How to Think About Abstract Algebra

Chalkdust

15 April 2022

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Lara Alcock is a reader in mathematics education at Loughborough University, and head of the Mathematics Education Centre at Loughborough. How to Think About Abstract Algebra (Amazon UK, Waterstones, Oxford University Press) is a book that tells you how to think about abstract algebra.

Style

How to Think About Abstract Algebra is a book aimed at a very specific target audience: people in the early days of an undergraduate maths degree. It isn’t an algebra textbook; instead it guides the reader through some of the things they should be doing to make more sense of the kind of pure maths they are about to meet.

Control

How to Think About Abstract Algebra eases the reader into each topic, and includes makes examples, visualisations, and intuition. This allows to book to give the reader a much deeper understanding of the material than they might pick up by attending a lecture course. (This is of course not the lecturers’ faults, as teaching a course that included much detail for every topic would take forever.)

Damage

This book fills a nice in the maths book market, making it very different to the majority of other maths books. There are a few very good books about transitioning from school to university (eg Kevin Houston’s How to Think Like a Mathematician, and one of Lara’s other books How to Study for a Mathematics Degree spring to mind), but I don’t know of many books that cover this for a specific topic.

Aggression

I wish I’d had this book when I was starting my undergraduate degree. I’d very strongly recommend it to undergraduates studying maths, Sixth formers about to study maths, and anyone who did a maths degree a while ago and wants to revisit groups, rings and fields. I also recommend that any first year pure maths lecturers reading this should add this book to their course’s reading list.

If you’ve never been anywhere near a maths degree, then you don’t really fit into the target audience for this book, but you might still enjoy finding out some of the gritty details of what university pure maths is like.

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