Softcover ISBN:  9781470460303 
Product Code:  TEXT/65 
List Price:  $85.00 
MAA Member Price:  $63.75 
AMS Member Price:  $63.75 
Electronic ISBN:  9781470463069 
Product Code:  TEXT/65.E 
List Price:  $85.00 
MAA Member Price:  $63.75 
AMS Member Price:  $63.75 

Book DetailsAMS/MAA TextbooksVolume: 65; 2021; 478 ppMSC: 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 ringsfirst and groupsfirst 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 yearlong 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.ReadershipUndergraduate students interested in abstract algebra.

Table of Contents

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

Selected Answers


Additional Material

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


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 Book Details
 Table of Contents
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Thinking Algebraically presents the insights of abstract algebra in a welcoming and accessible way. It succeeds in combining the advantages of ringsfirst and groupsfirst 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 yearlong 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

Selected Answers

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