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Books
Mathematical Physics
An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics)
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Author: Gareth James
Brand: Brand: Springer

An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, treebased methods, support vector machines, clustering, and more. Color graphics and realworld examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical software platform. Two of the authors cowrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and nonstatisticians alike who wish to use cuttingedge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.
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Love and Math: The Heart of Hidden Reality
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Author: Edward Frenkel

A New York Times Science Bestseller
What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren’t even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry.
In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.
Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twentyfirst century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.
At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.
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The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory
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Author: Brian Greene

The international bestseller that inspired a major Nova special and sparked a new understanding of the universe, now with a new preface and epilogue. Brian Greene, one of the world's leading string theorists, peels away layers of mystery to reveal a universe that consists of eleven dimensions, where the fabric of space tears and repairs itself, and all matter—from the smallest quarks to the most gargantuan supernovas—is generated by the vibrations of microscopically tiny loops of energy. The Elegant Universe makes some of the most sophisticated concepts ever contemplated accessible and thoroughly entertaining, bringing us closer than ever to understanding how the universe works.
There is an illconcealed skeleton in the closet of physics: "As they are currently formulated, general relativity and quantum mechanics cannot both be right." Each is exceedingly accurate in its field: general relativity explains the behavior of the universe at large scales, while quantum mechanics describes the behavior of subatomic particles. Yet the theories collide horribly under extreme conditions such as black holes or times close to the big bang. Brian Greene, a specialist in quantum field theory, believes that the two pillars of physics can be reconciled in superstring theory, a theory of everything. Superstring theory has been called "a part of 21stcentury physics that fell by chance into the 20th century." In other words, it isn't all worked out yet. Despite the uncertainties"string theorists work to find approximate solutions to approximate equations"Greene gives a tour of string theory solid enough to satisfy the scientifically literate. Though Ed Witten of the Institute for Advanced Study is in many ways the human hero of The Elegant Universe, it is not a humansideofphysics story. Greene's focus throughout is the science, and he gives the nonspecialist at least an illusion of understandingor the sense of knowing what it is that you don't know. And that is traditionally the first step on the road to knowledge. Mary Ellen Curtin
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Mathematical Methods in the Physical Sciences
Lowest new price: $85.45
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Author: Mary L. Boas

Now in its third edition, Mathematical Concepts in the Physical Sciences provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.
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 ISBN13: 9780471198260
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Quantum Field Theory and the Standard Model
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Author: Matthew D. Schwartz

Providing a comprehensive introduction to quantum field theory, this textbook covers the development of particle physics from its foundations to the discovery of the Higgs boson. Its combination of clear physical explanations, with direct connections to experimental data, and mathematical rigor make the subject accessible to students with a wide variety of backgrounds and interests. Assuming only an undergraduatelevel understanding of quantum mechanics, the book steadily develops the Standard Model and stateofthe art calculation techniques. It includes multiple derivations of many important results, with modern methods such as effective field theory and the renormalization group playing a prominent role. Numerous worked examples and endofchapter problems enable students to reproduce classic results and to master quantum field theory as it is used today. Based on a course taught by the author over many years, this book is ideal for an introductory to advanced quantum field theory sequence or for independent study.
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Fourier Series (Dover Books on Mathematics)
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Author: Georgi P. Tolstov

Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is wellknown 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 Englishlanguage literature on Fourier series. This edition is organized into nine welldefined 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 FourierBessel 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 Englishlanguage 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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The Drunkard's Walk: How Randomness Rules Our Lives
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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 notsodumbeddown 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 Maxwell's Equations
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Author: Daniel Fleisch

Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the AmpereMaxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plainlanguage explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.
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Mathematical Methods for Physics and Engineering: A Comprehensive Guide
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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 standalone 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 passwordprotected web site, www.cambridge.org/9780521679718.
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The Road to Reality: A Complete Guide to the Laws of the Universe
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Author: Roger Penrose
Brand: Brand: Vintage

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, mathfriendly readers looking for a substantial and possibly even thrillingly difficult intellectual experience should pick up a copy (carefullyit'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 fundamentalsthe incontrovertible bricks that hold up the fanciful mathematical structures of later chapters. From such theoretical delights as complexnumber 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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