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2 weeks ago
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Our first live review in the new QF Book Review Series explored the opening chapter on Vector Spaces and sparked a lively debate about how mathematics should be taught to machine learning practitioners.
🔑 Key Points
1. Strong Start
Participants praised the book’s introduction for clearly explaining why mathematics is essential for understanding machine learning, not just coding it.
2. Main Critiques
The typography of the book’s digital version is quite poor. Other readers have raised similar complaints, so our observation is not an isolated one.
Symbols such as ℝ⁴ appearing before key definitions (e.g Cartesian product) . A preamble of notations and conventions at the start would have been helpful. It would be ok if the book assumes the reader is already familiar with the standard notations.
The vector diagrams, intended to build intuitive understanding before the formal definition of a vector space, could be made clearer, particularly in illustrating vector addition.
The definition of a vector space, while technically acceptable given the target audience of the book, feels somewhat overloaded (see clips 2 and 3 for reference). Although omitting the formal definition of a field is understandable, including it would greatly benefit readers, especially since the book positions itself as a guide to “Master Linear Algebra.” Likewise, providing a brief definition of groups would have strengthened the mathematical foundation and improved overall coherence.
One key axiom regarding scalar multiplication was left out. Namely, (a+b)x = ax +bx for all scalars a, b in the field F and x in the vector space V.
3. Rigour vs. Readability
The group debated how far to go with abstraction. Bambordé argued that starting from groups and fields builds stronger intuition, while others felt this might alienate beginners. The conversation itself captured what makes QF sessions special: sharp disagreement, yet always in pursuit of clearer mathematical understanding for learners.
4. Takeaway
Everyone agreed that the book succeeds in motivating learners and conveying the importance of mathematics in machine learning. However, the section reviewed so far could strike a better balance between mathematical precision and accessibility, ensuring that the exposition remains both rigorous for technically inclined readers and approachable for those coming from applied backgrounds.
You can watch the full recording of the event and access the supplementary slides here (available to paid Substack members).
If you would like to join the next live session on Saturday, 25 October at 5 p.m. GMT, you can register here: https://quantumformalism.academy/book-review
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Happy new week ahead!
QF Academy team
