January 2023 – Mathemafrica

Patterns, Predictions and Actions: Foundations of Machine Learning, by Hardt and Recht – a review

NB. I was sent this book as a review copy.

I’ve just taught a course on mathematics for data science. Sadly it was only ten hours long, so there was only so much that I could cover. However, I feel that was taught was sufficient to get my students to the point that they would feel both comfortable with, and highly motivated to read Patterns, Predictions and Actions.

The balance between theory, application and narrative in the book is, I think, just right, making it a genuinely pleasurable book to read cover to cover, or to dip into a given topic to find the mathematical details (or at least what you need to get started). As with any foundational book, each topic could be covered in massively more detail, but that would simply make it a book, different from the authors’ intentions. The jump between the ideas and mathematical principle of Support Vector Machines, as given on one page, the optimisation methods of linear programming, and the practical aspect of coding up of such an algorithm are missing, but given the aims of the book, this doesn’t feel like a loss.…

The Story of Proof: Logic and the History of Mathematics, by John Stillwell – a review

NB. I was sent this book as a review copy.

From Princeton University Press

The last book of Stillwell’s that I reviewed was Reverse Mathematics which was utterly fascinating, and truly mind-bending. I was very much looking forward to another of his books, and this one did not disappoint. It is a much less alternative perspective on mathematics than the previous, but no less beautifully written or compelling.

I teach pure mathematics to first year undergraduates (amongst others), and so often find that the very concept of a mathematical proof is something that is so hard to grasp. What is sufficient to concretely prove something? What can be assumed? What sort of proof is appropriate within a given context? High school maths generally sets students up very badly in this realm.

Stillwell’s book on the Story of Proof is perhaps a little beyond what could be grasped easily by most first year students, though very keen ones, with patience could certainly make their way through it, and would benefit enormously from doing so.…