Rating: WORTHY!
This is from an advance review copy for which I thank the publisher.
This was a comprehensive and fun book with quite a few tips, pointers (indicators - not the dogs, which I found a bit disap pointer ing...), and hints along the way, and it covered a surprising array of mathematical concepts from simple math to powers, and from geometry to negative numbers. It even finally got me a visual that clarified in my mind why the so-called Monty Hall problem makes sense!
This 'problem' is where a person offered a choice to open one of three doors (or maybe boxes). One of the options contains a nice prize, the other two contain a booby prize or nothing at all. The person chooses which door or box to open, then the host (Monty Hall in the original show, although the problem predates his show) opens one of the booby prize doors showing you that it was wise not to choose that one. Then he gives you the option to change your choice. Should you change? It seems counter-intuitive, but the fact is that you will more than likely improve your odds of winning if you change. Many people (even some mathematicians) find this hard to believe. I did initially, and even when I decided that changing your choice was the indeed the better option, I still couldn't get my mind around why! Now it's clear thanks to this book!
But the book contains much more than that, and it explains things clearly and simply, with good examples, and little exercises for the reader to follow (with the answers!). There were a couple of errors in the book - or at least what seemed like errors to me, but math isn't my strong suit, so maybe I'm wrong. I'll mention them anyway. There was a section on geometric progression which used the old story of starting with one grain of rice on a chess board, and doubling the number of grains on each subsequent square. It's a great demonstration, but on page 47 it's seemingly implied that a chess board has only 62 squares! Wrong! Eight squared isn't 62!
The other issue was on tessellation (I told you this book was comprehensive!) which is a fascinating topic and really only a fancy way of saying 'tiling', but it suggests that triangular tessellation requires adding 6 walls whereas hexagonal tessellation requires only 3 and this is what makes bees so smart? I could not get my mind around that concept at all - not the smart bees, but the walls. I had no clue in what context this was supposed to be true. I mean if you draw a triangle and want to add another triangle, you have to draw only two more walls, and there's your second triangle making use of an existing wall from the first. If you have one hexagon and want to add another, you have to draw five more walls!
If you have two hexagons side-by-side, you need to draw four walls to make another, whereas if you have two triangles, you need draw, again, only two walls to make a third! Admittedly, if you have three existing hexagons, making a shallow cup shape, then it's true you need add only three more walls on the concave side to make a fourth hexagon, but with three triangles, depending on how they are joined, you still need add only two walls - or perhaps even just one wall. Now maybe I am missing something or maybe the concept that was being conveyed here wasn't worded very well for clarity - or was over my head(!), so like I said, I may be wrong but it seemed to me this needed something more to be said!
But that was a minor issue and I'm happy to commend this as a worthy read and a great math tutor for young minds.
