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Chaos & Systems


Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity)

Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity) Lowest new price: $46.02
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Author: Steven H. Strogatz

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory.Richly illustrated, and with many exercises and worked examples, this book is ideal for an introductory course at the junior/senior or first-year graduate level. It is also ideal for the scientist who has not had formal instruction in nonlinear dynamics, but who now desires to begin informal study. The prerequisites are multivariable calculus and introductory physics.

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The Drunkard's Walk: How Randomness Rules Our Lives

The Drunkard's Walk: How Randomness Rules Our Lives Lowest new price: $7.38
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Author: Leonard Mlodinow

With the born storyteller's command of narrative and imaginative approach, Leonard Mlodinow vividly demonstrates how our lives are profoundly informed by chance and randomness and how everything from wine ratings and corporate success to school grades and political polls are less reliable than we believe.

By showing us the true nature of chance and revealing the psychological illusions that cause us to misjudge the world around us, Mlodinow gives us the tools we need to make more informed decisions. From the classroom to the courtroom and from financial markets to supermarkets, Mlodinow's intriguing and illuminating look at how randomness, chance, and probability affect our daily lives will intrigue, awe, and inspire.

 

Amazon Guest Review: Stephen Hawking
Published in 1988, Stephen Hawking’s A Brief History of Time became perhaps one of the unlikeliest bestsellers in history: a not-so-dumbed-down exploration of physics and the universe that occupied the London Sunday Times bestseller list for 237 weeks. Later successes include 1995’s A Briefer History of Time, The Universe in a Nutshell, and God Created the Integers: The Mathematical Breakthroughs that Changed History. Stephen Hawking is Lucasian Professor of Mathematics at the University of Cambridge.

In The Drunkard’s Walk Leonard Mlodinow provides readers with a wonderfully readable guide to how the mathematical laws of randomness affect our lives. With insight he shows how the hallmarks of chance are apparent in the course of events all around us. The understanding of randomness has brought about profound changes in the way we view our surroundings, and our universe. I am pleased that Leonard has skillfully explained this important branch of mathematics. --Stephen Hawking


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A Student's Guide to Entropy

A Student's Guide to Entropy Lowest new price: $23.81
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Author: Don S. Lemons

Striving to explore the subject in as simple a manner as possible, this book helps readers understand the elusive concept of entropy. Innovative aspects of the book include the construction of statistical entropy, the derivation of the entropy of classical systems from purely classical assumptions, and a statistical thermodynamics approach to the ideal Fermi and ideal Bose gases. Derivations are worked through step-by-step and important applications are highlighted in over 20 worked examples. Nearly 50 end-of-chapter exercises test readers' understanding. The book also features a glossary giving definitions for all essential terms, a time line showing important developments, and list of books for further study. It is an ideal supplement to undergraduate courses in physics, engineering, chemistry and mathematics.

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Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life

Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life Lowest new price: $4.99
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Author: Albert-Laszlo Barabasi

A cocktail party? A terrorist cell? Ancient bacteria? An international conglomerate?

All are networks, and all are a part of a surprising scientific revolution. Albert-László Barabási, the nation’s foremost expert in the new science of networks and author of Bursts, takes us on an intellectual adventure to prove that social networks, corporations, and living organisms are more similar than previously thought. Grasping a full understanding of network science will someday allow us to design blue-chip businesses, stop the outbreak of deadly diseases, and influence the exchange of ideas and information. Just as James Gleick and the Erdos–Rényi model brought the discovery of chaos theory to the general public, Linked tells the story of the true science of the future and of experiments in statistical mechanics on the internet, all vital parts of what would eventually be called the Barabási–Albert model.

 

How is the human brain like the AIDS epidemic? Ask physicist Albert-László Barabási and he'll explain them both in terms of networks of individual nodes connected via complex but understandable relationships. Linked: The New Science of Networks is his bright, accessible guide to the fundamentals underlying neurology, epidemiology, Internet traffic, and many other fields united by complexity.

Barabási's gift for concrete, nonmathematical explanations and penchant for eccentric humor would make the book thoroughly enjoyable even if the content weren't engaging. But the results of Barabási's research into the behavior of networks are deeply compelling. Not all networks are created equal, he says, and he shows how even fairly robust systems like the Internet could be crippled by taking out a few super-connected nodes, or hubs. His mathematical descriptions of this behavior are helping doctors, programmers, and security professionals design systems better suited to their needs. Linked presents the next step in complexity theory--from understanding chaos to practical applications. --Rob Lightner

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Differential Equations, Dynamical Systems, and an Introduction to Chaos, Third Edition

Differential Equations, Dynamical Systems, and an Introduction to Chaos, Third Edition Lowest new price: $30.69
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Author: Morris W. Hirsch

Hirsch, Devaney, and Smale's classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems.

