A Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe.Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems.With complicated ideas explained for a broad audience, this book offers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.“The remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe“An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe“Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist Read more

Quanta and Fields, the second book of Sean Carroll’s already internationally acclaimed series The Biggest Ideas in the Universe, is an adventure into the bare stuff of reality.   Sean Carroll is creating a profoundly new approach to sharing physics with a broad audience, one that goes beyond analogies to show how physicists really think. He cuts to the bare mathematical essence of our most profound theories, explaining every step in a uniquely accessible way.   Quantum field theory is how modern physics describes nature at its most profound level. Starting with the basics of quantum mechanics itself, Sean Carroll explains measurement and entanglement before explaining how the world is really made of fields. You will finally understand why matter is solid, why there is antimatter, where the sizes of atoms come from, and why the predictions of quantum field theory are so spectacularly successful. Fundamental ideas like spin, symmetry, Feynman diagrams, and the Higgs mechanism are explained for real, not just through amusing stories. Beyond Newton, beyond Einstein, and all the intuitive notions that have guided homo sapiens for millennia, this book is a journey to a once unimaginable truth about what our universe is. Read more

**WINNER OF THE 2020 NOBEL PRIZE IN PHYSICS**The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader, so that, for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book.Roger Penrose's purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections.The Road to Reality is rarely less than challenging, but the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams. In a single work of colossal scope one of the world's greatest scientists has given us a complete and unrivalled guide to the glories of the universe that we all inhabit.'Roger Penrose is the most important physicist to work in relativity theory except for Einstein. He is one of the very few people I've met in my life who, without reservation, I call a genius' Lee Smolin Read more

First he taught you classical mechanics. Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics. In this follow-up to the New York Times best-selling The Theoretical Minimum, Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic objects through mathematical abstractions. Unlike other popularizations that shy away from quantum mechanics' weirdness, Quantum Mechanics embraces the utter strangeness of quantum logic. The authors offer crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics, and each chapter includes exercises to ensure mastery of each area. Like The Theoretical Minimum, this volume runs parallel to Susskind's eponymous Stanford University-hosted continuing education course. An approachable yet rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace. Read more

An awesome, globe-spanning, and New York Times bestselling journey through the beauty and power of mathematics 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. Read more

A look inside the world of “quants” and how science can (and can’t) predict financial markets: “Entertaining and enlightening” (The New York Times).   After the economic meltdown of 2008, Warren Buffett famously warned, “beware of geeks bearing formulas.” But while many of the mathematicians and software engineers on Wall Street failed when their abstractions turned ugly in practice, a special breed of physicists has a much deeper history of revolutionizing finance. Taking us from fin-de-siècle Paris to Rat Pack–era Las Vegas, from wartime government labs to Yippie communes on the Pacific coast, James Owen Weatherall shows how physicists successfully brought their science to bear on some of the thorniest problems in economics, from options pricing to bubbles.   The crisis was partly a failure of mathematical modeling. But even more, it was a failure of some very sophisticated financial institutions to think like physicists. Models—whether in science or finance—have limitations; they break down under certain conditions. And in 2008, sophisticated models fell into the hands of people who didn’t understand their purpose, and didn’t care. It was a catastrophic misuse of science. The solution, however, is not to give up on models; it’s to make them better.   This book reveals the people and ideas on the cusp of a new era in finance, from a geophysicist using a model designed for earthquakes to predict a massive stock market crash to a physicist-run hedge fund earning 2,478.6% over the course of the 1990s. Weatherall shows how an obscure idea from quantum theory might soon be used to create a far more accurate Consumer Price Index. The Physics of Wall Street will change how we think about our economic future.   “Fascinating history . . . Happily, the author has a gift for making complex concepts clear to lay readers.” —Booklist Read more

In his monumental 1687 work, Philosophiae Naturalis Principia Mathematica, known familiarly as the Principia, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles. This authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the Principia also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system. The illuminating Guide to Newton's Principia by I. Bernard Cohen makes this preeminent work truly accessible for today's scientists, scholars, and students. Read more

