Friday, June 24, 2016


I teach mathematics at the University of Hertfordshire. To contact me send an email to
My Homepage is at

Linear Algebra Step by Step:

In general I will be writing articles about mathematics, in particular adding comments to the book "Engineering Mathematics through Applications"

Review of How Big is Infinity? By Tony Crilly

This is genuinely a mathematics book for the layman. There are putatively many books on mathematics for the layman but once you start reading them, they are so specialized that you need to be at least an undergraduate to understand them. This is not so for this book. You will be able to comprehend most of this book with just GCSE mathematics background.
The book has the subtitle ‘The 20 Big Maths Questions’ which refers to the 20 chapters (sections) the book is divided into. Each of these 20 question headings are a good hook for any reader such as ‘What is mathematics for?, Are Statistics lies?, Is mathematics beautiful? Moreover, the content under these questions is pertinent and interesting.
The book is a very incisive and lucid reminiscence of important questions of mathematics. It also includes some history of mathematics and manages to describe the latest work in mathematics research.
My only reservation is that many of the applications and mathematics itself has been discussed in a number of different books over time. However, the book is a good blend of erudition and entertainment.
It doesn’t matter how many times you check, recheck a mathematics book, errors and typos always manage to creep in. Here is list of I picked up:
Page 17; The prize money (for the Poincare conjecture) should be in dollars, not pounds.
Page 58; The last digit in the value of e to six decimal places should be 2 and not 1.
Page 116; we draw in the third paragraph is repeated twice.
Page 122: Solve is misspelt as Sove in the penultimate paragraph.

Page 269; The left-hand side of the infinite series should say π/4 and not π. 

Monday, May 25, 2015

Publishing and the Advancement of Science by Michael Rogers

An Excellent Introduction to Publishing Science books
The author spent over 30 years of his working life being a science editor for various publishing companies. He was the commissioning editor for popular science books as well as science textbooks.
Most of this book describes the authors’ time at Oxford University Press (OUP) but also significantly the work involved in commissioning books such as Selfish Genes by Richard Dawkins and Physical Chemistry by Peter Atkins. Both of these books have achieved enormous sales.
The book under review is not an autobiography but emphasises Rogers working life as an editor. There are some really interesting anecdotes regarding his meetings with various authors and the pressures of publishing companies.
Anyone wanting to write a textbook or popular science book should purchase this as it reveals real insight into publishing such books and how to go about such a task.

Kuldeep Singh 25Th May 2015

Wednesday, April 15, 2015

Love and Math by Edward Frenkel
The author is a professional mathematician and describes what it means to do mathematical research. There are some real gems in this book such as:
Which functions (Euler phi function) are used to encrypt credit card numbers.
Which is larger 2/3 or 3/5 – Most people know that 2 bottles of vodka for 3 people is better than 3 bottles for 5 people.
How we can obtain the Fibonacci sequence from its generating function.
What does a finite field mean.
There is also a good explanation of the Langlands Program.
Very few typos (the only two I picked up were both on page 85 - should be divisible not visible and penultimate paragraph should start with ‘As we’.)
It is really pleasing to see that the author does not shy away from the mathematics in his writing.
However this is not a book for the layman because the mathematics is totally inaccessible to the general audience. This is not a piece of writing for a popular audience as I mistakenly believed it was after reading a review before purchasing. To fully appreciate this book you should at least be an undergraduate in mathematics or physics as it is tough going in places.
Throughout the book the author has highlighted his personal struggles of being Jewish with the regime of the Soviet Union. This is really interesting as I was unaware of how the regime thought of all Jews as opponents, criminals, foes (these are my words). When depicting this the author mentions a number of locations in Russia which he should have illustrated with maps as most of us in the West will not be able to visualize the locations.
Additionally I have a few minor quibbles:
There are a number of terms omitted from the glossary such as invariant, winding number.
Should have explained the term monodromy through illustrations.
The author claims ‘It is customary to exclude 1 from this list” (of primes). I always thought of 1 as neither prime nor composite, just a unit.
I conclude that this is not a book for the layman.

Kuldeep Singh 15th April 2015

Monday, November 10, 2014

The Education of a Mathematician by Philip Davies

This book is different from most other books for the mathematics layman. It is a very tangible and personal journey of the author from the 1930’s to end of the 20 century. In general I found it a very readable book on mathematics as well as mathematics education. There is also philosophy discussions in the book.
The author is a professional mathematician who gives his personal experience and what it means to be a mathematician with his travels to various countries.
The author discuss some really important questions such as the future role of mathematics and it applications. Also he reflects back at how mathematics has affected all of us in the past.
The last chapter describes the authors’ talk at the ‘The International Congress of Mathematicians’ in August 1998 given in Berlin. I really like this chapter with subheading such as Male vs Female Mathematics and Soft Mathematics vs Traditional Mathematics.

My only reservation is that it was hard to follow in places as the author is also a philosopher. 

Thursday, October 30, 2014

Review of Mathematics in Victorian Britain by R. Flood, A. Rice and R. Wilson

This book is divided up into mathematics of various era and geographical locations. It gives a flavour of mathematics and mathematicians not only in Britain but also in the Commonwealth.

Since each chapter is written by a new author I found some of the chapters pretty technical and others very accessible where the emphasis is on the people involved. A glossary might have made the book more accessible on the technical side but it would have to be such a large glossary that the book loses its compactness.

There are some really interesting snippets about mathematicians and their social life. I found the last chapter by Jeremy Gray the most interesting and controversial and will let you read this to find out why.

However I do have one serious reservation – the size of the font is far too small and in general I struggled to read this book. Hence the three stars.

Any serious history of mathematics student should purchase this book as it provides good motivation to the methods and approaches that lie behind the mathematics.

Thursday, July 10, 2014

The Simpsons and their Mathematical Secrets by Simon Singh

Until I read this book I was unaware of the sprinkling of mathematics in the Simpsons.

The book discusses the mathematicians on the writing teams of the Simpsons and Futurama. I must say that I was surprised to learn that most of the writers on these programmes are graduates or postgraduates of mathematics or physics.

It is an excellent book for a layman as all the mathematics is explained in detailed.

My reservation is that the book is a series of detached mathematical stories whose only common theme is that these stories appeared in the Simpsons or Futurama. Also these mathematical stories are so common that if you have read any mathematical popular book you would have come across them. So nothing new here.

However I do think any serious mathematics student should purchase this book as it provides good motivation to study mathematics at undergraduate level.


Monday, May 05, 2014

I am so proud that the front cover of my book is Mandela Bridge in South Africa.