  • Classic text by three of the world's most prominent mathematicians
  • Continues the tradition of expository excellence
  • Contains updated material and expanded applications for use in applied studies

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The Physics of Wall Street: A Brief History of Predicting the Unpredictable

The Physics of Wall Street: A Brief History of Predicting the Unpredictable Lowest new price: $5.90
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Author: James Owen Weatherall

“Weatherall probes an epochal shift in financial strategizing with lucidity, explaining how it occurred and what it means for modern finance.”—Peter Galison, author of Einstein’s Clocks, Poincare’s Maps

After the economic meltdown of 2008, many pundits placed the blame on “complex financial instruments” and the physicists and mathematicians who dreamed them up. But how is it that physicists came to drive Wall Street? And were their ideas really the cause of the collapse?
In The Physics of Wall Street, the physicist James Weatherall answers both of these questions. He tells the story of how physicists first moved to finance, bringing science to bear on some of the thorniest problems in economics, from bubbles to options pricing. The problem isn’t simply that economic models have limitations and can break down under certain conditions, but that at the time of the meltdown those models were in the hands of people who either didn’t understand their purpose or didn’t care. It was a catastrophic misuse of science. However, Weatherall argues that the solution is not to give up on the models but to make them better. Both persuasive and accessible, The Physics of Wall Street is riveting history that will change how we think about our economic future.

Q&A with James Owen Weatherall

James Owen Weatherall

Q. What is The Physics of Wall Street all about?

A. Over the past few years, we've heard a lot about a new kind of Wall Street elite known as "quants." These are often physicists and mathematicians who have moved to finance and brought radically new ideas along with them. This book is an attempt to understand these quants and the mathematical models they use to predict market behavior. It's two parts history and one part argument: I tell the surprisingly fun story of how physicists and their ideas made it to Wall Street in the first place, and along the way I argue that this history reveals something important about how we should think about the models and practices they have introduced--especially in light of the 2007-2008 financial crisis.

Q. You say the history is surprisingly fun. Can you give an example?

A. The physicists and mathematicians I write about in the book are (or were) very smart, creative people who put their scientific training to use in surprising new ways. Their stories are fascinating. For instance, Edward Thorp, who invented the modern quantitative hedge fund, was also the first person to prove that card counting could be used to reliably get an edge in blackjack. He spent a good amount of time working the card tables in Las Vegas. And Norman Packard and Doyne Farmer, who started a pioneering financial services firm in the early 1990s, spent their graduate school years at UC Santa Cruz inventing the new science of chaos theory while trying to build a computer to beat the odds in roulette--the profits from which were intended to start a yippie commune in the Pacific Northwest.

Q. What surprised you most about the history you uncovered?

A. One thing that surprised me was that derivatives contracts such as options, futures, and swaps, which are often discussed as though they were a troubling new innovation, have actually been around for thousands of years. For example, scientists have found cuneiform tablets containing records of futures traded by ancient Sumerians. Even the idea of using mathematical methods to price options is quite old. I pick up the story in 1900, with the visionary work of a French physicist named Louis Bachelier, but some strands go back further, to the mid-nineteenth century. Plus, there are some striking historical connections in the book. For instance, I explain the relationship between the invention of nylon and the development of the atomic bomb--and how both influenced at least one physicist's to switch to a financial career. And I tell the story of how the space race and the Vietnam War were partly responsible for many physicists moving to Wall Street banks in the 1980s.

Q. What can this history teach us about models used in finance?

A. If you look at how the physicists and mathematicians who came up with the earliest financial models thought about what they were doing, the role of simplifying assumptions and idealizations becomes very clear. The goal was to get a toehold on some very hard problems, and not to come up with a final, overarching theory of financial markets. Making simplified assumptions can lead to the solution of a problem that you otherwise couldn’t solve--but that solution is only going to be a reliable guide to how the world works when the assumptions you’ve made are approximately true. The important question, and the one that physicists are always trained to ask, is when do your assumptions fail and what happens when they do? I don’t think the importance of this question has been recognized as widely as it should be among the traders who rely on these models.

Q. At the end of the book, you describe an "Economic Manhattan Project." What would that be like?

A. The Economic Manhattan Project was proposed in 2008 by the mathematical physicist and hedge fund manager Eric Weinstein. The idea is that economic and financial security--that is, regulating the economy to avoid future calamities--should be at the very top of our agenda. Yet the resources we devote to physical security, to military technology and defense, far outstrip what we spend on developing better economic theories. In the past, America has set goals--for the original Manhattan Project, the race to the moon, and others--when we have funneled resources into serious innovation. And whenever we have done so, we have succeeded in accomplishing great things. I think it is time to make a similar kind of commitment to developing the next generation of economic models, with the goal of finding radical new ideas to make the economy safer and more robust.

Q. You're a philosophy professor. Why did you write a book about finance?

A. The short answer is simply that I find the history and the ideas fascinating. I have a Ph.D. in physics and I like thinking about how physics can be applied to novel problems. The longer answer is that the issues in this book aren't so far removed from philosophy. Philosophers spend a lot of time thinking about what we can know about the world and how to deal with fundamental uncertainty. Philosophy has a reputation for being abstract and distant from everyday concerns. And sometimes it is. But when it comes to mathematical models, philosophical issues really matter for how we make important economic and financial decisions--decisions that have significant real-world ramifications. And for me, at least, the most interesting and important philosophical questions are those that we face as practicing scientists and policymakers--and even as investors.

