Author: Leonard Mlodinow
By Allen Lane

Let us not be outperformed by a rat, 2008-10-08
I was surprised to learn that the Greeks did not have a theory of probability. Their belief "that the future unfolded according to the will of the gods" and their taste for "absolute truth" did not encourage the study of chance. Where pristine philosophy failed, the more grubby pastime of gambling succeeded in motivating probability theory. And, in true statistical style, it only took a handful of gamblers out of a large enough sample to get things going.

Today we might as well be Greeks for all that we understand or even recognize uncertainty. Even if we do not share the view that everything happens for a reason, it is still easy to ignore the role chance plays in our lives. We humans, with our big brains and clever language and propensity for story telling, are well equipped for this kind of failure. When it comes to recognizing randomness, we can be "outperformed by a rat". If this fact piques your curiosity or lowers your self-esteem, read on, and this superb book should satisfy one and restore the other. It is anything but a drunkard's walk through an intellectual maze. Mathematics, the social sciences, psychology, economics, brain studies, all contribute to the modern understanding of this fascinating area. By the end, several important ideas should have become straightened out into the intellectual equivalent of broad, tree-lined avenues, and you might agree with a quotation from Max Born: "Chance is a more fundamental conception than causality."

First off, do not panic. Even a Harvard professor specializing in probability and statistics admits we're not cut out for this kind of thinking - which makes Mlodinow's achievement in writing an entertaining book from which you can actually learn something all the more remarkable. For example, I've come across the Monty Hall problem before, and thought I'd understood it, sort of, although it was like having to read a novel by following the words with my finger. This time, it was easier, partly to do with the way in which Mlodinow introduces the concept of the sample space and breaks down the problem into manageable pieces, and partly because his style is so engaging. It helps that he writes in the first person, and is neither afraid to draw on personal experience nor cringe making when he does so.

One major theme is the "fundamental clash between our need to feel we are in control and our ability to recognize randomness." Research by scientists like Kahneman and Tversky shows how deep-rooted this is. Most of us have been duped by optical illusions, but while these "seldom have much relevance in our everyday world" cognitive biases or systematic errors, on the other hand, "play an important role in human decision making." For example, confirmation bias occurs when we attempt to prove our ideas correct instead of searching for ways to prove them wrong, and "it presents a major impediment to our ability to break free from the misinterpretation of randomness."

Abstract notions are never allowed to wander far before being pinned down by concrete illustrations, often taken from remarkably current affairs. There are two graphs - proper sciency pictures with numbers and axes and everything - which are striking in their portrayal of a startling truth: they show the performance of fund managers over two five-year periods, and while one is a nice orderly ranking from good to bad, the other looks "like random noise". You could have no better illustration of the small print that past performance is no guide to future returns - so why do we pay huge fees to these so-called experts to manage our money, when a large chunk of their "performance" is down to luck? It is salutary to learn that even Wall Street superstars cannot consistently beat the average market return. "People systematically fail to see the role of chance in the success of ventures": the CEO of Merrill Lynch could one year "be celebrated as the risk-taking genius responsible" for the company's success and then, "after the credit market collapsed, derided as the risk-taking cowboy responsible" for its failure. These are important lessons to learn, especially now that even red-blooded capitalists are beginning to question the stratospheric pay packets of financiers.

We need to move beyond "the deterministic view of the marketplace" in which "it is mainly the intrinsic qualities of the person or the product that governs success." The "nondeterministic view" - not confined to the stock market - holds that "there are many high-quality but unknown books, singers, actors, and what makes one or another come to stand out is largely a conspiracy of random and minor factors - that is, luck. In this view the traditional executives are just spinning their wheels." Such a wholesale change in our thinking seems too much to hope for, given how much "we rely on gut instinct" in everyday life and how tempting it is to see purpose where there is none, to "pay lip service to the concept of chance" but to "behave as though chance events are subject to control."

Uncertainty is a modern sin that dare not speak its name. There are always pundits on hand to explain the past and prophesy the future, to nurture some of society's "shared illusions". If you want to "learn to view both explanations and prophecies with skepticism" then the "Drunkard's Walk" is an excellent introduction.

Author: Ian Stewart
By Profile Books Ltd

Author: Alistair W Kerr, Howard K Hall, Stephen A Kozub
By Sage Publications Ltd

SPSS, 2003-10-01
Doing Statistics with SPSS is an extremely useful book to use alongside the SPSS software. It has a long reference section at the back which provides quick and easy meanings of words terms and phrases. It easily explains what your results show and is reader and user friendly. I liked the book for just that. Being confused with SPSS and statistics from the begining of my module i found this book a god send and thanks to it i passed. This book will be helpful for those studying one module of statistics and is still advanced enough to help those doing statistics, maths and psychology.

