"How to Think about Abstract Algebra" offers an engaging and readable introduction to the field of Abstract Algebra, which includes group theory and ring theory. Abstract Algebra is central to most undergraduate mathematics studies, as it captures regularities that appear in various mathematical structures - many find it beautiful for this reason. However, its abstract nature can make the understanding of its fundamental ideas challenging, and even the best students may find themselves following some of the logic without truly understanding what is happening.
This book aims to solve this problem. It is not like other Abstract Algebra books and is not a textbook with standard content. Instead, it is designed to be read before beginning an Abstract Algebra course or as a supplementary text once a course has started. It gathers essential information into five themes: binary operations, groups, fractional groups, isomorphisms and homomorphisms, and rings. It provides numerous examples, tables, and diagrams, and its explanations are based on research in mathematics education.
The book also offers study advice focused on the skills students need to successfully learn in their own Abstract Algebra courses. It explains how to productively interact with axioms, definitions, theorems, and proofs, as well as how research in psychology should inform our beliefs about effective learning.
