Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program"

    Unique in basing relativity on the Principle of Equivalence of Gravitation and Inertia over Riemannian geometry, this book explores relativity experiments and observational cosmology to provide a sound foundation upon which analyses can be made. Covering special and general relativity, tensor analysis, gravitation, curvature, and more, this book provides an engaging, insightful introduction to the forces that shape the universe.

    His work won him the Nobel Prize in 1922 and his ideas continue to propel physics towards new discoveries. But what is quantum theory? Most of us do not understand even the basics of one of the most significant scientific advances ever made, opening up a whole new field in science, whose ambiguities still challenge scientists around the world.Bohr and Quantum Theory offers an accessible and absorbing account of the man who was both a part of The Manhattan Project but also an advocate of peace.He held the key to understanding such intricate realities as black holes and nuclear energy. Bohr's Big Idea explains complex and crucial ideas in a clear and engaging way, placing quantum theory in the context of a man's life, work and time and examining its important implications for our future.The Big Idea series is a fascinating look at the greatest advances in our scientific history, and at the men and women who made these fundamental breakthroughs.

    Shankar, a well-known physicist and contagiously enthusiastic educator, was among the first to offer a course through the innovative Open Yale Course program. His popular online video lectures on introductory physics have been viewed over a million times. In this concise and self-contained book based on his online Yale course, Shankar explains the fundamental concepts of physics from Galileo’s and Newton’s discoveries to the twentieth-century’s revolutionary ideas on relativity and quantum mechanics.   The book begins at the simplest level, develops the basics, and reinforces fundamentals, ensuring a solid foundation in the principles and methods of physics. It provides an ideal introduction for college-level students of physics, chemistry, and engineering, for motivated AP Physics students, and for general readers interested in advances in the sciences. Instructor resources--including problem sets and sample examinations--and more information about Professor Shankar's course are available at http://oyc.yale.edu/physics/phys-200.

    In Burn Math Class, Jason Wilkes takes the traditional approach to how we learn math -- with its unwelcoming textbooks, unexplained rules, and authoritarian assertions-and sets it on fire. Focusing on how mathematics is created rather than on mathematical facts, Wilkes teaches the subject in a way that requires no memorization and no prior knowledge beyond addition and multiplication. From these simple foundations, Burn Math Class shows how mathematics can be (re)invented from scratch without preexisting textbooks and courses. We can discover math on our own through experimentation and failure, without appealing to any outside authority. When math is created free from arcane notations and pretentious jargon that hide the simplicity of mathematical concepts, it can be understood organically -- and it becomes fun! Following this unconventional approach, Burn Math Class leads the reader from the basics of elementary arithmetic to various "advanced" topics, such as time-dilation in special relativity, Taylor series, and calculus in infinite-dimensional spaces. Along the way, Wilkes argues that orthodox mathematics education has been teaching the subject backward: calculus belongs before many of its so-called prerequisites, and those prerequisites cannot be fully understood without calculus. Like the smartest, craziest teacher you've ever had, Wilkes guides you on an adventure in mathematical creation that will radically change the way you think about math. Revealing the beauty and simplicity of this timeless subject, Burn Math Class turns everything that seems difficult about mathematics upside down and sideways until you understand just how easy math can be.

    Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading.

    A modern classic by an accomplished mathematician and best-selling author has been updated to encompass and explain the recent headline-making advances in the field in non-technical terms.

    In this free collection of excerpts, enjoy a taste of all of Vince Flynn’s thrillers starring CIA superagent Mitch Rapp.

