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
Resource Information
The item Summing it up : from one plus one to modern number theory, Avner Ash and Robert Gross represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of San Diego Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Summing it up : from one plus one to modern number theory, Avner Ash and Robert Gross represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of San Diego Libraries.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- 1 online resource
- 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
- Isbn
- 9781400880539
- 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
- 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
- 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
- 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
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.sandiego.edu/portal/Summing-it-up--from-one-plus-one-to-modern/IcnX0IZibxM/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.sandiego.edu/portal/Summing-it-up--from-one-plus-one-to-modern/IcnX0IZibxM/">Summing it up : from one plus one to modern number theory, Avner Ash and Robert Gross</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.sandiego.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.sandiego.edu/">University of San Diego Libraries</a></span></span></span></span></div>
