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Number Theory Through Inquiry
 
Number Theory Through Inquiry
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-6159-1
Product Code:  TEXT/9.S
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
eBook ISBN:  978-0-88385-983-4
Product Code:  TEXT/9.E
List Price: $59.00
MAA Member Price: $44.25
AMS Member Price: $44.25
Softcover ISBN:  978-1-4704-6159-1
eBook: ISBN:  978-0-88385-983-4
Product Code:  TEXT/9.S.B
List Price: $124.00 $94.50
MAA Member Price: $102.75 $85.05
AMS Member Price: $96.25 $75.60
Number Theory Through Inquiry
Click above image for expanded view
Number Theory Through Inquiry
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-6159-1
Product Code:  TEXT/9.S
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
eBook ISBN:  978-0-88385-983-4
Product Code:  TEXT/9.E
List Price: $59.00
MAA Member Price: $44.25
AMS Member Price: $44.25
Softcover ISBN:  978-1-4704-6159-1
eBook ISBN:  978-0-88385-983-4
Product Code:  TEXT/9.S.B
List Price: $124.00 $94.50
MAA Member Price: $102.75 $85.05
AMS Member Price: $96.25 $75.60
  • Book Details
     
     
    AMS/MAA Textbooks
    Volume: 92007; 140 pp

    Number Theory Through Inquiry is an innovative textbook that leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. One goal is to help students develop mathematical thinking skills, particularly, theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for an independent study experience, or for a course designed as an introduction to abstract mathematics. Math or related majors, future teachers, and students or adults interested in exploring mathematical ideas on their own will enjoy Number Theory Through Inquiry.

    Number theory is the perfect topic for an introduction-to-proofs course. Every college student is familiar with basic properties of numbers, and yet the exploration of those familiar numbers leads us to a rich landscape of ideas. Number Theory Through Inquiry contains a carefully arranged sequence of challenges that lead students to discover ideas about numbers and to discover methods of proof on their own. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors' materials explain the instructional method. This style of instruction gives students a totally different experience compared to a standard lecture course. Here is the effect of this experience: Students learn to think independently: they learn to depend on their own reasoning to determine right from wrong; and they develop the central, important ideas of introductory number theory on their own. From that experience, they learn that they can personally create important ideas, and they develop an attitude of personal reliance and a sense that they can think effectively about difficult problems. These goals are fundamental to the educational enterprise within and beyond mathematics.

    Ancillaries:

  • Table of Contents
     
     
    • Chapters
    • Chapter 0. Introduction
    • Chapter 1. Divide and Conquer
    • Chapter 2. Prime Time
    • Chapter 3. A Modular World
    • Chapter 4. Fermat’s Little Theorem and Euler’s Theorem
    • Chapter 5. Public Key Cryptography
    • Chapter 6. Polynomial Congruences and Primitive Roots
    • Chapter 7. The Golden Rule: Quadratic Reciprocity
    • Chapter 8. Pythagorean Triples, Sums of Squares, and Fermat’s Last Theorem
    • Chapter 9. Rationals Close to Irrationals and the Pell Equation
    • Chapter 10. The Search for Primes
    • A. Mathematical Induction: The Domino Effect
  • Additional Material
     
     
  • 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: 92007; 140 pp

Number Theory Through Inquiry is an innovative textbook that leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. One goal is to help students develop mathematical thinking skills, particularly, theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for an independent study experience, or for a course designed as an introduction to abstract mathematics. Math or related majors, future teachers, and students or adults interested in exploring mathematical ideas on their own will enjoy Number Theory Through Inquiry.

Number theory is the perfect topic for an introduction-to-proofs course. Every college student is familiar with basic properties of numbers, and yet the exploration of those familiar numbers leads us to a rich landscape of ideas. Number Theory Through Inquiry contains a carefully arranged sequence of challenges that lead students to discover ideas about numbers and to discover methods of proof on their own. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors' materials explain the instructional method. This style of instruction gives students a totally different experience compared to a standard lecture course. Here is the effect of this experience: Students learn to think independently: they learn to depend on their own reasoning to determine right from wrong; and they develop the central, important ideas of introductory number theory on their own. From that experience, they learn that they can personally create important ideas, and they develop an attitude of personal reliance and a sense that they can think effectively about difficult problems. These goals are fundamental to the educational enterprise within and beyond mathematics.

Ancillaries:

  • Chapters
  • Chapter 0. Introduction
  • Chapter 1. Divide and Conquer
  • Chapter 2. Prime Time
  • Chapter 3. A Modular World
  • Chapter 4. Fermat’s Little Theorem and Euler’s Theorem
  • Chapter 5. Public Key Cryptography
  • Chapter 6. Polynomial Congruences and Primitive Roots
  • Chapter 7. The Golden Rule: Quadratic Reciprocity
  • Chapter 8. Pythagorean Triples, Sums of Squares, and Fermat’s Last Theorem
  • Chapter 9. Rationals Close to Irrationals and the Pell Equation
  • Chapter 10. The Search for Primes
  • A. Mathematical Induction: The Domino Effect
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
Please select which format for which you are requesting permissions.