Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
An Experimental Introduction to Number Theory
 
Benjamin Hutz :  Saint Louis University, Saint Louis, MO
An Experimental Introduction to Number Theory
Hardcover ISBN:  978-1-4704-3097-9
Product Code:  AMSTEXT/31
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-4672-7
Product Code:  AMSTEXT/31.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-3097-9
eBook: ISBN:  978-1-4704-4672-7
Product Code:  AMSTEXT/31.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
Add to cart
An Experimental Introduction to Number Theory
Click above image for expanded view
An Experimental Introduction to Number Theory
Benjamin Hutz :  Saint Louis University, Saint Louis, MO
Hardcover ISBN:  978-1-4704-3097-9
Product Code:  AMSTEXT/31
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-4672-7
Product Code:  AMSTEXT/31.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-3097-9
eBook ISBN:  978-1-4704-4672-7
Product Code:  AMSTEXT/31.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
Add to cart
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    Volume: 31; 2018; 314 pp
    MSC: Primary 11; 37

    This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems.

    The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.
    Readership

    Undergraduate students interested in number theory.
  • Table of Contents
     
     
    • Cover
    • Title page
    • Contents
    • Preface
    • Note to the Instructor
    • Organization
    • Acknowledgments
    • Introduction
    • Chapter 1. Integers
    • 1. The Integers and the Well Ordering Property
    • 2. Divisors and the Division Algorithm
    • 3. Greatest Common Divisor and the Euclidean Algorithm
    • 4. Prime Numbers and Unique Factorization
    • Exercises
    • Chapter 2. Modular Arithmetic
    • 1. Basic Arithmetic
    • 2. Inverses and Fermat’s Little Theorem
    • 3. Linear Congruences and the Chinese Remainder Theorem
    • Exercises
    • Chapter 3. Quadratic Reciprocity and Primitive Roots
    • 1. Quadratic Reciprocity
    • 2. Computing 𝑚th Roots Modulo 𝑛
    • 3. Existence of Primitive Roots
    • Exercises
    • Chapter 4. Secrets
    • 1. Basic Ciphers
    • 2. Symmetric Ciphers
    • 3. Diffie–Hellman Key Exchange
    • 4. Public Key Cryptography (RSA)
    • 5. Hash Functions and Check Digits
    • 6. Secret Sharing
    • Exercises
    • Chapter 5. Arithmetic Functions
    • 1. Euler Totient Function
    • 2. Möbius Function
    • 3. Functions on Divisors
    • 4. Partitions
    • Exercises
    • Chapter 6. Algebraic Numbers
    • 1. Algebraic or Transcendental
    • 2. Quadratic Number Fields and Norms
    • 3. Integers, Divisibility, Primes, and Irreducibles
    • 4. Application: Sums of Two Squares
    • Exercises
    • Chapter 7. Rational and Irrational Numbers
    • 1. Diophantine Approximation
    • 2. Height of a Rational Number
    • 3. Heights and Approximations
    • 4. Continued Fractions
    • 5. Approximating Irrational Numbers with Convergents
    • Exercises
    • Chapter 8. Diophantine Equations
    • 1. Introduction and Examples
    • 2. Working Modulo Primes
    • 3. Pythagorean Triples
    • 4. Fermat’s Last Theorem
    • 5. Pell’s Equation and Fundamental Units
    • 6. Waring Problem
    • Exercises
    • Chapter 9. Elliptic Curves
    • 1. Introduction
    • 2. Addition of Points
    • 3. Points of Finite Order
    • 4. Integer Points and the Nagel–Lutz Theorem
    • 5. Mordell–Weil Group and Points of Infinite Order
    • 6. Application: Congruent Numbers
    • Exercises
    • Chapter 10. Dynamical Systems
    • 1. Discrete Dynamical Systems
    • 2. Dynatomic Polynomials
    • 3. Resultant and Reduction Modulo Primes
    • 4. Periods Modulo Primes
    • 5. Algorithms for Rational Periodic and Preperiodic Points
    • Exercises
    • Chapter 11. Polynomials
    • 1. Introduction to Polynomials
    • 2. Factorization and the Euclidean Algorithm
    • 3. Modular Arithmetic for Polynomials
    • 4. Diophantine Equations for Polynomials
    • Exercises
    • Bibliography
    • List of Algorithms
    • List of Notation
    • Index
    • Back Cover
  • Additional Material
     
     
  • Reviews
     
     

    • If you see the value of stressing calculation and computers in a first course in number theory, then this book is one that you will want to take a good look at the next time you teach number theory.
      Mark Hunacek, MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Pure and Applied Undergraduate Texts
Volume: 31; 2018; 314 pp
MSC: Primary 11; 37

This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems.

