Mathematical Theory

Are you ready to become a master of strategic thinking? Look no further than The Game Theory Bible, your comprehensive guide to navigating complex decision-making scenarios. With 17 chapters covering everything from basic concepts to real-life applications, this eBook is packed with insights that will change the way you approach problem-solving. Whether you're a business owner looking to gain an edge over the competition or a student hoping to excel in game theory courses, this book gives you the tools you need to succeed. In Chapter 2, you'll learn the fundamental principles of game theory...

Nearly a hundred years after its publication, Kurt Gödel's famous proof that every mathematical system must contain propositions that are true - yet never provable - continues to unsettle mathematics, philosophy, and computer science. Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life.

In the 18th century, the British minister and mathematician Thomas Bayes devised a theorem that allowed him to assign probabilities to events that had never happened before. It languished in obscurity for centuries until computers came along and made it easy to crunch the numbers. Now, as the foundation of big data, Bayes's formula has become a linchpin of the digital economy. But here's where things get interesting: Bayes's theorem can also be used to lay odds on the existence of extraterrestrial intelligence, and on the biggest question of all: how long will humanity survive?

For the past few decades, the financial world has often displayed an unreasonable willingness to believe that "the model is right, the market is wrong," in spite of the fact that these theoretical machinations were largely responsible for the stock market crash of 1987, the LTCM crisis of 1998, the credit crisis of 2008, and many other blow-ups, large and small.

On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules.

William Stanley Jevons was an English economist and logician. In Brief Account of a General Mathematical Theory of Political Economy, which is essentially a condensed version of his most important piece of work, The Theory of Political Economy, first published in 1850, Javons discusses the marginal utility theory of value, pushing economic thought into the modern era. This piece is a must for both budding young mathematicians and aspiring economists with an interest in the recent history of their fields.

Models are at the centre of everything we do. They act as metaphors that help us better understand the increasingly complex problems facing us in the modern world. Yet in recent years, the validity of the models we use has been hotly debated and there has been renewed awareness of the disastrous consequences when the makers and interpreters of models get things wrong. Drawing on contemporary examples from finance, climate and health policy, Erica Thompson explores what models are, why we need them, how they work and what happens when they go wrong.