Coverart for item
The Resource Summing it up : from one plus one to modern number theory, Avner Ash and Robert Gross

Summing it up : from one plus one to modern number theory, Avner Ash and Robert Gross

Label
Summing it up : from one plus one to modern number theory
Title
Summing it up
Title remainder
from one plus one to modern number theory
Statement of responsibility
Avner Ash and Robert Gross
Creator
Contributor
Subject
Genre
Language
eng
Summary
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 numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series--long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+ ... =? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem. Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers
Cataloging source
N$T
http://library.link/vocab/creatorDate
1949-
http://library.link/vocab/creatorName
Ash, Avner
Index
index present
Language note
In English
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1959-
http://library.link/vocab/relatedWorkOrContributorName
Gross, Robert
http://library.link/vocab/subjectName
  • Mathematik
  • Number theory
  • Mathematics
  • MATHEMATICS
  • Mathematics
  • Number theory
  • Addition
  • Zahl
  • Zahlentheorie
  • Philosophie
  • MATHEMATICS / General
Label
Summing it up : from one plus one to modern number theory, Avner Ash and Robert Gross
Instantiates
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 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
  • Frontmatter
  • 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
  • CONTENTS
  • PREFACE
  • ACKNOWLEDGMENTS
  • INTRODUCTION: WHAT THIS BOOK IS ABOUT
  • PART ONE. FINITE SUMS
  • CHAPTER 1. PROEM
  • CHAPTER 2. SUMS OF TWO SQUARES
Control code
ocn946158222
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9781400880539
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
JSTOR
Other control number
  • 40026175053
  • 10.1515/9781400880539
http://library.link/vocab/ext/overdrive/overdriveId
  • 4333589
  • 22573/ctvc616vg
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)946158222
Label
Summing it up : from one plus one to modern number theory, Avner Ash and Robert Gross
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 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
  • Frontmatter
  • 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
  • CONTENTS
  • PREFACE
  • ACKNOWLEDGMENTS
  • INTRODUCTION: WHAT THIS BOOK IS ABOUT
  • PART ONE. FINITE SUMS
  • CHAPTER 1. PROEM
  • CHAPTER 2. SUMS OF TWO SQUARES
Control code
ocn946158222
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9781400880539
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
JSTOR
Other control number
  • 40026175053
  • 10.1515/9781400880539
http://library.link/vocab/ext/overdrive/overdriveId
  • 4333589
  • 22573/ctvc616vg
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)946158222

Library Locations

    • Copley LibraryBorrow it
      5998 Alcalá Park, San Diego, CA, 92110-2492, US
      32.771354 -117.193327
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