Softcover ISBN:  9781470461591 
Product Code:  TEXT/9.S 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
eBook ISBN:  9780883859834 
Product Code:  TEXT/9.E 
List Price:  $59.00 
MAA Member Price:  $44.25 
AMS Member Price:  $44.25 
Softcover ISBN:  9781470461591 
eBook: ISBN:  9780883859834 
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 
Softcover ISBN:  9781470461591 
Product Code:  TEXT/9.S 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
eBook ISBN:  9780883859834 
Product Code:  TEXT/9.E 
List Price:  $59.00 
MAA Member Price:  $44.25 
AMS Member Price:  $44.25 
Softcover ISBN:  9781470461591 
eBook ISBN:  9780883859834 
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 DetailsAMS/MAA TextbooksVolume: 9; 2007; 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, theoremproving 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 introductiontoproofs 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

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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, theoremproving 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 introductiontoproofs 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