The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.
Readership

Undergraduate students interested in number theory.
  • Cover
  • Title page
  • Contents
  • Preface
  • Note to the Instructor
  • Organization
  • Acknowledgments
  • Introduction
  • Chapter 1. Integers
  • 1. The Integers and the Well Ordering Property
  • 2. Divisors and the Division Algorithm
  • 3. Greatest Common Divisor and the Euclidean Algorithm
  • 4. Prime Numbers and Unique Factorization
  • Exercises
  • Chapter 2. Modular Arithmetic
  • 1. Basic Arithmetic
  • 2. Inverses and Fermat’s Little Theorem
  • 3. Linear Congruences and the Chinese Remainder Theorem
  • Exercises
  • Chapter 3. Quadratic Reciprocity and Primitive Roots
  • 1. Quadratic Reciprocity
  • 2. Computing 𝑚th Roots Modulo 𝑛
  • 3. Existence of Primitive Roots
  • Exercises
  • Chapter 4. Secrets
  • 1. Basic Ciphers
  • 2. Symmetric Ciphers
  • 3. Diffie–Hellman Key Exchange
  • 4. Public Key Cryptography (RSA)
  • 5. Hash Functions and Check Digits
  • 6. Secret Sharing
  • Exercises
  • Chapter 5. Arithmetic Functions
  • 1. Euler Totient Function
  • 2. Möbius Function
  • 3. Functions on Divisors
  • 4. Partitions
  • Exercises
  • Chapter 6. Algebraic Numbers
  • 1. Algebraic or Transcendental
  • 2. Quadratic Number Fields and Norms
  • 3. Integers, Divisibility, Primes, and Irreducibles
  • 4. Application: Sums of Two Squares
  • Exercises
  • Chapter 7. Rational and Irrational Numbers
  • 1. Diophantine Approximation
  • 2. Height of a Rational Number
  • 3. Heights and Approximations
  • 4. Continued Fractions
  • 5. Approximating Irrational Numbers with Convergents
  • Exercises
  • Chapter 8. Diophantine Equations
  • 1. Introduction and Examples
  • 2. Working Modulo Primes
  • 3. Pythagorean Triples
  • 4. Fermat’s Last Theorem
  • 5. Pell’s Equation and Fundamental Units
  • 6. Waring Problem
  • Exercises
  • Chapter 9. Elliptic Curves
  • 1. Introduction
  • 2. Addition of Points
  • 3. Points of Finite Order
  • 4. Integer Points and the Nagel–Lutz Theorem
  • 5. Mordell–Weil Group and Points of Infinite Order
  • 6. Application: Congruent Numbers
  • Exercises
  • Chapter 10. Dynamical Systems
  • 1. Discrete Dynamical Systems
  • 2. Dynatomic Polynomials
  • 3. Resultant and Reduction Modulo Primes
  • 4. Periods Modulo Primes
  • 5. Algorithms for Rational Periodic and Preperiodic Points
  • Exercises
  • Chapter 11. Polynomials
  • 1. Introduction to Polynomials
  • 2. Factorization and the Euclidean Algorithm
  • 3. Modular Arithmetic for Polynomials
  • 4. Diophantine Equations for Polynomials
  • Exercises
  • Bibliography
  • List of Algorithms
  • List of Notation
  • Index
  • Back Cover

  • If you see the value of stressing calculation and computers in a first course in number theory, then this book is one that you will want to take a good look at the next time you teach number theory.
    Mark Hunacek, MAA Reviews
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
You may be interested in...
Powered by MathJax
Please select which format for which you are requesting permissions.