**AMS/MAA Textbooks**

Volume: 65;
2021;
592 pp;
Softcover

MSC: Primary 20; 16; 12; 06;

**Print ISBN: 978-1-4704-6030-3
Product Code: TEXT/65**

List Price: $85.00

AMS Member Price: $63.75

MAA Member Price: $63.75

**Electronic ISBN: 978-1-4704-6306-9
Product Code: TEXT/65.E**

List Price: $85.00

AMS Member Price: $63.75

MAA Member Price: $63.75

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# Thinking Algebraically: An Introduction to Abstract Algebra

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*Thomas Q. Sibley*

MAA Press: An Imprint of the American Mathematical Society

Thinking Algebraically presents the insights of abstract
algebra in a welcoming and accessible way. It succeeds in combining
the advantages of rings-first and groups-first approaches while
avoiding the disadvantages. After an historical overview, the first
chapter studies familiar examples and elementary properties of groups
and rings simultaneously to motivate the modern understanding of
algebra. The text builds intuition for abstract algebra starting from
high school algebra. In addition to the standard number systems,
polynomials, vectors, and matrices, the first chapter introduces
modular arithmetic and dihedral groups. The second chapter builds on
these basic examples and properties, enabling students to learn
structural ideas common to rings and groups: isomorphism,
homomorphism, and direct product. The third chapter investigates
introductory group theory. Later chapters delve more deeply into
groups, rings, and fields, including Galois theory, and they also
introduce other topics, such as lattices. The exposition is clear and
conversational throughout.

The book has numerous exercises in each section as well as
supplemental exercises and projects for each chapter. Many examples
and well over 100 figures provide support for learning. Short
biographies introduce the mathematicians who proved many of the
results. The book presents a pathway to algebraic thinking in a
semester- or year-long algebra course.

#### Readership

Undergraduate students interested in abstract algebra.