Author: David Howell
By Wadsworth Publishing Co Inc

a must for every introductory stats course, 2002-01-16
this book is essential for every psychology student embarking into the daunting field of statistics. its fun to read, there is sufficient detail to let you understand the ideas and it has lots of exercises...

Author: Greg Attwood, Gillian Dyer, G.E. Skipworth
By Heinemann Educational Publishers

+ Detailed, thorough and a HUGE range of questions. - Confused, irrelevant material and *some* difficult explanations, 2007-08-19
This book offers a real mixed bag.

On the one hand, examples are usually very detailed, each of the topics is developed to the required depth and a *huge* range of practice and exam level questions are given.

Unfortunately, this is where the positives end. The book is very confused, and a significant minority of examples are extremely difficult to follow. Some of the stated methods are *very* complicated compared to what is required, and irrelevant material NOT required for the S1 exam is provided. In most cases, the distinction between what is needed and what isn't is not clear. Finally, there are several mistakes in the answers section.

Unfortunately, there is not a massive amount of choice regarding Edexcel S1 learning resources. I would recommend Cambridge's SMP S1 book even less, and for want of a better book, this may actually be the best option.

Despite the problems, this book led to me (an average maths student) scoring 100/100 on the S1 unit examination.

Author: Jon Curwin, Roger Slater
By Cengage Learning

Author: Geoff Renshaw
By OUP Oxford

Fantastic Book, 2007-08-24
If you were like me and struggling to understand the concepts because nobody had explained the foundations, here is the book to help you through. Its clear, precise and allows one to gradually build up your knowledge as you work through the textbook, every detail is explained. I looked at all other mathematics for economics texts and this in my opinion was the best (2006).

Author: Keith Pledger et al
By Heinemann Educational Publishers

Author: Simon Singh
By Fourth Estate Ltd

When Cambridge mathematician Andrew Wiles announced a solution for Fermat's last theorem in 1993, it electrified the world of mathematics. After a flaw was discovered in the proof, Wiles had to work for another year--he had already laboured in solitude for seven years--to establish that he had solved the 350-year-old problem. Simon Singh's book is a lively, comprehensible explanation of Wiles's work and of the colourful history that has build up around Fermat's last theorem over the years. The book contains some problems that offer a taste for the maths, but it also includes limericks to give a feeling for the quirkier side of mathematicians.
Mathematics as you've never seen it before, 2008-05-21
I was never a fan of maths at school. It did not come easily to me and I failed to see the relevance of trigonometry to my everyday life.

I say this so you realise I am not some sort of science geek who was best friends with a calculator. That's because I found this book absolutely fascinating. It made me laugh 3 times in the first 20 pages alone!

What Simon Singh does is through Fermat's puzzle describe the history of mathematics from Pythagoras right up to the 1990's. To the layman names like Euclid put in the mind very dull old guys, but they are brought to life with fascinating anecdotes. For example there's the tortured young French mathematician Galois who is dead by 20, his final mathematical theories frantically scribbled down before a dual. Then there's the story that Pythagoras himself drowned a man when he discovered a certain type of number he objected to!

All of this is carefully woven into the story of Andrew Wiles' life long obsession to prove Fermat's last theorem a puzzle that had foxed the whole world for over 350 years!

Everything is explained in a way that it can be digested by someone who has only a passing interest in maths and as a whole is a remarkable book.

Author: Rob Eastaway
By JR Books Ltd

A treat to read for oneself and a wonderful gift for family or friends. , 2008-10-04
Two trains are approaching each other on the same track, both traveling at 50 mph. When they are exactly 100 miles apart, a fly, traveling at 60 mph, leaves the front window of one train and heads directly towards the 2nd train. When it reaches the front window of the 2nd train it turns (instantaneously) and heads back towards the 1st train, always maintaining its speed of 60mph. When it reaches the front window of the 1st train it turns again and heads back to the 2nd train. It keeps flying between the trains in this manner until the trains meet and the fly is killed. The question is: what total distance does the fly travel before the trains meet?

A mother is 21 years older than her son. In 6 years time she will be 5 times the age of her son. The question is: Where is the father?

Such are the some of the delightful problems or puzzles that the author sets us and then proceeds to show us how to answer in surprisingly easy ways, using everyday maths. So don't be put off by the idea that maths is dull, boring or not something that we can all use and enjoy. After all, everyone does use maths in some form every day in lots of ways.

By the time you are finished this highly engaging book you will be able to square (in your head!) any number between 1 and 100. For instance, 37 x 37 = 1369 and so on. I have already impressed my long suffering family with that one.

He also shows us some card tricks and how to win at Penney Ante 88% of the time - definitely worth a congratulatory round of drinks down at the pub. And there are some chapters on some of the more striking properties of triangles, rectangles etc, and some thoughts on the inherent consistency and beauty of numbers. A wonderful book which can be read in one sitting, or dipped into or revisited from time to time. A treat to read for oneself and a wonderful gift for family or friends.