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A world-class mathematician and regular contributor to the New York Times hosts a delightful tour of the greatest ideas of math, revealing how it connects to literature, philosophy, law, medicine, art, business, even pop culture in ways we never imagined

Did O.J. do it? How should you flip your mattress to get the maximum wear out of it? How does Google search the Internet? How many people should you date before settling down? Believe it or not, math plays a crucial role in answering all of these questions and more.

Math underpins everything in the cosmos, including us, yet too few of us understand this universal language well enough to revel in its wisdom, its beauty — and its joy. This deeply enlightening, vastly entertaining volume translates math in a way that is at once intelligible and thrilling. Each trenchant chapter of The Joy of x offers an “aha!” moment, starting with why numbers are so helpful, and progressing through the wondrous truths implicit in π, the Pythagorean theorem, irrational numbers, fat tails, even the rigors and surprising charms of calculus. Showing why he has won awards as a professor at Cornell and garnered extensive praise for his articles about math for the New York Times, Strogatz presumes of his readers only curiosity and common sense. And he rewards them with clear, ingenious, and often funny explanations of the most vital and exciting principles of his discipline.

All of life is a game, and evolution by natural selection is no exception. The evolutionary game theory developed in this 2005 book provides the tools necessary for understanding many of nature's mysteries, including co-evolution, speciation, extinction and the major biological questions regarding fit of form and function, diversity, procession, and the distribution and abundance of life. Mathematics for the evolutionary game are developed based on Darwin's postulates leading to the concept of a fitness generating function (G-function). G-function is a tool that simplifies notation and plays an important role developing Darwinian dynamics that drive natural selection. Natural selection may result in special outcomes such as the evolutionarily stable strategy (ESS). An ESS maximum principle is formulated and its graphical representation as an adaptive landscape illuminates concepts such as adaptation, Fisher's Fundamental Theorem of Natural Selection, and the nature of life's evolutionary game.

The spectacular success of the scientific enterprise over the last four hundred years has led to the promise of an all encompassing vision of the natural world. In this elegant picture, everything we observe is based upon just a few fundamental processes and entities. The almost infinite variety and complexity of the world is thus the product of emergence. But the concept of emergence is fraught with controversy and confusion. This book ponders the question of how emergence should be understood within the scientific picture, and whether a complete vision of the world can be attained that includes consciousness.

The discipline of nonlinear dynamics has developed explosively in all areas of physics over the last two decades. This comprehensive primer summarizes the main developments in the mathematical theory of dynamical systems, chaos, pattern formation and complexity. An introduction to mathematical concepts and techniques is given in the first part of the book, before being applied to stellar, interstellar, galactic and large scale complex phenomena in the Universe. Oded Regev demonstrates the possible application of ideas including strange attractors, Poincaré sections, fractals, bifurcations, and complex spatial patterns, to specific astrophysical problems.

From one of the most original and influential neuroscientists at work today, here is an exploration of consciousness unlike any other—as told by Galileo, who opened the way for the objectivity of science and is now intent on making subjective experience a part of science as well.
 
Galileo’s journey has three parts, each with a different guide. In the first, accompanied by a scientist who resembles Francis Crick, he learns why certain parts of the brain are important and not others, and why consciousness fades with sleep. In the second part, when his companion seems to be named Alturi (Galileo is hard of hearing; his companion’s name is actually Alan Turing), he sees how the facts assembled in the first part can be unified and understood through a scientific theory—a theory that links consciousness to the notion of integrated information (also known as phi). In the third part, accompanied by a bearded man who can only be Charles Darwin, he meditates on how consciousness is an evolving, developing, ever-deepening awareness of ourselves in history and culture—that it is everything we have and everything we are.
 
Not since Gödel, Escher, Bach has there been a book that interweaves science, art, and the imagination with such originality. This beautiful and arresting narrative will transform the way we think of ourselves and the world.

From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines this with an in-depth look at their aesthetics, history, and structure. Whether using trigonometry and vectors to explain why Gothic arches are structurally superior to Roman arches, or showing how simple ruler and compass constructions can produce sophisticated architectural details, Alexander Hahn describes the points at which elementary mathematics and architecture intersect.

Beginning in prehistoric times, Hahn proceeds to guide readers through the Greek, Roman, Islamic, Romanesque, Gothic, Renaissance, and modern styles. He explores the unique features of the Pantheon, the Hagia Sophia, the Great Mosque of Cordoba, the Duomo in Florence, Palladio's villas, and Saint Peter's Basilica, as well as the U.S. Capitol Building. Hahn celebrates the forms and structures of architecture made possible by mathematical achievements from Greek geometry, the Hindu-Arabic number system, two- and three-dimensional coordinate geometry, and calculus. Along the way, Hahn introduces groundbreaking architects, including Brunelleschi, Alberti, da Vinci, Bramante, Michelangelo, della Porta, Wren, Gaudí, Saarinen, Utzon, and Gehry.