In a highly accessible style, this book presents a narrative history of the quantum theory with the new developments that intrigue all inquisitive minds. Quantum theory is counter-intuitive and sometimes downright weird. Even Nobel Laureate physicists like Richard Feynman admit that they do not understand it. Yet, so far, there is not a shred of experimental data that conflicts with its predictions. Its effect on our lives is bound to increase with the quantum information era ushered in by the great Bohr–Einstein debate. Tantalizing applications of quantum information like teleportation, spy-proof communication, super-fast quantum computers, and more are going to influence our lives and change our beliefs about the nature of physical reality. This book takes the reader on an exhilarating journey through the intellectual history of quantum that is turning out to be more surprising every day. Read more

CONTENTS: This textbook covers the mechanics portion of first-year calculus-based physics, including the following topics:Uniform and non-uniform accelerationVector addition and coordinate systemsApplying Newton's laws of motionUniform circular motion (including satellites)Work, power, and conservation of energyCenter of mass, collisions, and rocketsThorough coverage of rotation AUDIENCE: This calculus-based physics textbook is geared toward independent learners who can handle the rigors of calculus and who seek to develop a strong introduction to the fundamentals of physics, both mathematically and conceptually. It could also serve as a useful reference for physics and engineering students who have gone beyond the first year of physics, but who would like to review the fundamentals as they explore more advanced fields of physics. PREREQUISITES: No previous exposure to physics is assumed. The student should be familiar with the basic techniques of differentiation and integration, including polynomials and trig functions, and should be fluent in algebra and familiar with the basic trig functions. COREQUISITES: The textbook teaches Calculus II skills as needed, such as the technique of integrating via trigonometric substitution. The textbook also reviews some Calculus I skills which students often forget, such as the mean-value theorem, l'Hopital's rule, and the chain rule. This is not done in an introductory chapter or an appendix, but in the main text as these ideas first become useful. IMPORTANT DISTINCTIONS: Boxes of important distinctions are included in order to help students distinguish between similar concepts--like average speed and average velocity, between velocity and acceleration, or between mass and weight. TABLE OF EQUATIONS: There is a handy table of equations organized by topic on the back cover of the textbook. The equations in the text (but not on the cover) also include notes to help students understand any limitations that the equations may have (e.g. some equations only apply if acceleration is uniform or if mass is constant). MATHEMATICAL & CONCEPTUAL EMPHASIS: There is much emphasis both on learning the mathematics precisely and understanding the concepts at a deep, precise level. An underlying idea is that students should not guess at concepts, but that concepts are mathematically motivated: Let the equations be your guide. PROBLEM-SOLVING STRATEGIES: All of the main problem-solving strategies--like projectile motion, applying Newton's second law, or conserving energy--are highlighted and described step-by-step and in detail. Examples illustrate how to carry out all of the problem-solving strategies. NOTES: Several notes are boxed to describe important points, common mistakes, and exceptions. Hundreds of footnotes are included to discuss subtleties without interrupting the flow of the text. EXAMPLES: Conceptual and problem-solving examples were selected based on their instructiveness in elucidating important concepts or illustrating how to carry out important problem-solving strategies; quality was favored over quantity. Simple plug-and-chug examples and problems are scarce, since the audience for this book is independent students. HINTS & ANSWERS: 100% of the conceptual questions have both hints and answers, since it's crucial to develop a solid understanding of the concepts in order to succeed in physics. Some of the practice problems have answers to help independent students gain confidence by reproducing the same answers, while 100% of the practice problems have hints so that students can see if they are solving the problems correctly (even if the problem doesn't have the answer in the back). Read more

For students who are already fluent with single-variable derivatives and integrals, this workbook offers practice with essential skills from multivariable calculus (including vector calculus). Each chapter begins with a review of the essential ideas and includes fully solved examples to help serve as a guide. The full solution to every exercise can be found at the back of the book. Authored by experienced teacher, Chris McMullen, Ph.D., this self-study math workbook covers:partial derivativesextreme values with multiple variables (including saddle points)vectors, vector analysis (such as the dot and cross products), and vector calculusthe gradient, divergence, and curlthe main coordinate systems: Cartesian, 2D polar, spherical, and cylindricalpath integrals, surface integrals, and volume integralsflux integrals, center of mass, and moment of inertiatangent and normal vectorsand moreThe author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his strategies for solving calculus problems with multiple variables or vectors. Read more