    In leader David Miscavige's inner sanctum, they built their mental prison as they melded into its radicalized lifestyle where danger, captivity and abuse were normalized. After three escapes, Karen chose between two unbearable options. Escaping Scientology Part I sweeps you into the lives of two young adults filled with hope and love as designer Karen and her award-winning musician-composer husband Peter overcome obstacles to succeed in the music and fashion industries together. Scientology re-focuses their goals toward the importance of clearing the planet and recruiting celebrities to build Scientology's social capital. Karen portrays the basic beliefs of Scientology that led to her radicalization into the Sea Org at the Celebrity Centre, a fortress where artists aspire to achieve greatness while attaining spiritual freedom through L. Ron Hubbard’s teachings. Karen shows how celebrities are lured into Scientology and develop a co-dependent relationship from which few break out. Part II reveals Karen as a flawed and complex woman when she and Peter move to the secretive International Management headquarters, where they join 800 fanatical Sea Org members that made billion-year commitments to make this a Scientology world without war, criminality, or insanity. Karen finds the dystopian outpost and its global operations to be proof that Time magazine’s 1991 article, “The Thriving Cult of Greed and Power” captures the essence of Scientology’s mindset, that she describes as “war is everything and everything is war.” She is no passive victim as she attempts to stay in the driver’s seat and keep their marriage intact while fighting the pressures of the Int base culture that attempt to break them apart. Scientology goes under “Cruise Control” as Miscavige becomes obsessed with his biggest trophy, Tom Cruise, and stiffens his control and abusive punishment methods on the Int base staff. Karen rebels against regulations and spends time in Scientology’s prison camp. After two attempts to escape the Int base, she is trailed by security guards and coerced into returning. Failing to escape, she questions the evidence of her own senses, and makes a mind-twisting re-commitment to become the best version of a Sea Org member she can be. Karen carves out a world she can live within as she is promoted into the highest echelons of management, appointed by the Chairman of the Board RTC to Int Management Public Relations Officer and later to take charge of the image of Sea Org staff internationally from the Int Finance Office. While working on special projects under David and Shelley Miscavige, she travels to Scientology bases around the world where she sees human rights violations set in place by Hubbard’s policies that cause her to conclude Scientology is a for-profit business that builds billions of dollars of assets on the backs of Sea Org slave labor, while hiding behind the banner of the First Amendment, claiming benefits and protection as a non-profit religion. The epilogue of Part III portrays the mind-wrenching process of physical escape, and psychological anguish as Karen plies herself out of Scientology’s grip and endures its cruel disconnection policy. She re-acclimates herself to life on the outside while, brick by brick, she disassembles the walls of the mental prison she had built, and survives with the help of her accomplice and the love and support of her family. Karen's narrative memoir shows that Scientology's plan, authored by L.

    Half a century later, only robots have been to the Red Planet and our astronauts rarely venture beyond Earth orbit.Now Mars is back With everyone from Elon Musk to Ridley Scott and Donald Trump talking about it, interplanetary exploration is back on the agenda and Mars is once again the prime destination for future human expansion and colonisation. In Destination Mars, astrophysicist and science writer Andrew May traces the history of our fascination with the Red Planet and explores the science upon which a crewed mission would be based, from assembling a spacecraft in Earth orbit to surviving solar storms. With expert insight, he analyses the new space race and assesses what the future holds for human life on Mars.

    Includes such gems as:? There are 42 eyes in a deck of cards, and 42 dots on a pair of dice ? In order to fill in a map so that neighboring regions never get the same color, one never needs more than four colors ? Hells Angels use the number 81 in their insignia because the initials H and A are the eighth and first numbers in the alphabet respectively

    In those twelve months, Einstein shattered many cherished scientific beliefs with five extraordinary papers that would establish him as the world's leading physicist. This book brings those papers together in an accessible format. The best-known papers are the two that founded special relativity: On the Electrodynamics of Moving Bodies and Does the Inertia of a Body Depend on Its Energy Content? In the former, Einstein showed that absolute time had to be replaced by a new absolute: the speed of light. In the second, he asserted the equivalence of mass and energy, which would lead to the famous formula E = mc2.The book also includes On a Heuristic Point of View Concerning the Production and Transformation of Light, in which Einstein challenged the wave theory of light, suggesting that light could also be regarded as a collection of particles. This helped to open the door to a whole new world--that of quantum physics. For ideas in this paper, he won the Nobel Prize in 1921.The fourth paper also led to a Nobel Prize, although for another scientist, Jean Perrin. On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat concerns the Brownian motion of such particles. With profound insight, Einstein blended ideas from kinetic theory and classical hydrodynamics to derive an equation for the mean free path of such particles as a function of the time, which Perrin confirmed experimentally. The fifth paper, A New Determination of Molecular Dimensions, was Einstein's doctoral dissertation, and remains among his most cited articles. It shows how to calculate Avogadro's number and the size of molecules.These papers, presented in a modern English translation, are essential reading for any physicist, mathematician, or astrophysicist. Far more than just a collection of scientific articles, this book presents work that is among the high points of human achievement and marks a watershed in the history of science. Coinciding with the 100th anniversary of the miraculous year, this new paperback edition includes an introduction by John Stachel, which focuses on the personal aspects of Einstein's youth that facilitated and led up to the miraculous year.

    This guide provides explanations of eigenvalues, eigenvectors, linear transformations, linear equations, vectors, and matrices.

    The material of this book is indispensable for anyone who wishes to understand the real spiritual roots of Western civilization.