Engineering Mathematics

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.

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.

Life is uncertain. We are all the result of an unforeseen and unforeseeable sequence of small occurrences. But what underlies this fragile chain of events? Is it random or just complex? And what role does luck play in our lives? David Spiegelhalter has spent his career crunching data in order to help understand uncertainty and assess the chances of what might happen. In The Art of Uncertainty, he gives listeners a window onto how we can all do this better.

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.

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.

A brilliant research mathematician reveals math to be a creative art form on par with painting, poetry, and sculpture, and rejects the standard anxiety-producing teaching methods used in most schools today. Witty and accessible, Paul Lockhart's controversial approach will provoke spirited debate among educators and parents alike, altering the way we think about math forever.

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.

The techniques of Vedic Mathematics have helped millions of students all over the world get rid of their fear of numbers and improve their scores in quantitative subjects.

Why do mobile phones work when you're on a train? What happens when you pull a pop song apart into pure sine waves and play it back on a piano? And what did mathematicians have to do with the great pig stampede of 2012? The answer to each of these questions can be found in the triangle. Join Matt Parker, stand-up comedian and author of the first ever maths book to be a No. 1 bestseller, as he uncovers the secrets of trigonometry and shares extraordinary stories about the mathematicians, philosophers and engineers who dared to take triangles seriously.

In Fantastic Numbers and Where to Find Them, leading theoretical physicist and YouTube star Antonio Padilla takes us on an irreverent cosmic tour of nine of the most extraordinary numbers in physics. These include Graham's number, which is so large that if you thought about it in the wrong way, your head would collapse into a singularity; TREE(3), whose finite value could never be reached before the universe reset itself; and 10^{-120}, which measures the desperately unlikely balance of energy the universe needs to exist....

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.

We are living through a revolution in artificial intelligence that is not slowing down. This major shift is based on simple mathematics, some of which goes back centuries: linear algebra and calculus, the stuff of eighteenth-century mathematics. Indeed by the mid-1850s, a lot of the groundwork was all done. In this enlightening book, Anil Ananthaswamy explains the fundamental maths behind AI, which suggests that the basics of natural and artificial intelligence might follow the same mathematical rules.

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.

PLAYING WITH REALITY explores the riveting history of games since the Enlightenment, weaving an unexpected path through military theory, biology, artificial intelligence, neuroscience, cognitive psychology, and the future of democracy. As neuroscientist and physicist Kelly Clancy shows us, games have been deeply intertwined with the arc of history. War games shaped the outcomes of real wars in nineteenth and twentieth century Europe. Game theory warped our understanding of human behavior and brought us to the brink of annihilation.

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.

This book reveals how statistics and probability are fundamental to our everyday lives—from advertisements to public opinion polls, weather forecasts to government policies, scientific research to stock market information. Haim Shapira then presents a myriad of anecdotes, riddles, case studies and practical exercises in his trademark witty voice to guide the listner through the importance of statistics and probability in everyday life.

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.

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.

Mathematics is a fundamental part of life, yet every one of us has a unique relationship with learning and understanding the subject. Working with numbers may inspire confidence in our abilities or provoke anxiety and trepidation. Stanford researcher, mathematics education professor, and the leading expert on math learning Dr. Jo Boaler argues that our differences are the key to unlocking our greatest mathematics potential.