Rich in detail, this book takes readers on an expedition around the globe, providing a deeper understanding of the mathematical forces at play in the world's most elegant buildings.

Complex adaptive systems (cas), including ecosystems, governments, biological cells, and markets, are characterized by intricate hierarchical arrangements of boundaries and signals. In ecosystems, for example, niches act as semi-permeable boundaries, and smells and visual patterns serve as signals; governments have departmental hierarchies with memoranda acting as signals; and so it is with other cas. Despite a wealth of data and descriptions concerning different cas, there remain many unanswered questions about "steering" these systems. In Signals and Boundaries, John Holland argues that understanding the origin of the intricate signal/border hierarchies of these systems is the key to answering such questions. He develops an overarching framework for comparing and steering cas through the mechanisms that generate their signal/boundary hierarchies.

Holland lays out a path for developing the framework that emphasizes agents, niches, theory, and mathematical models. He discusses, among other topics, theory construction; signal-processing agents; networks as representations of signal/boundary interaction; adaptation; recombination and reproduction; the use of tagged urn models (adapted from elementary probability theory) to represent boundary hierarchies; finitely generated systems as a way to tie the models examined into a single framework; the framework itself, illustrated by a simple finitely generated version of the development of a multi-celled organism; and Markov processes.

Drawing on a wealth of new archival material, including personal correspondence and diaries, Robert Leonard tells the fascinating story of the creation of game theory by Hungarian Jewish mathematician John von Neumann and Austrian economist Oskar Morgenstern. Game theory first emerged amid discussions of the psychology and mathematics of chess in Germany and fin-de-siècle Austro-Hungary. In the 1930s, on the cusp of anti-Semitism and political upheaval, it was developed by von Neumann into an ambitious theory of social organization. It was shaped still further by its use in combat analysis in World War II and during the Cold War. Interweaving accounts of the period's economics, science, and mathematics, and drawing sensitively on the private lives of von Neumann and Morgenstern, Robert Leonard provides a detailed reconstruction of a complex historical drama.

Imagine knowing what the brain craves from every tale it encounters, what fuels the success of any great story, and what keeps readers transfixed. Wired for Story reveals these cognitive secrets—and it’s a game-changer for anyone who has ever set pen to paper.
     The vast majority of writing advice focuses on “writing well” as if it were the same as telling a great story. This is exactly where many aspiring writers fail—they strive for beautiful metaphors, authentic dialogue, and interesting characters, losing sight of the one thing that every engaging story must do: ignite the brain’s hardwired desire to learn what happens next. When writers tap into the evolutionary purpose of story and electrify our curiosity, it triggers a delicious dopamine rush that tells us to pay attention. Without it, even the most perfect prose won’t hold anyone’s interest.
     Backed by recent breakthroughs in neuroscience as well as examples from novels, screenplays, and short stories, Wired for Story offers a revolutionary look at story as the brain experiences it. Each chapter zeroes in on an aspect of the brain, its corresponding revelation about story, and the way to apply it to your storytelling right now.

The costs of either rebuilding or relocating in response are enormous but unavoidable. Furthermore, since the economies of many coastal communities are based on fisheries and tourism, the impacts of anthropogenic climate change threaten their long-term sustainability. Given their vulnerability, coastal communities are on the front line of global warming. But do they have the capacity to adapt to so much environmental change? Do their responses to past challenges suggest strategies for coping with future change? Can we predict which communities are most vulnerable and help them to become more resilient?

Pryzant L-K, Bruno JF (2012) What to Do When the Oceans Rise. PLoS Biol 10(9): e1001387. http://dx.doi.org/10.1371/journal.pbio.1001387

After billions of dollars, thousands of studies, and immeasurable effort by educators at all levels, why is the performance of students and teachers so unaffected by technology? Moreover, what should be done to extract genuine benefit from the information and communication technology (ICT) revolution? In this groundbreaking book, technology and education experts Alan Bain and Mark Weston provide research-based evidence for how the widespread application of ICT can provide powerful learning opportunities that lead to lasting gains and achievement. They show how the integrated use of technology at all levels of the educational system can greatly expand collaborative learning opportunities by giving all educational stakeholders powerful problem-solving tools and solutions. The approaches presented here are grounded in over twenty years of experience working with classroom teachers, school leaders, association members, and policymakers.

