It includes rewritten and clarified proofs and derivations, as well as new topics such as Arnoldi iteration, and domain decomposition methods.

    In this indispensable volume, a primer for the information age, Hans Christian von Baeyer presents a clear description of what information is, how concepts of its measurement, meaning, and transmission evolved, and what its ever-expanding presence portends for the future. Information is poised to replace matter as the primary stuff of the universe, von Baeyer suggests; it will provide a new basic framework for describing and predicting reality in the twenty-first century. Despite its revolutionary premise, von Baeyer's book is written simply in a straightforward fashion, offering a wonderfully accessible introduction to classical and quantum information. Enlivened with anecdotes from the lives of philosophers, mathematicians, and scientists who have contributed significantly to the field, Information conducts readers from questions of subjectivity inherent in classical information to the blurring of distinctions between computers and what they measure or store in our quantum age. A great advance in our efforts to define and describe the nature of information, the book also marks an important step forward in our ability to exploit information--and, ultimately, to transform the nature of our relationship with the physical universe. (20040301)

    A wealth of accompanying figures and exercises illustrate and develop the material in more depth. They describe what a quantum computer is, how it can be used to solve problems faster than familiar "classical" computers, and the real-world implementation of quantum computers. Their book concludes with an explanation of how quantum states can be used to perform remarkable feats of communication, and of how it is possible to protect quantum states against the effects of noise.

    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.