Engineering Mathematics

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.

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.

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.

Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler - Stanford researcher, professor of math education, and expert on math learning - has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students.

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.

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.

We are living through a revolution in machine learning-powered AI that shows no signs of slowing down. This technology is based on relatively simple mathematical ideas, some of which go back centuries, including linear algebra and calculus, the stuff of seventeenth- and eighteenth-century mathematics. It took the birth and advancement of computer science and the kindling of 1990s computer chips designed for video games to ignite the explosion of AI that we see today. In this enlightening book, Anil Ananthaswamy explains the fundamental math behind machine learning.

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.

Are the secrets of the universe written in words - or is it all about the digits? K. C. Cole follows up her paean to the power of physics, Sympathetic Vibrations, with this engaging and accessible guide to the might and majesty of mathematics. The Universe and the Teacup uses relatable examples and humorous prose to demonstrate math's ability to "translate the complexity of the world into manageable patterns".

In the bestselling The Signal and the Noise, Nate Silver showed how forecasting would define the age of Big Data. Now, in this timely and riveting new book, Silver investigates "The River," or those whose mastery of risk allows them to shape—and dominate—so much of modern life. These professional risk takers—poker players and hedge fund managers, crypto true-believers and blue-chip art collectors—can teach us much about navigating the uncertainty of the 21st century.

Trigonometry is perhaps the most essential concept humans have ever devised. The simple yet versatile triangle allows us to record music, map the world, launch rockets into space, and be slightly less bad at pool. Triangles underpin our day-to-day lives and civilization as we know it. In Love Triangle, Matt Parker argues we should all show a lot more love for triangles, along with all the useful trigonometry and geometry they enable.

At its simplest, Bayes’s theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. But in Everything Is Predictable, Tom Chivers lays out how it affects every aspect of our lives. He explains why highly accurate screening tests can lead to false positives and how a failure to account for it in court has put innocent people in jail. A cornerstone of rational thought, many argue that Bayes’s theorem is a description of almost everything. But who was the man who lent his name to this theorem?

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.

Stop making bad decisions because of misunderstood numbers. Learn the math essentials that give you the clarity you've missed. Your future is a sum of your decisions. Transform your life's trajectory—one calculation at a time. From budgets to big dreams, unlock the math standing between you and the life you want to lead.

As GTO poker gets more popular, and more solvers become available, it’s more important than ever to fully understand key GTO concepts. So we took our years of GTO solver exploration and distilled the major takeaways that you can actually use. We call these the gems.

In this captivating, sweeping history, Michael Brooks makes clear that mathematics was one of the foundational innovations that catapulted humanity from a nomadic existence to civilization, and that it has been instrumental in every subsequent great leap of humankind: from charting the movements of celestial bodies to navigating the globe to tracking the dissemination of viruses.

We play games to learn about the world, to understand our minds and the minds of others, and to make predictions about the future. Games are an essential aspect of humanity and a powerful tool for modeling reality. They’re also a lot of fun. But games can be dangerous, especially when we mistake the model worlds of games for reality itself and let gamification co-opt human decision making. Playing with Reality explores the riveting history of games since the Enlightenment.

From Aristotle to Ada Lovelace: a brief history of the mathematical ideas that have forever changed the world and the everyday people and pioneers behind them. The story of our best invention yet. From our ability to calculate the passing of time to the algorithms that control computers and much else in our lives, numbers are everywhere. They are so indispensable that we forget how fundamental they are to our way of life.

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.

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.