Unlock the intricacies of classical mechanics with a comprehensive guide that bridges theory and practical application. Dive into the depths of Lagrangian and Hamiltonian dynamics, where each chapter is enhanced with Python code to provide hands-on experience and deepen your understanding.Key Features:Comprehensive coverage of foundational principles and advanced topics in classical mechanics.Integration of Python code to illustrate concepts and offer practical exercises.Detailed explorations of both Lagrangian and Hamiltonian formulations, bridging classical mechanics to modern physics.Suitable for students, researchers, and professionals seeking to enhance their understanding of dynamical systems.Book Description:Embark on a transformative journey through classical mechanics with this extensive guide to Lagrangian and Hamiltonian dynamics. Perfect for both beginners and seasoned physicists, this book delves deeply into the principles governing dynamical systems and illuminates each concept with accompanying Python scripts. From the essence of Newton's laws to the complexity of symplectic geometry and Hamiltonian chaos, you'll discover a rich tapestry of knowledge woven through clear explanations and practical coding exercises. Whether you're studying simple oscillatory motion or the subtleties of non-Euclidean frames, this guide will equip you with the insights and tools necessary to master the landscape of classical mechanics.What You Will Learn:Understand Newton's Second Law of Motion and its foundational role in classical mechanics.Explore D'Alembert's Principle as a method to reformulate Newtonian mechanics.Apply the Principle of Virtual Work in analyzing mechanical systems.Discover the Lagrangian Function and its critical role in mechanics.Derive and implement the Euler-Lagrange Equation in practical problems.Grasp Hamilton's Principle and its connection with the action integral.Learn how symmetrical properties give rise to Conservation Laws.Delve into Noether's Theorem and its far-reaching applications.Utilize the Legendre Transformation in transitioning to Hamiltonian Mechanics.Define the Hamiltonian Function and explore its uses.Derive Hamilton's Equations of Motion and apply them in various contexts.Uncover the benefits of Canonical Transformations in simplifying systems.Utilize Poisson Brackets in analyzing properties of Hamiltonian systems.Understand Liouville's Theorem and the conservation of phase space volume.Solve mechanical problems using the Hamilton-Jacobi Equation.Incorporate Action-Angle Variables in analyzing integrable systems.Evaluate small oscillations and identify Normal Modes within systems.Apply Routhian Reduction in systems with cyclic coordinates for simplification.Use Lagrange Multipliers to manage constraints in mechanical systems.Address Non-Holonomic Constraints in dynamic systems.Analyze the behavior of Damped Harmonic Oscillators using advanced methods.Investigate Driven Harmonic Oscillators within the Lagrangian framework.Master the Calculus of Variations and its applications in mechanics.Rediscover historical insights with Maupertuis' Principle of Least Action.Tackle Central Force Problems using advanced dynamic techniques.Solve the Kepler Problem by applying modern dynamical methods.Conduct Scattering Analysis under Central Potentials with precision.Analyze Rigid Body Dynamics through the Euler-Lagrange and Hamiltonian systems.Derive and apply Euler's Equations for complex rigid body rotations. Read more

