How to Think About Abstract Algebra

by Lara Alcock

How to Think about Abstract Algebra provides an engaging and readable introduction to its subject, which encompasses group theory and ring theory. Abstract Algebra is central in most undergraduate mathematics degrees, and it captures regularities that appear across diverse mathematical structures - many people find it beautiful for this reason. But its abstraction can make its central ideas hard to grasp, and even the best students might find that they can follow some of the reasoning without really understanding what it is all about.

This book aims to solve that problem. It is not like other Abstract Algebra texts and is not a textbook containing standard content. Rather, it is designed to be read before starting an Abstract Algebra course, or as a companion text once a course has begun. It builds up key information on five binary operations, groups, quotient groups, isomorphisms and homomorphisms, and rings. It provides numerous examples, tables and diagrams, and its explanations are informed by research in mathematics education.

The book also provides study advice focused on the skills that students need in order to learn successfully in their own Abstract Algebra courses. It explains how to interact productively with axioms, definitions, theorems and proofs, and how research in psychology should inform our beliefs about effective learning.

Genres: Mathematics, Science, Nonfiction

320 pages, Kindle Edition

Published February 4, 2021

Reviews

[Austin · Rating 5 out of 5]

Lives up to its name. This should be required material for every abstract algebra student, if not every math student. Any student who has been frustrated by unmotivated and uninspiring algebra textbooks has wanted to write a book like this, and Alcock has done it. The explanations are clearly written for the dedicated student, and are further enhanced with generous diagrams and footnotes.

The first few chapters are a bit inconsistent when assuming the reader's mathematical maturity, but I believe the majority of this book is accessible to motivated teenagers. This book covers basic group theory up the First Isomorphism Theorem, and only has a brief discussion of rings.

[Gary Bridgwater · Rating 5 out of 5]

Why I appreciate this Book.

I am 76, retired, majored in chemistry, became a medical doctor, but always wanted learn more math. This author would have helped me do that 55 years ago. Teaching math is special. This book shows how to deal with conflicting approaches, how to not get discouraged.