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Systems Thinking, Third Edition: Managing Chaos and Complexity: A Platform for Designing Business Architecture

Systems Thinking, Third Edition: Managing Chaos and Complexity: A Platform for Designing Business Architecture Lowest new price: $25.99
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Author: Jamshid Gharajedaghi

In a global market economy, a viable business cannot be locked into a single form or function anymore. Rather, success is contingent upon a self-renewing capacity to spontaneously create structures, functions, and processes responsive to a fluctuating business landscape. Now in its third edition, Systems Thinking synthesizes systems theory and interactive design, providing an operational methodology for defining problems and designing solutions in an environment increasingly characterized by chaos and complexity.

The current edition has been updated to include all new chapters on self-organizing systems, Holistic, Operational, and Design thinking. Gharajedaghi covers recent crises in financial systems and job markets, the housing bubble, and environment, assessing their impact on systems thinking. A companion website to accompany the book is available at www.interactdesign.com.

  • Four NEW chapters on self-organizing systems, holistic thinking, operational thinking, and design thinking
  • Covers the recent crises in financial systems and job markets globally, the housing bubble, and the environment, assessing their impact on systems thinking
  • Companion website to accompany the book is available at interactdesign.com

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Ubiquity: Why Catastrophes Happen

Ubiquity: Why Catastrophes Happen Lowest new price: $8.45
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Author: Mark Buchanan

Why do catastrophes happen? What sets off earthquakes, for example? What about mass extinctions of species? The outbreak of major wars? Massive traffic jams that seem to appear out of nowhere? Why does the stock market periodically suffer dramatic crashes? Why do some forest fires become superheated infernos that rage totally out of control?

Experts have never been able to explain the causes of any of these disasters. Now scientists have discovered that these seemingly unrelated cataclysms, both natural and human, almost certainly all happen for one fundamental reason. More than that, there is not and never will be any way to predict them.

Critically acclaimed science journalist Mark Buchanan tells the fascinating story of the discovery that there is a natural structure of instability woven into the fabric of our world. From humble beginnings studying the physics of sandpiles, scientists have learned that an astonishing range of things–Earth’s crust, cars on a highway, the market for stocks, and the tightly woven networks of human society–have a natural tendency to organize themselves into what’s called the “critical state,” in which they are poised on what Buchanan describes as the “knife-edge of instability.” The more places scientists have looked for the critical state, the more places they’ve found it, and some believe that the pervasiveness of instability must now be seen as a fundamental feature of our world.

Ubiquity is packed with stories of real-life catastrophes, such as the huge earthquake that in 1995 hit Kobe, Japan, killing 5,000 people; the forest fires that ravaged Yellowstone National Park in 1988; the stock market crash of 1987; the mass extinction that killed off the dinosaurs; and the outbreak of World War I. Combining literary flair with scientific rigor, Buchanan introduces the researchers who have pieced together the evidence of the critical state, explaining their ingenious work and unexpected insights in beautifully lucid prose.

At the dawn of this new century, Buchanan reveals, we are witnessing the emergence of an extraordinarily powerful new field of science that will help us comprehend the bewildering and unruly rhythms that dominate our lives and may even lead to a true science of the dynamics of human culture and history.


From the Hardcover edition.

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Simply Complexity: A Clear Guide to Complexity Theory

Simply Complexity: A Clear Guide to Complexity Theory Lowest new price: $9.38
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Author: Neil Johnson

What do traffic jams, stock market crashes, and wars have in common? They are all explained using complexity, an unsolved puzzle that many researchers believe is the key to predicting – and ultimately solving—everything from terrorist attacks and pandemic viruses right down to rush hour traffic congestion.

Complexity is considered by many to be the single most important scientific development since general relativity and it promises to make sense of no less than the very heart of the Universe. Using it, scientists can find order emerging from seemingly random interactions of all kinds, from something as simple as flipping coins through to more challenging problems such as the patterns in modern jazz, the growth of cancer tumours, and predicting shopping habits.

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Chaos: A Very Short Introduction

Chaos: A Very Short Introduction Lowest new price: $5.73
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Author: Lenny Smith

Chaos exists in systems all around us. Even the simplest system can be subject to chaos, denying us accurate predictions of its behavior, and sometimes giving rise to astonishing structures of large-scale order. Here, Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He uses accessible math and physics to explain Chaos Theory, and points to numerous examples in philosophy and literature that illuminate the problems. This book provides a complete understanding of chaotic dynamics, using examples from mathematics, physics, philosophy, and the real world, with an explanation of why chaos is important and how it differs from the idea of randomness. The author's real life applications include the weather forecast, a pendulum, a coin toss, mass transit, politics, and the role of chaos in gambling and the stock market. Chaos represents a prime opportunity for mathematical lay people to finally get a clear understanding of this fascinating concept.

About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

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