Mathematics for Data Science and AI
A follow-on book built on the Grade 7 to university mathematics path
This book is the natural continuation of Wayward House Mathematics for readers who want to move from mathematical foundations into data science, machine learning, and AI.
The existing eight-volume series already builds most of the mathematical spine: functions, sequences, calculus, probability, inference, linear algebra, numerics, optimisation, signals, estimation, and computational modelling. What this follow-on book adds is the ML/AI-specific structure that those tools are usually absorbed into too quickly: objectives, losses, representations, uncertainty, information, and learned systems.
The goal is not to imitate a standard “math for ML” reference. The goal is to show how the mathematics grows into modelling, learning, and decision-making without pretending the reader appeared fully formed at matrix calculus.
0.1 Book shape
The book is organised into parts so the heavy topics have room to breathe. Between chapters, you are expected to pause, try a few exercises, and build one small example that you can carry forward.
| Part | Chapters | Core move |
|---|---|---|
| Orientation | How to Use This Book, Prerequisite Map | Decide how you will read, and where you will go back for foundations |
| Modelling → Learning | 1–3 | Turn situations into objectives, then turn objectives into learnable rules |
| Representations | 4, 7, 8 | Treat “learning” as building representations and objectives that make sense |
| Uncertainty and Dynamics | 5–6 | Handle noise, belief, time, filtering, and latent state |
| Synthesis | Mini-Projects and Pathways, Exercise Answers | Reuse the mathematics in coherent mini-projects and prompts |
0.2 Why this structure resembles real programs
Degree programs and applied courses rarely teach “machine learning” as a single monolithic thing. They braid multiple strands:
- mathematics and statistics (so models are interpretable)
- computing and data handling (so models can be built and checked)
- communication and context (so decisions are accountable)
- projects and constraints (so learning happens in the real world)
For example, MRU’s Data Science planning guide highlights programming, databases, data acquisition/processing, visualization, regression/time series, and machine learning, alongside broader professional and community context. In a different but related way, UAlberta’s CH E 358 frames data analytics in terms of process data, regression, dimensionality reduction, classification, deep learning, and experimental design — with a lab component.
This book does not try to replicate the whole degree. It provides the mathematical spine those pathways depend on, and it adds enough modelling prose and example structure that the topics feel connected rather than assorted.
0.3 Relationship to the main series
This is a sibling book, not Volume 9 of the current sequence. It assumes the reader can move backward into the main series whenever a prerequisite feels shaky. The point is not to repeat the whole mathematics path. The point is to use it well.