Numbercrunch: A Mathematician's Toolkit for Making Sense of Your World

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A fine and valuable read. Johnson applies careful analysis and great common sense to an extraordinary range of applications of mathematical ideas, from football to filter bubbles - explaining formal ideas with minimum technicalities, and weighing their relevance to the real world. Not to mention the things much closer to home: ever wondered when the best time is to leave a party? I am interested in the relationship between properties of entropy and limit theorems, such as the Central Limit Theorem and Law of Small Numbers (Poisson convergence). This includes trying to understand relationships between information-theoretic properties such as the Entropy Power Inequality and maximum entropy theorems and probabilistic ideas such as log-Sobolev inequalities and transportation of measure. I have a particular interest in developing discrete analogues of these results.

Professor Johnson said: “Even if you’ve grown out of advent calendars, it’s impossible to escape the importance of numbers at Christmas. For instance, if you get the timings wrong on defrosting your turkey or miscount the number of places needed at the dinner table, it’s likely to cause some serious festive frustration. But there are also some lesser-known and rather intriguing ways maths can make your celebrations a little merrier.”Lucid, surprising, and endlessly entertaining, Numbercrunch equips you with a definitive mathematician's toolkit to make sense of your world. Children are rightly amazed by Santa Claus’ incredible ability to travel fast enough to visit every house in the world in just one night. The vast distances and sheer volume of stops are so mind-boggling, they would stretch the most sophisticated supercomputer. However, there are limits to this data-driven approach to sport. In particular, it is valuable to understand the uses and limitations of “expected goals”, one of the most visible new statistics. Expected goals are calculated using a huge database of past matches, analysing the outcomes of shots from different positions on the field and in different circumstances. For example, if a shot from the corner of the penalty area gives a goal 10% of the time, then creating such an opportunity gives a team 0.1 of an expected goal. These fractions of goals are added up over the course of the game.

converse results. This has led to a recent survey monograph, published by Foundations and Trends in Communications and Information Theory. By the same token, the 35 total presents I've received by Day 5 are made up as the 20 presents I'd received the day before, plus the 15 new presents arriving that day. That means, for those doing the math, by the twelfth day I will have received 364 presents in total. The presents I will have most of are the geese a-laying and swans a-swimming which first arrive on Days 6 and 7." Children are rightly amazed by Santa Claus' incredible ability to travel fast enough to visit every house in the world in just one night. The vast distances and sheer volume of stops are so mind-boggling, they would stretch the most sophisticated supercomputer.

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Lucid and entertaining. With barely an equation in sight, Numbercrunch makes a passionate case for how just a little bit more numeracy could help us all' - Tom Whipple, The Times'The perfect introduction to the power of mathematics - fluent, friendly and practical' - Tim Harford, bestselling author of How to Make the World Add UpIn our hyper-modern world, we are bombarded with more facts, stats and information than ever before.