The Riemann Hypothesis, by Roland van der Veen and Jan van de Craats, Mathematical Association of America, Washington, D. C., 2015. 144 pp., $45.00 (paper). ISBN 9780883856505.
Five out of five stars
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
Computation engine link