Nate Silver has come to prominence recently through the seemingly simple method of predicting election results through statistics. I’ve just finished reading his book, The Signal and the Noise and it’s certainly one of my favourite books of the year. It covers all sorts of predictions, in baseball, chess, politics, earthquakes, terrorism, stocks, and more besides. If I were to recommend a Christmas book for a maths geek, then this would be the one. He recently gave a Google talk which you can see...

## A Mathematician Comes of Age by Steven Krantz...

posted by Kevin Houston

I’m a big fan of Steven Krantz. His book on teaching mathematics is the one I recommend most to beginning maths lecturers. The second edition is a must have since it contains short replies to his book from other lecturers, some of them highly critical. Currently, I’m reading his recent book A Mathematician Comes of Age. This is concerned with how a mathematician becomes mathematically mature. From the back cover: “It describes and analyzes how a student develops from a neophyte who can manipulate simple arithmetic problems to a sophisticated thinker who can understand abstract concepts, can think rigorously, and can analyze and manipulate proofs.” I must admit I’ve been diving in and out of the book at random and although I don’t agree with everything he says (or agree with the inclusion of certain topics – why are North Americans so concerned about “Math anxiety”?) there are thought-provoking passages every page or so. The parody of the Evolution of Teaching Math on page 49 is very funny and includes 1980s: A framer sells a bag of potatoes for $10. His production costs are $8 and his profit is $2. Underline the word “potatoes” and discuss with your classmates. Leaving aside the humour, I particularly like the section on Reading and Thinking (p95): It has been observed [No reference given – KH] that the key things that a good teacher does are engage the students in the learning process pace the students teach the students to read Now, reading mathematics is something I’ve thought about and try to get my students to do, see Chapter 2 of How to Think Like a Mathematician (follow the link for free samples of chapters 3 and 4). Like in HTTLAM Krantz mentions the importance of reading with...

## Predicting the future with mathematics...

posted by Kevin Houston

Game theory is an important application of mathematics. The central theme of Bruce Bueno de Mesquita’s new(ish) book Prediction: How to See and Shape the Future with Game Theory, is that it can be applied to give startling predictions within social areas such as politics. He claims that by applying a bit of game theory you can even change the outcome of negotiations or advance your career. He puts his money where his mouth is and makes predictions about the future. Some of these have come to pass since the first printing. The first example in the book is excellent: How to get the best deal when buying a car. You can actually apply the method in many different transactions not just car buying and knowing it will pay back the price of the book many times over. I love the idea of game theory. I tried (and failed) when I was an undergraduate to read von Neumann and Morgenstern’s seminal classic Theory of Games and Economic Behaviour. I would love to read a geat book written from the mathematical perspective but this isn’t it. There is not much mathematical theory in the book and even that is relegated to an appendix but to be honest for me it raised more mathematical questions than it solved. Nonetheless, this is a great book which I enjoyed reading. Some extra diagrams would have been useful. The description of the probability of finding a sports drug cheat I think can be best described using a picture for example. Maybe I’ll draw one some time to show just how easy it is. Ok, so I don’t think that this is the best book about Game Theory from a mathematical viewpoint. It was never intended as such (hence there...