inevitable? Then use the mini-project prompts at the end of the book to build that example in your own context.

2.4 The running real-world thread: Fire and Smoke (Alberta-first)

Alongside the small illustrative examples, the book carries one consistent real-world thread: Alberta wildfire smoke and station PM2.5.

Treat it as a living capstone:

  • Chapter 1: write the modelling brief (features, target, hidden variables, loss).
  • Chapters 2–7: build disciplined evaluation, uncertainty, and objective choices.
  • Chapter 8: add deep models only once baselines and splits are honest.

This thread is designed to sit beside a companion essay on the main Wayward House site (“Fire and Smoke”). The essay can carry more narrative and context; the book carries the mathematics and the reusable modelling grammar.

2.5 How to read (actively)

  • Treat each chapter’s “prerequisite anchors” as permission to go backwards.
  • Do not aim to memorise notation; aim to recognise structure.
  • When a new concept arrives, write down:
    • what problem it solves
    • what mistake it prevents
    • what assumption it quietly makes

That habit is the difference between “knowing formulas” and “having a modelling language”.