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Thinking Algebraically: An Introduction to Abstract Algebra

Thomas Q. Sibley St. John’s University, Collegeville, MN
MAA Press: An Imprint of the American Mathematical Society
Available Formats:
Softcover ISBN: 978-1-4704-6030-3
Product Code: TEXT/65
List Price: $85.00 MAA Member Price:$63.75
AMS Member Price: $63.75 Electronic ISBN: 978-1-4704-6306-9 Product Code: TEXT/65.E List Price:$85.00
MAA Member Price: $63.75 AMS Member Price:$63.75
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $127.50 MAA Member Price:$95.63
AMS Member Price: $95.63 Click above image for expanded view Thinking Algebraically: An Introduction to Abstract Algebra Thomas Q. Sibley St. John’s University, Collegeville, MN MAA Press: An Imprint of the American Mathematical Society Available Formats:  Softcover ISBN: 978-1-4704-6030-3 Product Code: TEXT/65  List Price:$85.00 MAA Member Price: $63.75 AMS Member Price:$63.75
 Electronic ISBN: 978-1-4704-6306-9 Product Code: TEXT/65.E
 List Price: $85.00 MAA Member Price:$63.75 AMS Member Price: $63.75 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$127.50 MAA Member Price: $95.63 AMS Member Price:$95.63
• Book Details

AMS/MAA Textbooks
Volume: 652021; 478 pp
MSC: Primary 20; 16; 12; 06;

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.

An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to textbooks@ams.org for more information.

Undergraduate students interested in abstract algebra.

• Chapters
• Prologue
• A transition to abstract algebra
• Relationships between systems
• Groups
• Rings, integral domains, and fields
• Vector spaces and field extensions
• Topics in group theory
• Topics in algebra
• Epilogue

• Reviews

• This textbook for a course in abstract algebra proceeds from realizing the utter disconnect between students' high school experience of algebra (manipulate symbols, solve equations) and the emphasis in abstract algebra on structures and their properties. The book starts by identifying properties of number systems familiar to students (including modular arithmetics), investigates mappings (isomorphism, homomorphism), introduces cyclic and abelian groups, and then explores rings. Further chapters feature vector spaces, Galois theory, and topics in group theory and ring theory (symmetry groups, Sylow theorems, lattices, Boolean algebras). There are abundant exercises, plus biographical sketches of many of the mathematicians involved.

Mathematics Magazine
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
Volume: 652021; 478 pp
MSC: Primary 20; 16; 12; 06;

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.

An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to textbooks@ams.org for more information.

Undergraduate students interested in abstract algebra.

• Chapters
• Prologue
• A transition to abstract algebra
• Relationships between systems
• Groups
• Rings, integral domains, and fields
• Vector spaces and field extensions
• Topics in group theory
• Topics in algebra
• Epilogue