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Author: Nikolai Saveliev
Brand: Brand: Springer
The book gives a systematic exposition of the diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered include: constructions and classification of homology 3-spheres, Rokhlin invariant, Casson invariant and its extensions, and Floer homology and gauge-theoretical invariants of homology cobordism. Many of the topics covered in the book appear in monograph form for the first time. The book gives a rather broad overview of ideas and methods and provides a comprehensive bibliography. The text will be a valuable source for both the graduate student and researcher in mathematics and theoretical physics.
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Author: David Deutsch
Brand: David Deutsch
For David Deutsch, a young physicist of unusual originality, quantum theory contains our most fundamental knowledge of the physical world. Taken literally, it implies that there are many universes “parallel” to the one we see around us. This multiplicity of universes, according to Deutsch, turns out to be the key to achieving a new worldview, one which synthesizes the theories of evolution, computation, and knowledge with quantum physics. Considered jointly, these four strands of explanation reveal a unified fabric of reality that is both objective and comprehensible, the subject of this daring, challenging book. The Fabric of Reality explains and connects many topics at the leading edge of current research and thinking, such as quantum computers (which work by effectively collaborating with their counterparts in other universes), the physics of time travel, the comprehensibility of nature and the physical limits of virtual reality, the significance of human life, and the ultimate fate of the universe. Here, for scientist and layperson alike, for philosopher, science-fiction reader, biologist, and computer expert, is a startlingly complete and rational synthesis of disciplines, and a new, optimistic message about existence.
"Our best theories are not only truer than common sense, they make more sense than common sense," writes physicist David Deutsch. In The Fabric of Reality, Deutsch traces what he considers the four main strands of scientific explanation: quantum theory, evolution, computation, and the theory of knowledge. "The four of them taken together form a coherent explanatory structure that is so far-reaching, and has come to encompass so much of our understanding of the world, that in my view it may already properly be called the first Theory of Everything." Deutsch covers some difficult material with unusual clarity. Each chapter ends with a summary and definitions of important terms, which makes the work an invaluable sourcebook.
The Fabric of Reality The Science of Parallel Universes and Its Implications
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Author: James Owen Weatherall
Brand: Mariner Books
“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
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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Author: K. F. Riley
Brand: Brand: Cambridge University Press
The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.
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Author: Paul J. Nahin
Brand: Paul J Nahin
What’s the point of calculating definite integrals since you can’t possibly do them all?.
What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future.
This book is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you.
Inside Interesting Integrals A Collection of Sneaky Tricks Sly Substitutions and Numerous Other Stupendously Clever Awesomely Wicked and Devili Undergraduate Lecture Notes in Physics
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Author: Russell Stannard
Brand: Russell Stannard
If you move at high speed, time slows down, space squashes up and you get heavier. Travel fast enough and you could weigh as much as a jumbo jet, be flattened thinner than a CD without feeling a thing-and live forever! As for the angles of a triangle, they do not always have to add up to 180 degrees. And then, of course, there are black holes. These are but a few of the extraordinary consequences of Einstein's theory of relativity. It is now over a hundred years since he made these discoveries, and yet the general public is still largely unaware of them. Filled with illuminating anecdotes and fascinating accounts of experiments, this book aims to introduce the interested lay person to the subject of relativity in a way which is accessible and engaging and at the same time scientifically rigorous. With relatively few mathematical equations--nothing more complicated than the Pythagoras's Theorem--this VSI packs a lot time into very little space, and for anyone who has felt intimidated by Einstein's groundbreaking theory, it offers the perfect place to start.
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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Author: Frederick W. Byron
This textbook is designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism, and quantum mechanics. Organized around the central concept of a vector space, the book includes numerous physical applications in the body of the text as well as many problems of a physical nature. It is also one of the purposes of this book to introduce the physicist to the language and style of mathematics as well as the content of those particular subjects with contemporary relevance in physics. Chapters 1 and 2 are devoted to the mathematics of classical physics. Chapters 3, 4 and 5 — the backbone of the book — cover the theory of vector spaces. Chapter 6 covers analytic function theory. In chapters 7, 8, and 9 the authors take up several important techniques of theoretical physics — the Green's function method of solving differential and partial differential equations, and the theory of integral equations. Chapter 10 introduces the theory of groups. The authors have included a large selection of problems at the end of each chapter, some illustrating or extending mathematical points, others stressing physical application of techniques developed in the text. Essentially self-contained, the book assumes only the standard undergraduate preparation in physics and mathematics, i.e. intermediate mechanics, electricity and magnetism, introductory quantum mechanics, advanced calculus and differential equations. The text may be easily adapted for a one-semester course at the graduate or advanced undergraduate level.
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Author: Mark Srednicki
Brand: Brand: Cambridge University Press
Quantum field theory is the basic mathematical framework that is used to describe elementary particles. This textbook provides a complete and essential introduction to the subject. Assuming only an undergraduate knowledge of quantum mechanics and special relativity, this book is ideal for graduate students beginning the study of elementary particles. The step-by-step presentation begins with basic concepts illustrated by simple examples, and proceeds through historically important results to thorough treatments of modern topics such as the renormalization group, spinor-helicity methods for quark and gluon scattering, magnetic monopoles, instantons, supersymmetry, and the unification of forces. The book is written in a modular format, with each chapter as self-contained as possible, and with the necessary prerequisite material clearly identified. It is based on a year-long course given by the author and contains extensive problems, with password protected solutions available to lecturers at www.cambridge.org/9780521864497.
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Author: Daniel A. Fleisch
Brand: Daniel Fleisch
Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch explains vectors and tensors in plain language. Written for undergraduate and beginning graduate students, the book provides a thorough grounding in vectors and vector calculus before transitioning through contra and covariant components to tensors and their applications. Matrices and their algebra are reviewed on the book's supporting website, which also features interactive solutions to every problem in the text where students can work through a series of hints or choose to see the entire solution at once. Audio podcasts give students the opportunity to hear important concepts in the book explained by the author.