Linear Equations; Vector Spaces; Linear Transformations; Polynomials; Determinants; Elementary canonical Forms; Rational and Jordan Forms; Inner Product Spaces; Operators on Inner Product Spaces; Bilinear Forms For all readers interested in linear algebra.

    This user-friendly self-study guide is aimed at the general reader who is motivated to tackle that not insignificant challenge. The book is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution (which gives a good approximation of the spacetime of our Solar System); simple black holes and relativistic cosmology. Following the historic 2015 LIGO (Laser Interferometer Gravitational-Wave Observatory) detection, there is now an additional chapter on gravitational waves, ripples in the fabric of spacetime that potentially provide a revolutionary new way to study the universe. Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes.Understand even the basics of Einstein's amazing theory and the world will never seem the same again. ContentsPrefaceIntroduction1 Foundation mathematics2 Newtonian mechanics3 Special relativity4 Introducing the manifold5 Scalars, vectors, one-forms and tensors6 More on curvature7 General relativity8 The Newtonian limit9 The Schwarzschild metric10 Schwarzschild black holes11 Cosmology12 Gravitational wavesAppendix: The Riemann curvature tensorBibliographyAcknowledgementsJanuary 2019. This third edition has been revised to make the material even more accessible to the enthusiastic general reader who seeks to understand the mathematics of relativity.

    In this experiment, a particle going through one of a pair of holes seems to be aware of what is going on at the other hole, and changes its behaviour according to whether that hole is open or closed. This is closely linked to the puzzle of entanglement, where one particle instantly reacts to what is happening to another particle, even when they are widely separated. And in a final example of the mind-boggling nature of the quantum world, these effects seem to operate across time as well as space: What is going to happen in the future affects the behaviour of a particle now. In The Quantum Mystery, John Gribbin, the best-selling author of In Search of Schrödinger’s Cat, describes the history of the double-slit experiment, the wave-particle duality of the quantum world, and the latest experiments which show these bizarre effects at work before our very eyes.

    Einstein's Heroes takes you on a journey of discovery about just such a miraculous language--the language of mathematics--one of humanity's mostamazing accomplishments. Blending science, history, and biography, this remarkable book reveals the mysteries of mathematics, focusing on the life and work of three of Albert Einstein's heroes: Isaac Newton, Michael Faraday, and especially James Clerk Maxwell, whose work directly inspired the theory of relativity. RobynArianrhod bridges the gap between science and literature, portraying mathematics as a language and arguing that a physical theory is a work of imagination involving the elegant and clever use of this language. The heart of the book illuminates how Maxwell, using the language of mathematics in a newand radical way, resolved the seemingly insoluble controversy between Faraday's idea of lines of force and Newton's theory of action-at-a-distance. In so doing, Maxwell not only produced the first complete mathematical description of electromagnetism, but actually predicted the existence of theradio wave, teasing it out of the mathematical language itself. Here then is a fascinating look at mathematics: its colorful characters, its historical intrigues, and above all its role as the uncannily accurate language of nature.

    Ten dimensions? Most of us have barely gotten used to the idea that there are four.Using simple geometry and an easygoing writing style, author Rob Bryanton starts with the lower dimensions that we are all familiar with, then uses those concepts to build one layer upon another, ultimately arriving at a way of imagining the tenth dimension.Part scientific exploration, part philosophy, this unique book touches upon such diverse topics as dark matter, Feynman's "sum over paths", the quantum observer, and the soul. It is aimed at anyone interested in leading-edge theories about cosmology and the nature of reality, but it is not about mainstream physics. Rather, Imagining the Tenth Dimension is a mind-expanding exercise that could change the way you view this incredible universe in which we live.

    Its organization and thoroughness are unsurpassed, putting it above similar review books. Students who thoroughly read this book should have no trouble successfully completing their psychiatry clerkship and passing the shelf exam. As course director for the core psychiatry clerkship at my institution, I will recommend this book to students."--Doody's Review Service"First Aid for the Psychiatry Clerkship" gives you the core information needed to impress on the wards and pass the psychiatry clerkship exam. Written by students who know what it takes to succeed, and based on the national guidelines for the psychiatry clerkship, the book is filled with mnemonics, ward and exam tips, tables, clinical images, algorithms, and newly added mini-cases.Features Completely revised based on the psychiatry clerkship's core competencies Written by medical students who passed and reviewed by faculty for accuracy NEW integrated mini-cases illustrate classic patient presentations and/or commonly tested scenarios NEW illustrations and management algorithms Updated throughout with enhanced sections on medications, depression/anxiety, and child psychiatry Helps students hone in on the most important concepts for the clerkship and the examThe content you need to ace the clerkship: Section I: How to Succeed in the Psychiatry Clerkship Section II: High-Yield Facts; Examination and Diagnosis; Psychotic Disorders; Mood Disorders; Anxiety and Adjustment Disorders; Personality Disorders; Substance-Related Disorders; Cognitive Disorders; Geriatric Disorders; Psychiatric Disorders in Children; Dissociative Disorders; Somataform and Factitious Disorders; Impulse Control Disorders; Eating Disordes; Disorders; Sleep Disorders; Sexual Disorders; Psychtherapies; Psychopharmacology; Legal Issues; Section III: Awards and Opportunities.