Have you ever wondered how the universe works at its most fundamental level? How space and time intertwine, why black holes exist, or what quantum mechanics reveals about reality? This book offers a clear, step-by-step guide to modern theoretical physics, presenting its most groundbreaking ideas in a way that is engaging, accessible, and free of complex equations.Written for curious minds, students, and science enthusiasts alike, this non-technical yet comprehensive introduction breaks down the deep mysteries of physics in a structured, easy-to-follow format. Whether you want to understand the laws governing motion, explore the strange world of quantum mechanics, or dive into the cosmic vastness of general relativity, this book will take you on an eye-opening journey through the pillars of modern physics.____What You’ll Discover Inside:✅ Classical Mechanics – Explore Newton’s laws, energy conservation, and the deep principles that describe motion and forces.✅ Relativity & The Nature of Space and Time – Grasp Einstein’s revolutionary ideas, from time dilation and spacetime curvature to the mind-bending implications of black holes.✅ Quantum Mechanics – Unravel the bizarre world of wave-particle duality, superposition, uncertainty, and entanglement—ideas that challenge our very understanding of reality.✅ Quantum Field Theory & The Standard Model – Discover how fundamental forces and particles interact, from quarks and leptons to the Higgs boson.✅ Cosmology & The Fate of the Universe – Understand the Big Bang, dark matter, dark energy, and the expanding cosmos.✅ The Quest for a Unified Theory – Explore groundbreaking ideas like string theory, loop quantum gravity, and the search for a "Theory of Everything."✅ The Philosophy of Physics – Reflect on the nature of reality, free will vs. determinism, and how mathematical beauty shapes scientific theories.✅ The Historical Timeline of Theoretical Physics – Follow the key discoveries that revolutionized our understanding of the universe.____Who Is This Book For?🔹 Curious Learners & Science Enthusiasts – No physics background? No problem! This book is designed to explain complex ideas in simple terms without requiring advanced mathematics.🔹 Students & Aspiring Physicists – Whether you’re a high school or college student, this book will strengthen your understanding of physics fundamentals before diving into more advanced studies.🔹 Lifelong Learners & Thinkers – If you love big ideas, deep questions, and expanding your understanding of reality, this book is a must-read.____Why This Book?✔️ Step-by-Step Approach – Each chapter builds on the last, guiding you through theoretical physics without overwhelming complexity.✔️ No Advanced Math Required – While physics is mathematical at its core, this book explains concepts intuitively, making it accessible to all readers.✔️ Comprehensive Yet Easy to Follow – Covers all the major topics in modern theoretical physics without unnecessary jargon.✔️ Engaging and Thought-Provoking – Discover the mysteries of the universe in a way that sparks curiosity and deep thinking.____Are You Ready to Explore the Universe?This book is your gateway to understanding the deepest laws of nature—from the forces that govern motion to the fundamental structure of reality itself. Whether you’re looking to build a strong foundation in physics or simply want to explore the biggest questions in science, this book will take you on an inspiring intellectual adventure. Read more

This introduction to complex numbers by experienced teacher and author, Chris McMullen, Ph.D., begins with the arithmetic of complex numbers and works its way up to roots of complex numbers and polynomials, and includes a variety of fascinating problems such as, "What is the square root of the imaginary number i?" Prerequisite: basic trigonometry. (No calculus is needed to use this workbook.) Read more

A rising star in theoretical physics offers his awesome vision of our universe and beyond, all beginning with a simple question: Why does time move forward?Time moves forward, not backward—everyone knows you can’t unscramble an egg. In the hands of one of today’s hottest young physicists, that simple fact of breakfast becomes a doorway to understanding the Big Bang, the universe, and other universes, too. In From Eternity to Here, Sean Carroll argues that the arrow of time, pointing resolutely from the past to the future, owes its existence to conditions before the Big Bang itself—a period modern cosmology of which Einstein never dreamed. Increasingly, though, physicists are going out into realms that make the theory of relativity seem like child’s play. Carroll’s scenario is not only elegant, it’s laid out in the same easy-to- understand language that has made his group blog, Cosmic Variance, the most popular physics blog on the Net. From Eternity to Here uses ideas at the cutting edge of theoretical physics to explore how properties of spacetime before the Big Bang can explain the flow of time we experience in our everyday lives. Carroll suggests that we live in a baby universe, part of a large family of universes in which many of our siblings experience an arrow of time running in the opposite direction. It’s an ambitious, fascinating picture of the universe on an ultra-large scale, one that will captivate fans of popular physics blockbusters like Elegant Universe and A Brief History of Time.Watch a Video Read more

Discover the fascinating world of Elliptic Partial Differential Equations with this comprehensive guide, packed with theory and practical applications. This book, equipped with Python code and multiple-choice review questions for each chapter, is perfect for both beginners and experienced mathematicians looking to delve deeper into this intriguing field.Key Features:- A comprehensive exploration of various types of elliptic partial differential equations, from Laplace's equation to the De Giorgi-Nash-Moser theorem.- Practical applications in diverse fields such as electrostatics, heat transfer, acoustics, and more, providing real-world relevance to the concepts discussed.- Each chapter includes Python code examples, allowing readers to understand and implement the theories in a practical way.- Multiple-choice review questions at the end of each chapter help reinforce key concepts and test your understanding.Book Description:Elliptic Partial Differential Equations: Theory and Practical Applications is an in-depth guide that takes you on a journey through the theoretical foundations and practical implications of elliptic partial differential equations. Each chapter provides a thorough exploration of a specific equation, starting with its historical background and mathematical formulation. From there, you'll dive into fundamental solutions, boundary value problems, and their applications in various fields, including electrostatics, heat transfer, acoustics, and more.Throughout the book, Python code examples are provided to help you grasp the concepts discussed and implement them in your own projects. Whether you're a beginner looking to understand the fundamentals of elliptic partial differential equations or an experienced mathematician seeking to expand your knowledge, this book offers a comprehensive and practical approach to the subject.What You Will Learn:- The history, mathematical formulation, and fundamental solutions of various types of elliptic partial differential equations.- Practical applications of these equations in fields such as electrostatics, heat transfer, acoustics, fluid dynamics, and more.- Implementation of elliptic partial differential equations using Python code examples.- Theoretical insights into the regularity of solutions and maximum principles for these equations.- Analytical and numerical techniques to solve elliptic partial differential equations.- Understanding of complex analysis, quantum mechanics, and their applications in Schrödinger equations.Who This Book Is For:This book is perfect for mathematics students, researchers, and professionals interested in exploring the theory and practical applications of elliptic partial differential equations. It is also suitable for those with a background in Python programming who want to deepen their understanding of this intriguing field. The multiple-choice review questions at the end of each chapter make it an excellent resource for self-study and exam preparation. Read more

