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johnson o numbercrunch mathematician s toolkit making sense 2023

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Textbook in PDF format ‘The essence of mathematics is not to make simple things complicated, but to make complicated things simple.’ Stanley P. Gudder, A Mathematical Journey Our everyday lives are increasingly ruled by data and by algorithms. We can make ourselves understood by talking to Siri, and instantaneously receive almost professional-quality translations of foreign language text using Google Translate. Netflix can match our previous viewing to profiles of similar users, to recommend the next box set that we are most likely to get hooked on. However, it may be less obvious that this kind of ‘Artificial Intelligence’ or ‘Machine Learning’ emerged from mathematics and from statistics. These ideas have had a rebrand for the 21st century and been supercharged by ever-increasing computing power, but it’s always mathematics under the bonnet. These Silicon Valley marvels rely on ideas like the geometry of clouds of points in a world of millions of dimensions, techniques for finding structure and form in randomness and mathematically rigorous ways of dealing with vast amounts of data. Most people don’t know what a professional mathematician does all day. Perhaps they imagine that we are memorising harder and harder times tables (‘one 19,573 is 19,573, two 19,573s are 39,146’) or competing to see who can remember the most digits of pi. Maybe they imagine a dusty old man writing incomprehensible chalk equations full of Greek letters on a blackboard (and to be fair, this isn’t always so far wrong). Some of this is the mathematicians’ fault. We haven’t exactly gone out of our way to explain why what we do matters. This book is an attempt to redress that balance. I believe that navigating everyday life now requires making sense of endless numbers and facts, as more and more data about an ever-increasing number of fast-evolving global scenarios is available faster than ever before via our phones, tablets and computers. Further, I believe that mathematical ideas offer the right way of thinking about the world, to make sense of this barrage of data and of complex situations, and to avoid being led astray by misleading interpretations of them. I would like to teach you some of those tricks, and to help you understand the world through a mathematician’s eyes. Twitter is a fantastic place to get short and timely messages across, but it doesn’t allow you to show your working as mathematicians like to. I will try to do that here and explain why I think about things in the way that I do. At the heart of all this lies the idea of a mathematical model. In a sense, we all have a mental model of how things work. For example, we know that if we drop something, then due to gravity it will fall to the ground. However, it was Isaac Newton’s fundamental work in turning this idea into mathematical equations that meant that the effect could really be understood. In our hyper-modern world, we are bombarded with more facts, stats and information than ever before. So, what can we grasp hold of to make sense of it all? Oliver Johnson reveals how mathematical thinking can help us understand the myriad data all around us. From the exponential growth of viruses to social media filter-bubbles; from share price fluctuations to the cost of living; from the datafication of our sports pages to quantifying climate change. Not to mention the things much closer to home: ever wondered when the best time is to leave a party? What are the chances of rain ruining your barbecue this weekend? How about which queue is the best to join in the supermarket? Journeying through three sections - Randomness, Structure, and Information - we meet a host of brilliant minds, such Alan Turing, Enrico Fermi and Claude Shannon, and are equipped with the tools to cut through the noise all around us - from the Law of Large Numbers to Entropy to Brownian Motion. Lucid, surprising, and endlessly entertaining, Numbercrunch equips you with a definitive mathematician's toolkit to make sense of your world. ‘The perfect introduction to the power of mathematics – fluent, friendly and practical.’ - Tim Harford, author of How to Make the World Add Up '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 ‘Oliver Johnson provides useful and timely insights by deploying simple but powerful mathematical techniques. Numbercrunch shows how to apply crucial ideas to a range of real-life problems. A valuable and topical guide to navigating the world of numbers, from sports transfers to medical testing.’ - Adam Kucharski, author of The Rules of Contagion Contents: Introduction Part 1: Structure Chapter 1: The right picture is worth a thousand words Chapter 2: Getting it in the right ballpark Chapter 3: Captain’s log Chapter 4: Following the rules Part 2: Randomness Chapter 5: Data is random Chapter 6: Vital statistics Chapter 7: Positives and negatives Chapter 8: Odds and trends Part 3: Information Chapter 9: Information is power Chapter 10: Drunkards, queues and networks Chapter 11: Measure for measure Chapter 12: Game theory Part 4: Lessons Chapter 13: Learning from error Acknowledgements Glossary Further reading Index Sources

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johnson o numbercrunch mathematician s toolkit making sense 2023

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