     This top-selling, theorem-proof text presents a careful treatment of the principal topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate.

    He's certainly been thinking about it lately. May, a freshly minted astrophysics Ph.D., joins forces with legendary astronomer Patrick Moore and astrophysicist Chris Lintott in Bang! to consider the history of the universe from the Big Bang to Heat Death.Space, time, and matter were birthed 13.7 billion years ago and will continue on longer than we are able to comprehend. Infinitesimally small at first, the Universe is immense and ever expanding. Bang! explains how it all started, takes you on a tour of what is known about the evolution of the Universe, and posits how the end of time will come about.This fascinating book includes photographs, short biographies of key figures, an at-a-glance timeline, a glossary of terms, and suggested resources for further exploration.Based on the work of history’s most brilliant scientific minds, this amazing story features clear, straightforward discussions of the most perplexing and compelling aspects of existence—from the formation of stars, planets, and other galactic bodies to black holes, quasars, anti-matter, and dark matter to the emergence of life and the possibility that it could exist elsewhere.Pick up a copy of Bang! It will, it will rock you.

    In What If the Earth Had Two Moons, Neil Comins leads us on a fascinating ten-world journey as we explore what our planet would be like under alternative astronomical conditions. In each case, the Earth would be different, often in surprising ways. The title chapter, for example, gives us a second moon orbiting closer to Earth than the one we have now. The night sky is a lot brighter, but that won't last forever. Eventually the moons collide, with one extra-massive moon emerging after a period during which Earth sports a Saturn-like ring. This and nine and other speculative essays provide us with insights into the Earth as it exists today, while shedding new light on the burgeoning search for life on planets orbiting other stars. Appealing to adult and young adult readers alike, this book follows on the author's previous bestseller, What If the Moon Didn't Exist?, with completely new scenarios backed by the latest astronomical research.

    Stimulating, illuminating, and always surprising, The Big Questions challenges readers to re-evaluate their most fundamental beliefs and reveals the relationship between the loftiest philosophical quests and our everyday lives.

    KEY TOPICS: This classic book enables readers to make connections between classical and modern physics - an indispensable part of a physicist's education. In this new edition, Beams Medal winner Charles Poole and John Safko have updated the book to include the latest topics, applications, and notation, to reflect today's physics curriculum. They introduce readers to the increasingly important role that nonlinearities play in contemporary applications of classical mechanics. New numerical exercises help readers to develop skills in how to use computer techniques to solve problems in physics. Mathematical techniques are presented in detail so that the book remains fully accessible to readers who have not had an intermediate course in classical mechanics. MARKET: For college instructors and students.

    New topics include managing and maintaining cellular devices, including tablets; configuring operating systems, including Windows 8, Android, and iOS; and enhanced, mobile-centered security and troubleshooting procedures. The All-in-One Exam Guide enables you to take the test with complete confidence. It also serves as a practical reference for IT support and technical personnel. Bonus electronic content includes: Practice exams with hundreds of accurate questions More than an hour of video training featuring Mike Meyers Performance-based simulations that prepare you for the performance-based questions on the exam A collection of Mike's favorite free PC tools Key Features include: Written with the “in the trenches” voice and clarity Mike Meyers is known for Features pre-assessment tests, exam tips, and “Try This!” sections to reinforce difficult topics Includes a coupon for 10% off of the exam fee, a $37 value

    But it's coming, and when it does, it will change our lives as much as any invention ever has. Imagine being able to program matter itself-to change it, with the click of a cursor, from hard to soft, from paper to stone, from fluorescent to super-reflective to invisible. Supported by organizations ranging from Levi Strauss and IBM to the Defense Department, solid-state physicists in renowned laboratories are working to make it a reality. In this dazzling investigation, Wil McCarthy visits the laboratories and talks with the researchers who are developing this extraordinary technology, describes how they are learning to control it, and tells us where all this will lead. The possibilities are truly astonishing.

    In the four main sections of the book, Stein tells the stories of the mathematical thinkers who discerned some of the most fundamental aspects of our universe. From their successes and failures, delusions, and even duels, the trajectories of their innovations—and their impact on society—are traced in this fascinating narrative. Quantum mechanics, space-time, chaos theory and the workings of complex systems, and the impossibility of a "perfect" democracy are all here. Stein's book is both mind-bending and practical, as he explains the best way for a salesman to plan a trip, examines why any thought you could have is imbedded in the number π , and—perhaps most importantly—answers one of the modern world's toughest questions: why the garage can never get your car repaired on time.Friendly, entertaining, and fun, How Math Explains the World is the first book by one of California's most popular math teachers, a veteran of both "math for poets" and Princeton's Institute for Advanced Studies. And it's perfect for any reader wanting to know how math makes both science and the world tick.