検索キーワード： 数学

Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy.

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.

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.

Game theory means rigorous strategic thinking. It’s the art of anticipating your opponent’s next moves, knowing full well that your rival is trying to do the same thing to you. Though parts of game theory involve simple common sense, much is counterintuitive, and it can only be mastered by developing a new way of seeing the world. Using a diverse array of rich case studies - from pop culture, TV, movies, sports, politics, and history - the authors show how nearly every business and personal interaction has a game-theory component to it.

Are you fascinated by the laws of nature, quantum physics, and its basic concepts that seem meaningless? Quantum mechanics is a field that attempts to understand the behavior of subatomic objects using mathematical notions. The book explains uncertainty and time dependence by further elaborating on the principles of quantum states. It also describes the entanglement of particle and wave states, thereby offering interested listeners the possibility of understanding physics at a slower tempo.

To score a job in data science, machine learning, computer graphics, and cryptography, you need to bring strong math skills to the party. Math for Programmers teaches the math you need for these hot careers, concentrating on what you need to know as a developer. Filled with lots of helpful graphics and more than 200 exercises and mini-projects, this book unlocks the door to interesting - and lucrative! - careers in some of today’s hottest programming fields about the technology.

Games are everywhere: Drivers maneuvering in heavy traffic are playing a driving game. Bargain hunters bidding on eBay are playing an auctioning game. The supermarket's price for corn flakes is decided by playing an economic game. This Very Short Introduction offers a succinct tour of the fascinating world of game theory, a groundbreaking field that analyzes how to play games in a rational way.

The study of geometry is at least 2500 years old, and it is within this field that the concept of mathematical proof first arose. To this day geometry remains a very active area of research in mathematics. This Very Short Introduction covers the areas of mathematics falling under geometry, starting with topics such as Euclidean and non-Euclidean geometries, and ranging to curved spaces, projective geometry in Renaissance art, and geometry of space-time inside a black hole. Throughout, Maciej Dunajski outlines the role geometry plays in the broader context of science and art.

This book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthily and see through scaremongering. They were known only by mathematicians - until now.

＜概要＞ 数学は、自然の法則を表現するための美しい言語です。 このポッドキャストでは、数学の基礎から応用まで様々なテーマを取り扱い、数学の魅力をお伝えします。数学が好きな人も、苦手意識を持っている人も、ぜひ数学の魅力に触れてみてください。 ＜初めての方へ＞ 数学沼ラジオのトピックレベルを知りたい場合　→　#1 みんな知ってる数学をさらに深堀りしたい場合　→　#6 日常生活の中でもっと数学を感じたい場合　　　→...

Simply put, an algorithm is a set of instructions-it's the code that makes computers run. A basic idea that proved elusive for hundreds of years and bent the minds of the greatest thinkers in the world, the algorithm is what made the modern world possible. Without the algorithm, there would have been no computer, no Internet, no virtual reality, no e-mail, or any other technological advance that we rely on every day.

Whether we are worried about the spread of COVID-19 or making a corporate budget, we depend on mathematical models to help us understand the world around us every day. But models aren’t a mirror of reality. In fact, they are fantasies, where everything works out perfectly, every time. And relying on them too heavily can hurt us. In Escape from Model Land, statistician Erica Thompson illuminates the hidden dangers of models.

Hello World takes us on a tour through the good, the bad, and the downright ugly of the algorithms that surround us on a daily basis. Mathematician Hannah Fry reveals their inner workings, showing us how algorithms are written and implemented, and demonstrates the ways in which human bias can literally be written into the code. By weaving in relatable, real world stories with accessible explanations of the underlying mathematics that power algorithms, Hello World helps us to determine their power, expose their limitations, and examine whether they really are improvements.

We have never had so much information at our fingertips and yet most of us don’t know how the world really works. This book explains seven of the most fundamental realities governing our survival and prosperity. From energy and food production, through our material world and its globalization, to risks, our environment and its future, How the World Really Works offers a much-needed reality check—because before we can tackle problems effectively, we must understand the facts.

Statistics are everywhere, as integral to science as they are to business, and in the popular media hundreds of times a day. In this age of big data, a basic grasp of statistical literacy is more important than ever if we want to separate the fact from the fiction, the ostentatious embellishments from the raw evidence - and even more so if we hope to participate in the future, rather than being simple bystanders.

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.

The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress - and also when it did not, because science was being stifled by militarism or religious fanaticism.

Alan Turing was the mathematician whose cipher-cracking transformed the Second World War. Taken on by British Intelligence in 1938, as a shy young Cambridge don, he combined brilliant logic with a flair for engineering. In 1940 his machines were breaking the Enigma-enciphered messages of Nazi Germany's air force. He then headed the penetration of the super-secure U-boat communications.

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.

In this irreverent and illuminating audiobook, acclaimed writer and scientist Leonard Mlodinow shows us how randomness, chance, and probability reveal a tremendous amount about our daily lives, and how we misunderstand the significance of everything from a casual conversation to a major financial setback. As a result, successes and failures in life are often attributed to clear and obvious causes, when in actuality they are more profoundly influenced by chance.