Summing it up : from one plus one to modern number theory /

We use addition on a daily basis--yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful nume...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Ash, Avner, 1949-
Autres auteurs: Gross, Robert, 1959-
Format: Électronique eBook
Langue:Inglés
Publié: Princeton : Princeton University Press, [2016]
Sujets:
Mathematik.
Number theory.
Mathematics > Popular works.
Théorie des nombres.
Mathématiques > Ouvrages de vulgarisation.
MATHEMATICS > Algebra > Intermediate.
MATHEMATICS > General.
Mathematics
Number theory
Addition
Zahl
Zahlentheorie
Philosophie
Popular works
Obras de divulgación.
Accès en ligne:Texto completo
Table des matières:
  • Frontmatter
  • CONTENTS
  • PREFACE
  • ACKNOWLEDGMENTS
  • INTRODUCTION: WHAT THIS BOOK IS ABOUT
  • PART ONE. FINITE SUMS
  • CHAPTER 1. PROEM
  • CHAPTER 2. SUMS OF TWO SQUARES
  • CHAPTER 3. SUMS OF THREE AND FOUR SQUARES
  • CHAPTER 4. SUMS OF HIGHER POWERS: WARING'S PROBLEM
  • CHAPTER 5. SIMPLE SUMS
  • CHAPTER 6. SUMS OF POWERS, USING LOTS OF ALGEBRA
  • PART TWO. INFINITE SUMS
  • CHAPTER 7. INFINITE SERIES
  • CHAPTER 8. CAST OF CHARACTERS
  • CHAPTER 9. ZETA AND BERNOULLI
  • CHAPTER 10. COUNT THE WAYS
  • PART III. MODULAR FORMS AND THEIR APPLICATIONS
  • CHAPTER 11. THE UPPER HALF-PLANE
  • CHAPTER 12. MODULAR FORMS
  • CHAPTER 13. HOW MANY MODULAR FORMS ARE THERE?
  • CHAPTER 14. CONGRUENCE GROUPS
  • CHAPTER 15. PARTITIONS AND SUMS OF SQUARES REVISITED
  • CHAPTER 16. MORE THEORY OF MODULAR FORMS
  • CHAPTER 17. MORE THINGS TO DO WITH MODULAR FORMS: APPLICATIONS
  • BIBLIOGRAPHY
  • INDEX.

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