The primary goal of the book is to present the ideas and research findings of active researchers such as physicists, economists, mathematicians and financial engineers working in the field of “Econophysics,” who have undertaken the task of modeling and analyzing systemic risk, network dynamics and other topics. Of primary interest in these studies is the aspect of systemic risk, which has long been identified as a potential scenario in which financial institutions trigger a dangerous contagion mechanism, spreading from the financial economy to the real economy. This type of risk, long confined to the monetary market, has spread considerably in the recent past, culminating in the subprime crisis of 2008. As such, understanding and controlling systemic risk has become an extremely important societal and economic challenge. The Econophys-Kolkata VI conference proceedings are dedicated to addressing a number of key issues involved. Several leading researchers in these fields report on their recent work and also review contemporary literature on the subject.

This monograph presents key method to successfully manage the growing  complexity of systems  where conventional engineering and scientific methodologies and technologies based on learning and adaptability come to their limits and new ways are nowadays required. The transition from adaptable to evolvable and finally to self-evolvable systems is highlighted, self-properties such as self-organization, self-configuration, and self-repairing are introduced and challenges and limitations of the self-evolvable engineering systems are evaluated.

Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever the quantitative modeling and analysis of complex, nonlinear phenomena are required, chaos theory and its methods can play a key role.    This second volume concentrates on reviewing further relevant, contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. This encompasses, but is not limited to, topics such as the spread of epidemics; electronic circuits; chaos control in mechanical devices; secure communication; and digital watermarking. Featuring contributions from active and leading research groups, this collection is ideal both as a reference work and as a ‘recipe book’ full of tried and tested, successful engineering applications.

The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define--and why so many questions still surround them.

That definition seems so simple: they are numbers that cannot be expressed as a ratio of two integers, or that have decimal expansions that are neither infinite nor recurring. But, as The Irrationals shows, these are the real "complex" numbers, and they have an equally complex and intriguing history, from Euclid's famous proof that the square root of 2 is irrational to Roger Apéry's proof of the irrationality of a number called Zeta(3), one of the greatest results of the twentieth century. In between, Havil explains other important results, such as the irrationality of e and pi. He also discusses the distinction between "ordinary" irrationals and transcendentals, as well as the appealing question of whether the decimal expansion of irrationals is "random".

Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

How do the great discoverers of science really work? Biographers, psychologists, and philosophers have written much on the phenomenon of scientific creativity. This collection of essays takes you into the minds of some of the world’s greatest scientists. You can read in their own words how they worked, thought, and discovered crucial insights. Hermann von Helmholtz, Hideki Yukawa, Ernst Mach, J.B.S. Haldane, Steven Weinberg, Peter Doherty, C.V. Raman, Sylvester James Gates, and many more deliver witty, irreverent, thoughtful, and profound advice to scientists of all kinds and abilities. Whether you are a science hobbyist, an undergraduate doing your first lab work, a postdoc, or a seasoned professional, these essays will help point you in the direction of insight and discovery.

Scientific Work and Creativity: Advice from the Masters
By the Citizen Scientists League
Edited by Reginald D. Smith

In this time of turbulence, scientists, economists, social innovators, corporate and civic leaders, and citizens alike are asking the same basic questions: What causes one system to break down and another to rebound? Are we merely subject to the whim of forces beyond our control? Or, in the face of constant disruption, can we build better shock absorbers—for ourselves, our communities, our economies, and for the planet as a whole?

The answers to these vital questions are shaping a new field of inquiry, and a new agenda, focused on resilience: the ability of people, communities, and systems to maintain their core purpose and integrity amid unforeseen shocks and surprises. By encouraging adaptation, agility, and cooperation, this new approach can not only help us weather disruptions, but also bring us to a different way of being in and engaging with the world.

Reporting firsthand from the coral reefs of Palau to the back streets of Palestine, Andrew Zolli and Ann Marie Healy relate breakthrough scientific discoveries, pioneering social and ecological innovations, and important new approaches to constructing a more resilient world. Along the way, they share insights to bolster our own psychological resilience, foster greater stability within our communities, and establish leadership imperatives for more resilient organizations. Zolli and Healy show how this new concept of resilience is a powerful lens through which we can assess major issues afresh: from business planning to social development, from urban planning to national energy security—circumstances that affect us all.

What do these scenarios have in common: a professional tennis player returning a serve, a woman evaluating a first date across the table, a naval officer assessing a threat to his ship, and a comedian about to reveal a punch line?

In this counterintuitive and insightful work, author Frank Partnoy weaves together findings from hundreds of scientific studies and interviews with wide-ranging experts to craft a picture of effective decision-making that runs counter to our brutally fast-paced world. Even as technology exerts new pressures to speed up our lives, it turns out that the choices we make––unconsciously and consciously, in time frames varying from milliseconds to years––benefit profoundly from delay. As this winning and provocative book reveals, taking control of time and slowing down our responses yields better results in almost every arena of life … even when time seems to be of the essence.