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"

    For the calculus-based General Physics course primarily taken by engineers and scientists.

    This concept is at the root of the computational worldview, which basically says that very complex systems — the world we live in — have their beginnings in simple mathematical equations. We've lately come to understand that such an algorithm is only the start of a never-ending story — the real action occurs in the unfolding consequences of the rules. The chip-in-a-box computers so popular in our time have acted as a kind of microscope, letting us see into the secret machinery of the world. In Lifebox, Rucker uses whimsical drawings, fables, and humor to demonstrate that everything is a computation — that thoughts, computations, and physical processes are all the same. Rucker discusses the linguistic and computational advances that make this kind of "digital philosophy" possible, and explains how, like every great new principle, the computational world view contains the seeds of a next step.

    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.

    For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky.Fernandez uses our everyday experiences to skillfully reveal the hidden calculus behind a typical day's events. He guides us through how math naturally emerges from simple observations-how hot coffee cools down, for example-and in discussions of over fifty familiar events and activities. Fernandez demonstrates that calculus can be used to explore practically any aspect of our lives, including the most effective number of hours to sleep and the fastest route to get to work. He also shows that calculus can be both useful-determining which seat at the theater leads to the best viewing experience, for instance-and fascinating-exploring topics such as time travel and the age of the universe. Throughout, Fernandez presents straightforward concepts, and no prior mathematical knowledge is required. For advanced math fans, the mathematical derivations are included in the appendixes.Whether you're new to mathematics or already a curious math enthusiast, Everyday Calculus invites you to spend a day discovering the calculus all around you. The book will convince even die-hard skeptics to view this area of math in a whole new way.

    The fastest-growing segment of the population, those beyond the age of fifty, are no longer content to simply cope with the losses of age. Mental acuity and vitality are becoming a life-long pursuit. Now, the science of the mind is catching up with the Baby Boom generation. In this landmark book, renowned psychiatrist Gene Cohen challenges the long-held belief that our brain power inevitably declines as we age, and shows that there are actually positive changes taking place in our minds. Based on the latest studies of the brain, as well as moving stories of men and women in the second half of life, The Mature Mind reveals for the first time how we can continue to grow and flourish. Cohen's groundbreaking theory-the first to elaborate on the psychology of later life-describes how the mind gives us "inner pushes" and creates new opportunities for positive change throughout adult life. He shows how we can jump-start that growth at any age and under any circumstances, fine-tuning as we go, actively building brain reserves and new possibilities. The Mature Mind offers a profoundly different and intriguing look at ourselves, challenging old assumptions, raising bold new questions, and providing exciting answers grounded in science and the realities of everyday life.

    On the cusp of decoding brain signals that govern motor skills, they are developing miraculous technologies to enable paraplegics and wounded soldiers to move prosthetic limbs, and the rest of us to manipulate computers and other objects through thought alone. These fiercely competitive scientists are vying for Defense Department and venture capital funding, prestige, and great wealth. Part life-altering cure, part science fiction, part military dream, these cutting-edge brain-computer interfaces promise to improve lives—but also hold the potential to augment soldiers' combat capabilities. In The Brain Electric, Malcolm Gay follows the dramatic emergence of these technologies, taking us behind the scenes into the operating rooms, start-ups, and research labs where the future is unfolding. With access to many of the field's top scientists, Gay illuminates this extraordinary race—where science, medicine, profit, and war converge—for the first time. But this isn't just a story about technology. At the heart of this research is a group of brave, vulnerable patient-volunteers whose lives are given new meaning through participating in these experiments. The Brain Electric asks us to rethink our relationship to technology, our bodies, even consciousness itself—challenging our assumptions about what it means to be human.

    Accordingly, he once derided as "spooky action at a distance" the notion that two elementary particles far removed from each other could nonetheless influence each other's properties—a hypothetical phenomenon his fellow theorist Erwin Schrödinger termed "quantum entanglement."In a series of ingenious experiments conducted in various locations—from a dank sewage tunnel under the Danube River to the balmy air between a pair of mountain peaks in the Canary Islands—the author and his colleagues have demonstrated the reality of such entanglement using photons, or light quanta, created by laser beams. In principle the lessons learned may be applicable in other areas, including the eventual development of quantum computers.

    Linear algebra is tightly integrated into the text.