How to Think About Abstract Algebra

Description

How to Think about Abstract Algebra provides an engaging and readable introduction to its subject, which encompasses group theory and ring theory.

• Psychologically natural introduction to the subject, informed by research in undergraduate mathematics education
• In-depth exploration of examples via tables and diagrams
• Focus on why: why definitions are sensible, why key results hold for some mathematical objects but not others, and why mathematicians care about what they care about

About the Author(s)

Lara Alcock, Reader and Head of Department, Mathematics, Education Centre, Loughborough University

Lara Alcock is a Reader in Mathematics Education at Loughborough University. She collaborates with colleagues, PhD students and project students to conduct research on mathematical thinking and learning, specializing in reasoning among undergraduate mathematics students and professional mathematicians. She is author of two previous research-informed study guides for undergraduate students: How to Study for a Mathematics Degree and How to Think about Analysis. She also authored the popular mathematics book Mathematics Rebooted: A Fresh Approach to Understanding.

Table of Contents

1:What is Abstract Algebra?
2:Axioms and Denitions
3:Theorems and Proofs
4:Studying Abstract Algebra
5:Binary Operations
6:Groups and Subgroups
7:Quotient Groups
8:Isomorphisms and Homomorphisms
9:Rings
References

Reviews

"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." - Chalkdust