How to Think About Abstract Algebra

Lara Alcock (Autor)

Buch | Softcover

320 Seiten

2021
Oxford University Press (Verlag)
978-0-19-884338-2 (ISBN)

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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 topics: 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.

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.

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

Erscheinungsdatum	19.02.2021
Verlagsort	Oxford
Sprache	englisch
Maße	127 x 195 mm
Gewicht	372 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften
ISBN-10	0-19-884338-0 / 0198843380
ISBN-13	978-0-19-884338-2 / 9780198843382
Zustand	Neuware