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Thinking Algebraically: An Introduction to Abstract Algebra
 
Thomas Q. Sibley St. John’s University, Collegeville, MN
Thinking Algebraically
MAA Press: An Imprint of the American Mathematical Society
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
eBook 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
Softcover ISBN:  978-1-4704-6030-3
eBook: ISBN:  978-1-4704-6306-9
Product Code:  TEXT/65.B
List Price: $170.00 $127.50
MAA Member Price: $127.50 $95.63
AMS Member Price: $127.50 $95.63
Thinking Algebraically
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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
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
eBook 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
Softcover ISBN:  978-1-4704-6030-3
eBook ISBN:  978-1-4704-6306-9
Product Code:  TEXT/65.B
List Price: $170.00 $127.50
MAA Member Price: $127.50 $95.63
AMS Member Price: $127.50 $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.

    Ancillaries:

    Readership

    Undergraduate 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
  • 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 publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
    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.

Ancillaries:

Readership

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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
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