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Author: Edward Frenkel
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 twenty-first 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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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, tree-based methods, support vector machines, clustering, and more. Color graphics and real-world 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 co-wrote 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 non-statisticians alike who wish to use cutting-edge 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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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 ill-concealed 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 21st-century 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 human-side-of-physics story. Greene's focus throughout is the science, and he gives the nonspecialist at least an illusion of understanding--or 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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Author: Daniel Fleisch
Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere-Maxwell 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, plain-language 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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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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Author: Kevin Cahill
Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.
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Author: Leonard Mlodinow
In this irreverent and illuminating book, acclaimed writer and scientist Leonard Mlodinow shows us how randomness, change, and probability reveal a tremendous amount about our daily lives, and how we misunderstand the significance of everything from a casual conversation to a major financial setback. As a result, successes and failures in life are often attributed to clear and obvious cases, when in actuality they are more profoundly influenced by chance.
The rise and fall of your favorite movie star of the most reviled CEO--in fact, of all our destinies--reflects as much as planning and innate abilities. Even the legendary Roger Maris, who beat Babe Ruth's single-season home run record, was in all likelihood not great but just lucky. And it might be shocking to realize that you are twice as likely to be killed in a car accident on your way to buying a lottery ticket than you are to win the lottery.
How could it have happened that a wine was given five out of five stars, the highest rating, in one journal and in another it was called the worst wine of the decade? Mlodinow vividly demonstrates how wine ratings, school grades, political polls, and many other things in daily life are less reliable than we believe. By showing us the true nature of change and revealing the psychological illusions that cause us to misjudge the world around us, Mlodinow gives fresh insight into what is really meaningful and how we can make decisions based on a deeper truth. From the classroom to the courtroom, from financial markets to supermarkets, from the doctor's office to the Oval Office, Mlodinow's insights will intrigue, awe, and inspire.
Offering readers not only a tour of randomness, chance, and probability but also a new way of looking at the world, this original, unexpected journey reminds us that much in our lives is about as predictable as the steps of a stumbling man fresh from a night at the bar.
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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Author: Georgi P. Tolstov
This reputable translation covers trigonometric Fourier series, orthogonal systems, double Fourier series, Bessel functions, the Eigenfunction method and its applications to mathematical physics, operations on Fourier series, and much more. Over 100 problems at ends of chapters. Answers in back of book. 1962 edition.
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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: 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.