Showing titles in Mathematics

Behind the familiar surfaces of the telephone, radio, and television lies a sophisticated and intriguing body of knowledge known as information theory. This is the theory that has permitted the rapid development of all sorts of communication, from color television to the clear transmission of photographs from the vicinity of Jupiter. Even more revolutionary progress is expected in the future.

In 1913, an unschooled young Indian clerk wrote a letter to G. H. Hardy, begging that preeminent English mathematician's opinion on several ideas he had about numbers. Hardy, realizing the letter was the work of a genius, arranged for Srinivasa Ramanujan to come to England. Thus began one of the most remarkable collaborations ever chronicled.

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.

Probing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

These stories from Quanta Magazine map the routes of mathematical exploration, showing listeners how cutting-edge research is done, while illuminating the productive tension between conjecture and proof, theory and intuition. Listeners of The Prime Number Conspiracy are headed on "breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge," says Quanta editor-in-chief Thomas Lin.

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.

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.

Inspired by Albert Einstein's theory of relativity and Bertrand Russell and David Hilbert's pursuit of the fundamental rules of mathematics, some of the most brilliant minds of the generation came together in post-World War I Vienna to present the latest theories in mathematics, science, and philosophy and to build a strong foundation for scientific investigation. Composed of such luminaries as Kurt Gödel and Rudolf Carnap, and stimulated by the works of Ludwig Wittgenstein and Karl Popper, the Vienna Circle left an indelible mark on science.

The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and listeners of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought.  

Throughout history, scientists have come up with theories and ideas that just don't seem to make sense. These we call paradoxes. The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds. With elegant explanations that bring the listener inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle.

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?

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.

Levitt and co-author Stephen J. Dubner show that economics is, at root, the study of incentives: how people get what they want, or need, especially when other people want or need the same thing. In Freakonomics, they explore the hidden side of...well, everything. The inner working of a crack gang...the truth about real-estate agents...the secrets of the Klu Klux Klan. What unites all these stories is a belief that the modern world is even more intriguing than we think. All it takes is a new way of looking, and Freakonomics will redefine the way we view the modern world.

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.

For seven years, Paul Lockhart's A Mathematician's Lament enjoyed a samizdat-style popularity in the mathematics underground, before demand prompted its 2009 publication to even wider applause and debate. An impassioned critique of K-12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here, Lockhart offers the positive side of the math education story by showing us how math should be done. Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living.

It's the ultimate in fantasy baseball: You get to pick the roster, set the lineup, and decide on strategies - with real players, in a real ballpark, in a real playoff race. That's what baseball analysts Ben Lindbergh and Sam Miller got to do when an independent minor-league team in California, the Sonoma Stompers, offered them the chance to run its baseball operations according to the most advanced statistics.

You cannot afford to be without it… Announcing a powerful, new perspective in a book of style that cannot be imitated—the fascinating, popular, and simple “Tips and Tricks for Winning the Lottery.” Do you want the luxury of feeling better, more confident, about your lotto playing abilities? Are you interested in valuable advice that could lead to enormous winnings and financial security in the future? Whatever your situation in life, it feels wonderful to consider what you would do with all that money after winning the jackpot. The proven bottom line is this: if it’s worth ...

Can a well-programmed machine do anything a human can - only better? Complex algorithms are buying our groceries, picking our partners, and driving our investments. They can navigate more data than a doctor or lawyer and act with greater precision. For many years we've taken solace in the notion that they can't create. But now that algorithms can learn and adapt, does the future of creativity belong to machines too?

Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K-12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur.

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.