Book Review

[Numbers]

Browsing round Amazon on Saturday I came across a book called "A Course in Arithmetic" by J.P. Serre. Turns out it’s about Hecke operators, p-adic fields and the Riemann zeta function, not what most people would consider to be arithmetic, and this brought home to me the old adage about not being able to tell a book by its covers.

So I thought it would be an idea to have a thread where people can post reviews of, recommendations for or warnings against books we have read. The general idea is that books should be “on-topic”, whatever your topic happens to be; “A Computational Approach To Galois Cohomology”, “Distributed Computing In A Non-Linear Society” or maybe even “Sieves I Have Known And Loved” (whatever takes your fancy). I guess that in time this distinction will become blurred and we will see a review for that old Horst Bucholz classic, “Brewing By Numbers”. C’est la vie.

[Numbers]

Prime Obsession
John Derbyshire
Joseph Henry Press
ISBN 0-309-08549-7

Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

Aimed more at the interested amateur rather than the post-graduate student, this elegantly written book justifiably claims that the Riemann Hypothesis can not be explained using maths more elementary than this. There’s a little bit of calculus, but most of the rest is just algebra and arithmetic.

Chapters alternate between maths and the people and places behind the story giving the reader an easy-paced introduction to such greats as Dedekind, Dirichlet, Euler and the inimitable Gauss between chapters dealing with the maths in easy, bite-sized chunks. Not much is known about Riemann outside of his work and he doesn’t exactly leap off the page as a full-blown character, but what a mind! By the time the reader is shown the Euler product formula even the non-mathematician knows enough to appreciate it for what it is; a thing of rare and signal beauty, and you are still only half way through the book!

When I got to the end I turned right back to the first page and read the book again. Not because I hadn’t understood it, but because I almost believed I had. It is hard to imagine that there will ever be a better non-specialist introduction to the subject than this.

[mfgoode]

The Universal History of Numbers (3 vols.)
Author Georges Ifrah.
A Penguin book.
The only number given is 10 9 8 7 6 5 4 3 2 1

"Numbers are one of two creations (the other being the alphabet) of the human spirit which have given us today's world. The 3 vols. of The Universal History of Numbers are probably the first comprehensive History of numbers and of counting prehistory to the modern age. They are also the story of how the human race has learnt to think logically"
Excellent for math historians.
Mally

[Richard Cameron]

Originally Posted by mfgoode

The Universal History of Numbers (3 vols.)
Author Georges Ifrah.
A Penguin book.
The only number given is 10 9 8 7 6 5 4 3 2 1
Mally

It may be worth mentioning that although this book was originally three volumes, the first two were bound together in the edition I have:

Harvill Press, London, 1998 ISBN 1 86046 324 X

and the third volume is

Harvill Press, London 2000 ISBN 1 86046 738 5


I don't know if these are still in print: I bought both remaindered.


Richard

[mfgoode]

You are right Richard. It was reissued as a two volume set in 2000 by Harvill press.
It was published in India in 2005 as a 3 vol. set only for the subcontinent.
BTW I picked up Roger Penrose's colossal HB The Road to Reality as recmmended by Paul Xilman, just today. Its brand new and cost me only £10
compared to £30 in the U.K.
I am also half way thru 'THe Development of Mathematics' by ET Bell a dover book renewed by Taine T Bell in 1972 . It covers math from 4000 B.C. to 1940 and how it developed during that period.
Mally.

[mfgoode]

Originally Posted by mfgoode

I am also half way thru 'THe Development of Mathematics' by ET Bell a dover book renewed by Taine T Bell in 1972 . It covers math from 4000 B.C. to 1940 and how it developed during that period.
Mally.

Since then I have completed this book whilst on holiday.
I recommend it to anyone interested in maths.
It gives considerable detail of the leading mathem'cians' dissertations from the 'Liber Abaci' (1202) of Leonardo of Pisa (1175-1250) thru Cantor's 'Megenlehre' to Laplace's 'Essai philosophique sur les probabilities' and beyond to Neumann and G.D.Birkoff right up to Gibbs' classic 'Elementary principles in Statistical Mechanics'. The 2nd edition is up to date till 1945 altho' E.T. Bell lived upto 1960. Theres not much on modern number theory tho' of the type studied by Hardy and Ramanujan.
Mally