This is an excellent little book. It's one of those gems produced by someone who really understands a field of knowledge and who can choose well how to present its key ideas.
I read as a reminder of much maths I had learned at school, but not been able to pursue beyond it. All the basic maths is in there- but the book hints at how much more there is behind it. What is amazing is how very simple starting points allow for so much discovery and implication.
The unity of mathematics is well described- the fact that constants such as pi and e are the same whichever way you encounter them is emphasised. The book is excellent at emphasising the coherence the mathematics, and at showing how the sub-specialities are easily absorbed within the whole.
I suspect this book would be most useful to A level and university students of maths and related subjects- either as revision or as inspiration.
The compression factor in the book is huge, and whilst this is good for clarity, and overview, there's a price in lack of space to show you exactly how to make these calculations and arguments, and in terms of full explanation of the implications of the mathematical theorems presented.
Overall however this book achieves what it sets out to achieve, and can be freely recommended to others who want to know something quickly about mathematics.
on 10 July 2012
Firstly, I came to this book with very little knowledge of mathematics other than the high school math I finished around eight years ago. However, I have a general interest in some of the abstract mathematical ideas, and I was also keen to expand on my knowledge for the master's degree I'm currently doing in which a little bit of math knowledge would be beneficial (although not a requirement). Given this, I didn't always find the book easy to understand, especially pages ~200 to ~300 (calculus, vectors, matrices, abstract algebra, and complex numbers), but I did find it pleasurable and quite addictive, nevertheless.
I really liked the format of the book: each of the 200 concepts is described on two pages - the first page giving a written description and the second page showing some relevant graphic or picture. There are a few slight deviations from this format where the written description spans two pages, but the general approach of the book is to describe the main properties of each concept in around 200 words. This makes the book very easy to read in short bursts. The converse of this approach is that each concept is dealt with pretty superficially, but for me personally this was not a bad thing.
Although superficial, the book didn't feel dumbed down - it doesn't shy away from using formulae, for example - and I imagine the more advanced reader might also find the book useful for recapping and seeing the connections between disparate mathematical ideas.
Although I can't really comment on the quality of the mathematics, I felt the quality of the book deserved a 5-star rating. I also think the price is very reasonable too. The only fault I can find is that some of it was a bit hard to understand, but this is probably more my weakness than the book's. Given that I enjoyed this one, I think I'll probably also buy the other two titles in the range, Science in Seconds and Big Ideas in Brief.
on 12 December 2013
A disappointment. Whilst efforts to introduce subjects such as maths to a wider audience in a brief and undaunting manner is an excellent dea, I thought that this was far far too brief. There are no takeaways! This is barely more than a contents page. I would far rather cover less but in slightly more detail - enough to want to find out more. I found "Alex in Numberland" by Alex Bessos managed that balance far better and I felt I actually learnt something.
Paul Glendinning is a mathematics professor at the University of Manchester. As he says in his introduction: "Only a lunatic would pretend that all mathematics could be presented in 200-bite sized chunks." And he doesn't. Instead, he had produced an excellent reference book, of 400 pages, in 5 inch by 5 inch format. On the left page is a succinct description of a mathematical concept, on the right page is a drawing or illustration that should enhance the reader's understanding of the concept. Due to the increasingly specialized nature of work in the scientific field, there are no "Renaissance Men" (or women) left... that is, humans who have a good grasp of most scientific knowledge. Thus, I believe even other professors of mathematics (given no professional jealousy) would find this "sampler" of mathematical concepts most useful. As for the non-mathematically included, portions of this book should also be considered essential, just like knowing how your car actually works: if some concepts are not mastered, you'll always be at the mercy of the specialists in the field, auto mechanics, or others.
The author starts with the very basic concepts, just what "numbers" and "natural numbers" are, as well as the concept of "1." He reminds us that "0" has not always been with us; in fact, it was a major philosophical breakthrough when the concept achieved widespread recognition. "Prime Numbers," "Irrational Numbers" and "Imaginary Numbers" soon follow. Glendinning sprinkles in some philosophical paradoxes, for example Xeno's and the Barber's. The mid-part of the book hit some familiar territory of long ago, that I simply don't use on a daily basis: parabolas, ellipses, polynomials and quadratic equations. I well remember, way back when even, on a parent night for middle school. The health teacher, in his talk to parents, used "quadratic equations" to underscore the importance of his course. How you might say? He asked the parents how many were taught quadratic equations in school. There was a fair showing of hands. Then he asked how many could write one on the black board. In six years of this gamut, he said only one parent could. His health course though, he boldly predicted, would be remembered through life. So, for the next "parent night" at school, Glendinning might prove an essential refresher course.
And towards the end of the author's sampling, there are all the concepts that certainly I was never taught in school, for example, Mobius transformations, fractals, homotopy and betti numbers. Caution: It would be an unusual cocktail party that eyes would not immediately glaze over if you tried to introduce these concepts. Nonetheless, renaissance person or just a wantabe, this guide to mathematical concepts should be an essential part of one's "literacy" library in an increasingly complex world. 5-stars.
on 2 June 2013
I saw a copy of this book in a bookshop and looked through it expecting to be amused by an attempt to describe so many mathematical concepts in such a small volume. (I did a degree in Maths 50 years ago, but have used it very little since). Instead of being amused, I was seriously impressed by the book's ability to summarize topics and remain understandable. I have bought the book in order to help me revive my rusty memory. The price is an extra reason to commend it.
on 13 January 2014
Having loved maths at school 50 years ago, I thought I'd enjoy a refresher course in topics like calculus and differential equations, just to keep the old brain ticking over, but sadly this didn't do it for me. My overall impression was of a book written by a mathematician rather than a linguist - the explanations were not clear, and frequently explained topics using terms which were themselves not explained. in summary, a book for someone who already knows the subject!
on 20 October 2012
This book doesn't teach you math, there are no exercises to try, but it beautifully explains as many concepts as I can recall and many I didn't know about on a single small page. The book is half size and easy to carry, great to get out and read a couple of pages on the train. Though it says math in minutes - that is true - it takes minutes to read - you might want to ponder a while each page and think a bit more.
Great little book - but I do still like math