Softcover ISBN:  9780883856505 
Product Code:  NML/46 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 
Electronic ISBN:  9780883859896 
Product Code:  NML/46.E 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 

Book DetailsAnneli Lax New Mathematical LibraryVolume: 46; 2015; 144 ppRecipient of the Mathematical Association of America's Beckenbach Book Prize in 2018!
The Riemann hypothesis concerns the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 … Ubiquitous and fundamental in mathematics as they are, it is important and interesting to know as much as possible about these numbers. Simple questions would be: how are the prime numbers distributed among the positive integers? What is the number of prime numbers of 100 digits? Of 1,000 digits? These questions were the starting point of a groundbreaking paper by Bernhard Riemann written in 1859. As an aside in his article, Riemann formulated his now famous hypothesis that so far no one has come close to proving: All nontrivial zeroes of the zeta function lie on the critical line. Hidden behind this at first mysterious phrase lies a whole mathematical universe of prime numbers, infinite sequences, infinite products, and complex functions.
The present book is a first exploration of this fascinating, unknown world. It originated from an online course for mathematically talented secondary school students organized by the authors of this book at the University of Amsterdam. Its aim was to bring the students into contact with challenging university level mathematics and show them what the Riemann Hypothesis is all about and why it is such an important problem in mathematics. 
Table of Contents

Chapters

Chapter 1. Prime numbers

Chapter 2. The zeta function

Chapter 3. The Riemann hypothesis

Chapter 4. Primes and the Riemann hypothesis

Appendix A. Why big primes are useful

Appendix B. Computer support

Appendix C. Further reading and internet surfing

Appendix D. Solutions to the exercises


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The Riemann hypothesis concerns the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 … Ubiquitous and fundamental in mathematics as they are, it is important and interesting to know as much as possible about these numbers. Simple questions would be: how are the prime numbers distributed among the positive integers? What is the number of prime numbers of 100 digits? Of 1,000 digits? These questions were the starting point of a groundbreaking paper by Bernhard Riemann written in 1859. As an aside in his article, Riemann formulated his now famous hypothesis that so far no one has come close to proving: All nontrivial zeroes of the zeta function lie on the critical line. Hidden behind this at first mysterious phrase lies a whole mathematical universe of prime numbers, infinite sequences, infinite products, and complex functions.
The present book is a first exploration of this fascinating, unknown world. It originated from an online course for mathematically talented secondary school students organized by the authors of this book at the University of Amsterdam. Its aim was to bring the students into contact with challenging university level mathematics and show them what the Riemann Hypothesis is all about and why it is such an important problem in mathematics.

Chapters

Chapter 1. Prime numbers

Chapter 2. The zeta function

Chapter 3. The Riemann hypothesis

Chapter 4. Primes and the Riemann hypothesis

Appendix A. Why big primes are useful

Appendix B. Computer support

Appendix C. Further reading and internet surfing

Appendix D. Solutions to the exercises