An easy-to-follow guide to introductory physics, from the Big Bang to relativityAll science, technology, engineering, and math majors in college and university require some familiarity with physics. Other career paths, like medicine, are also only open to students who understand this fundamental science. But don’t worry if you find physics to be intimidating or confusing. You just need the right guide! In Physics I For Dummies, you’ll find a roadmap to physics success that walks you through every major topic in introductory physics, including motion, energy, waves, thermodynamics, electromagnetism, relativity, and more. You’ll learn the basic principles and math formulas of physics through clear and straightforward examples and instruction, and without unnecessary jargon or complicated theory. In this book, you’ll also find: Up-to-date examples and explanations appearing alongside the latest discoveries and research in physics, discussed at a level appropriate for beginning studentsAll the info found in an intro physics course, arranged in an intuitive sequence that will give first-year students a head start in their high school or college physics classThe latest teaching techniques to ensure that you remember and retain what you read and practice in the bookPhysics I For Dummies is proof that physics can fun, accessible, challenging, and rewarding, all at the same time! Whether you’re a high school or undergraduate student looking for a leg-up on basic physics concepts or you’re just interested in how our universe works, this book will help you understand the thermodynamic, electromagnetic, relativistic, and everything in between. Read more

The Principia is "justly regarded as one of the most important works in the history of science". The Mathematical Principles of Natural Philosophy, often referred to as simply the Principia, is a work in three books by Sir Isaac Newton, in Latin, first published 5 July 1687. After annotating and correcting his personal copy of the first edition, Newton also published two further editions, in 1713 and 1726. The Principia states Newton's laws of motion, forming the foundation of classical mechanics, also Newton's law of universal gravitation, and a derivation of Kepler's laws of planetary motion (which Kepler first obtained empirically). The French mathematical physicist Alexis Clairaut assessed it in 1747: "The famous book of mathematical Principles of natural Philosophy marked the epoch of a great revolution in physics. The method followed by its illustrious author Sir Newton ... spread the light of mathematics on a science which up to then had remained in the darkness of conjectures and hypotheses." A more recent assessment has been that while acceptance of Newton's theories was not immediate, by the end of a century after publication in 1687, "no one could deny that" (out of the Principia) "a science had emerged that, at least in certain respects, so far exceeded anything that had ever gone before that it stood alone as the ultimate exemplar of science generally." In formulating his physical theories, Newton developed and used mathematical methods now included in the field of calculus. But the language of calculus as we know it was largely absent from the Principia; Newton gave many of his proofs in a geometric form of infinitesimal calculus, based on limits of ratios of vanishing small geometric quantities. In a revised conclusion to the Principia (see General Scholium), Newton used his expression that became famous, Hypotheses non fingo ("I contrive no hypotheses"). Read more

Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also understand the implications of quantum physics and symmetry considerations: Poincare invariance dictates both the characteristic properties of particles (mass, spin, ...) and the wave equations of spin 0, 1/2, 1, ... objects. Further, the work of C.N. Yang and R. Mills reveals the consequences of internal symmetries as exemplified in the symmetry group of elementary particle physics. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree motivated and inspired by considerations of symmetry. The treatment of symmetries in this monograph ranges from classical physics to now well-established theories of fundamental interactions, to the latest research on unified theories and quantum gravity. Read more

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. Read more