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Author: Georgi P. Tolstov
Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series. This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourier Series and the Fourier Integral, Bessel Functions and Fourier-Bessel Series, and the Eigenfunction Method and its Applications to Mathematical Physics. Every chapter moves clearly from topic to topic and theorem to theorem, with many theorem proofs given. A total of 107 problems will be found at the ends of the chapters, including many specially added to this English-language edition, and answers are given at the end of the text.
Richard Silverman's excellent translation makes this book readily accessible to mathematicians and math students, as well as workers and students in the fields of physics and engineering. He has also added a bibliography, containing suggestions for collateral and supplementary reading. 1962 edition.
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Author: Zeljko Ivezic
As telescopes, detectors, and computers grow ever more powerful, the volume of data at the disposal of astronomers and astrophysicists will enter the petabyte domain, providing accurate measurements for billions of celestial objects. This book provides a comprehensive and accessible introduction to the cutting-edge statistical methods needed to efficiently analyze complex data sets from astronomical surveys such as the Panoramic Survey Telescope and Rapid Response System, the Dark Energy Survey, and the upcoming Large Synoptic Survey Telescope. It serves as a practical handbook for graduate students and advanced undergraduates in physics and astronomy, and as an indispensable reference for researchers.
Statistics, Data Mining, and Machine Learning in Astronomy presents a wealth of practical analysis problems, evaluates techniques for solving them, and explains how to use various approaches for different types and sizes of data sets. For all applications described in the book, Python code and example data sets are provided. The supporting data sets have been carefully selected from contemporary astronomical surveys (for example, the Sloan Digital Sky Survey) and are easy to download and use. The accompanying Python code is publicly available, well documented, and follows uniform coding standards. Together, the data sets and code enable readers to reproduce all the figures and examples, evaluate the methods, and adapt them to their own fields of interest.
Describes the most useful statistical and data-mining methods for extracting knowledge from huge and complex astronomical data sets
Features real-world data sets from contemporary astronomical surveys
Uses a freely available Python codebase throughout
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Author: 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.
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Author: R. Shankar
Reviews from the First Edition:
"An excellent text … The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist)
"No matter how gently one introduces students to the concept of Dirac’s bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (Physics Bulletin)
Reviews of the Second Edition:
"This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details---all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. … It would be particularly useful to beginning students and those in allied areas like quantum chemistry." (Mathematical Reviews)
R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include:
- Clear, accessible treatment of underlying mathematics
- A review of Newtonian, Lagrangian, and Hamiltonian mechanics
- Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates
- Unsurpassed coverage of path integrals and their relevance in contemporary physics
The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book’s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.
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Author: Hans Petter Langtangen
Brand: Brand: Springer
The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example- and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology, and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background, and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By blending programming, mathematics and scientific applications, the book lays a solid foundation for practicing computational science.
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Author: Daniel Zwillinger
Brand: Brand: CRC Press
With over 6,000 entries, CRC Standard Mathematical Tables and Formulae, 32nd Edition continues to provide essential formulas, tables, figures, and descriptions, including many diagrams, group tables, and integrals not available online. This new edition incorporates important topics that are unfamiliar to some readers, such as visual proofs and sequences, and illustrates how mathematical information is interpreted. Material is presented in a multisectional format, with each section containing a valuable collection of fundamental tabular and expository reference material.
New to the 32nd Edition
A new chapter on Mathematical Formulae from the Sciences that contains the most important formulae from a variety of fields, including acoustics, astrophysics, epidemiology, finance, statistical mechanics, and thermodynamics
New material on contingency tables, estimators, process capability, runs test, and sample sizes
New material on cellular automata, knot theory, music, quaternions, and rational trigonometry
Updated and more streamlined tables
Retaining the successful format of previous editions, this comprehensive handbook remains an invaluable reference for professionals and students in mathematical and scientific fields.
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Author: Mark Newman
Brand: Brand: CreateSpace Independent Publishing Platform
A complete introduction to the field of computational physics, with examples and exercises in the Python programming language. Computers play a central role in virtually every major physics discovery today, from astrophysics and particle physics to biophysics and condensed matter. This book explains the fundamentals of computational physics and describes in simple terms the techniques that every physicist should know, such as finite difference methods, numerical quadrature, and the fast Fourier transform. The book offers a complete introduction to the topic at the undergraduate level, and is also suitable for the advanced student or researcher who wants to learn the foundational elements of this important field.
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Author: Roger Penrose
Roger Penrose, one of the most accomplished scientists of our time, presents the only comprehensive and comprehensible account of the physics of the universe. From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.
If Albert Einstein were alive, he would have a copy of The Road to Reality on his bookshelf. So would Isaac Newton. This may be the most complete mathematical explanation of the universe yet published, and Roger Penrose richly deserves the accolades he will receive for it. That said, let us be perfectly clear: this is not an easy book to read. The number of people in the world who can understand everything in it could probably take a taxi together to Penrose's next lecture. Still, math-friendly readers looking for a substantial and possibly even thrillingly difficult intellectual experience should pick up a copy (carefully--it's over a thousand pages long and weighs nearly 4 pounds) and start at the beginning, where Penrose sets out his purpose: to describe "the search for the underlying principles that govern the behavior of our universe." Beginning with the deceptively simple geometry of Pythagoras and the Greeks, Penrose guides readers through the fundamentals--the incontrovertible bricks that hold up the fanciful mathematical structures of later chapters. From such theoretical delights as complex-number calculus, Riemann surfaces, and Clifford bundles, the tour takes us quickly on to the nature of spacetime. The bulk of the book is then devoted to quantum physics, cosmological theories (including Penrose's favored ideas about string theory and universal inflation), and what we know about how the universe is held together. For physicists, mathematicians, and advanced students, The Road to Reality is an essential field guide to the universe. For enthusiastic amateurs, the book is a project to tackle a bit at a time, one with unimaginable intellectual rewards. --Therese Littleton
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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
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.