Engineering Mathematics

 The complexity of mathematics - its abstract rules and obscure symbols - can seem very distant from the everyday. There are those things that are real and present, it is supposed, and then there are mathematical concepts: creations of our mind, mysterious tools for those unengaged with the world. Yet, from its most remote history and deepest purpose, mathematics has served not just as a way to understand and order, but also as a foundation for the reality it describes.

How many people achieve a cult following because of their writing in mathematics? Only a handful, and Martin Gardner is among the most well-known and well-loved. Not only did he present a notoriously difficult subject in an engaging and accessible way, but in doing so, he attracted an incredibly broad readership. His “Mathematical Games” column in Scientific American ran nearly every month for 26 years and was one of the most popular in the magazine’s history.

This 10-part history of mathematics reveals the personalities behind the calculations: the passions and rivalries of mathematicians struggling to get their ideas heard. Professor Marcus du Sautoy shows how these masters of abstraction find a role in the real world and proves that mathematics is the driving force behind modern science.  

What is the best way to think about the world? How often do we consider how our own thinking might impact the way we approach our daily decisions? Could it help or hinder our relationships, our careers, or even our health? Thinking about thinking is something we rarely do, yet it is something science questions all the time. David Sumpter has spent decades studying what we could all learn from the mindsets of scientists, and Four Ways of Thinking is the result. Here he reveals the four easily applied approaches to our problems: statistical, interactive, chaotic and complex.

Around the World in 80 Games is about the mathematics of chance, game theory, gamification, gaming strategies and computer games. Traversing the globe, Marcus du Sautoy looks at the genesis of games new and old, explores how to invent a good game and explains the fascination of a popular lockdown game. The most simple games endure: board games, card games and dice games have captivated us for centuries and the acclaimed mathematician and author of The Creativity Code (among many others) will once again bring mathematics to the fore with insight and aplomb in Around the World in 80 Games.

The brain is made up of 85 billion neurons, which are connected by over 100 trillion synapses. For over a century, a diverse array of researchers have been trying to find a language that can be used to capture the essence of what these neurons do and how they communicate - and how those communications create thoughts, perceptions, and actions. The language they were looking for was mathematics, and we would not be able to understand the brain as we do today without it.

Bertrand Russell wrote that mathematics can exalt "as surely as poetry". This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity, or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections.

Thomas Bayes was an eighteenth-century Presbyterian minister and amateur mathematician whose obscure life belied the profound impact of his work. Like most research into probability at the time, his theorem - independently discovered a few years later by Pierre-Simon Laplace, the great French mathematician - was mainly seen as relevant to games of chance, like dice and cards. But its implications soon became clear, affecting fields as diverse as medicine, law and artificial intelligence.

Every time we download a song from iTunes, take a flight across the Atlantic or talk on our mobile phones, we are relying on great mathematical inventions. Maths may fail to provide answers to various of its own problems, but it can provide answers to problems that don't seem to be its own - how prime numbers are the key to Real Madrid's success, to secrets on the internet and to the survival of insects in the forests of North America. 

Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the 17th-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it.

Ever since the dawn of human civilisation, we have been trying to make predictions about what's in store for us. We do this on a personal level, so that we can get on with our lives efficiently (should I hang my laundry out to dry, or will it rain?). But we also have to predict on a much larger scale, often for the good of our broader society (how can we spot economic downturns or prevent terrorist attacks?). For just as long, we have been getting it wrong.

In this eye-opening and extraordinary audiobook, Yates explores the true stories of life-changing events in which the application - or misapplication - of mathematics has played a critical role: patients crippled by faulty genes and entrepreneurs bankrupted by faulty algorithms; innocent victims of miscarriages of justice and the unwitting victims of software glitches. We follow stories of investors who have lost fortunes and parents who have lost children, all because of mathematical misunderstandings.

We can learn many things from models. Scientists use models to test their ideas. Listeners will learn about the importance of making predictions, testing ideas, collecting data, and more. 

Mathematics shapes almost everything we do. From building rockets to the handheld technology that governs our day-to-day lives, we are all in debt to the mathematical geniuses of the past. But the history of mathematics is warped; it looks like a sixteenth-century map that enlarges Europe at the expense of Africa, Asia and the Americas. The Secret Lives of Numbers introduces listeners to a new group of mathematical boundary-smashers, those who have been erased by history because of their race, gender or nationality.

What's the Use? asks why there is such a vast gulf between public perceptions of mathematics and reality. It shows how mathematics is vital, often in surprising ways, behind the scenes of daily life. How politicians pick their voters. How an absurd little puzzle solved 300 years ago leads to efficient methods for kidney transplants. How an Irish mathematician's obsession with a new number system improves special effects in movies and computer games. How SatNav relies on at least six mathematical techniques.

In Calculating the Cosmos, Ian Stewart presents an exhilarating guide to the cosmos, from our solar system to the entire universe. He describes the architecture of space and time, dark matter and dark energy, how galaxies form, why stars implode, how everything began, and how it's all going to end. He considers parallel universes, the fine-tuning of the cosmos for life, what forms extraterrestrial life might take, and the likelihood of life on Earth being snuffed out by an asteroid.

Statistics is used in almost every field and industry imaginable. From healthcare to finance to marketing, statistics are used to make important decisions, identify patterns and trends, and predict future outcomes. Without a basic understanding of statistics, it's easy to be left behind and taken advantage of.

Math has a reputation for being inaccessible. People think that it requires a special gift or that comprehension is a matter of genes. Yet, the greatest mathematicians throughout history, from Rene Descartes to Alexander Grothendieck, have insisted that this is not the case.

Our universe has multiple origin stories, from religious creation myths to the Big Bang of scientists. But if we leave those behind and start from nothing – no matter, no cosmos, not even empty space – could we create a universe using only maths? In this new mathematical origin story, mathematician and award-winning novelist Manil Suri creates a natural progression of ideas needed to design our world, starting with numbers and continuing through geometry, algebra, and beyond.

Starting with hands, abacus, and slide rule, humans have always reached for tools to simplify math. Pocket-sized calculators ushered in modern mathematics, helped build the atomic bomb, took us to the bottom of the ocean, and accompanied us to the moon. The pocket calculator changed our world, until it was supplanted by more modern devices that, in a cruel twist of irony, it helped to create. Keith Houston transports listeners from the nascent economies of the ancient world to World War II, and into the technological arms race that led to the first affordable electronic pocket calculators.