The Riemann Hypothesis (Anneli Lax New Mathematical Library) by Roland van der Veen

Anneli Lax New Mathematical Library

by Roland van der Veen and Jan van de Craats

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 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 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.

Genres: Mathematics, Science

Paperback

First published December 1, 2016

Reviews

[Pablo Sebastián · Rating 5 out of 5]

This book introduces one of the hardest problems in current mathematics without the need to know advanced mathematics. A great book to read if you're planning on studying mathematics or if you're just curious about it. Most of these concepts are, in most places, explained by difficult mathematics if your not familiar with them. This book solves this problem really well. It also contains problems to work on which I haven't looked at yet, but seem accesible to people with knowledge of highschool mathematics. Really interesting concepts covered, would totally recommend.

[Charles · Rating 5 out of 5]

For approximately a century, the Riemann hypothesis has been the single, most significant unsolved problem in mathematics. Since it was first mentioned by Bernard Riemann in 1859, largely as an afterthought, the problem is one whose solution has remained elusive. It was the eighth problem in the famous list of 23 major problems to solve in the twentieth century that was put forward by David Hilbert in 1900. It is also one of the problems where the Clay Mathematical Institute offers one million dollars for a solution.
This book is a collection of material that was the text for a four week long web class on the Riemann hypothesis that was aimed at mathematically bright secondary students. It contains a large number of challenging exercises that the students were to work on, partial solutions are included. The students received the material, worked on the problems and communicated with each other and the teachers over the internet.
Instructors of special topics math classes will be able to use this book for a section on specialized number theory, with an emphasis on the zeta function. It is a self-contained short course in the topic. Mathematicians that are just interested in learning more about the Riemann hypothesis can also use it as a self-study tutorial. This book begins with the basics of the prime numbers and goes step-by-step through the background material until the zeta function and the Riemann hypothesis are explained.
A web site where the reader can access a Mathematica-like computation engine for number theory computations is also given. Snippets of computer code that will perform specific number theory computations are also given. I tested the website out and it is extremely easy to use.

This book was made available for free for review purposes