It is highly recommended for anyone planning to study advanced analysis, e.g., complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied. Many abstract ideas, such as metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom and the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.

    Groundbreaking in every way when first published, this book is a simple, straightforward, direct calculus text. It's popularity is directly due to its broad use of applications, the easy-to-understand writing style, and the wealth of examples and exercises which reinforce conceptualization of the subject matter. The author wrote this text with three objectives in mind. The first was to make the book more student-oriented by expanding discussions and providing more examples and figures to help clarify concepts. To further aid students, guidelines for solving problems were added in many sections of the text. The second objective was to stress the usefulness of calculus by means of modern applications of derivatives and integrals. The third objective, to make the text as accurate and error-free as possible, was accomplished by a careful examination of the exposition, combined with a thorough checking of each example and exercise.

    This edition was rewritten, updated, and released on April 28, 2015.When recently-divorced American John Hammond arrives on the Aegean island of Samos, he is unaware of events that happened nearly seven decades earlier that will embroil him in death and violence, and change his life forever.Late one night he finds Greek fisherman Petros Vangelos mortally wounded in an alley. Vangelos gives Hammond a coded map before he expires. With that map, Hammond becomes the link to a Turkish tramp steamer named Sabiya that sank in a storm in 1945 with a fortune in gold and jewels aboard. Also on the Sabiya, in a waterproof safe, are documents that implicate a long-dead German SS Officer in the theft of tens of millions of dollars in valuables from Holocaust victims and the laundering of those valuables by the Nazi’s Swiss banker partner. That partnership helped build a huge banking enterprise that is now run by that Swiss banker’s son who will stop at nothing to prevent disclosure of his father’s crimes.Hammond’s visit to Samos quickly turns into a roller coaster ride on which he encounters violence, new friendships, and a woman he loves, all of which irrevocably alter the course of his life.The Pythagorean Solution is a thrilling, non-stop adventure that will make the reader want to reserve a seat on a flight to Samos.> This is a new release of a previously published edition.

    Roger Penrose—one of the most innovative mathematicians of our time—turns around this predominant picture of the universe’s “heat death,” arguing how the expected ultimate fate of our accelerating, expanding universe can actually be reinterpreted as the “Big Bang” of a new one.Along the way to this remarkable cosmological picture, Penrose sheds new light on basic principles that underlie the behavior of our universe, describing various standard and nonstandard cosmological models, the fundamental role of the cosmic microwave background, and the key status of black holes. Ideal for both the amateur astronomer and the advanced physicist—with plenty of exciting insights for each—Cycles of Time is certain to provoke and challenge.Intellectually thrilling and accessible, this is another essential guide to the universe from one of our preeminent thinkers.

    This time, they introduce readers to Einstein's special relativity and Maxwell's classical field theory. Using their typical brand of real math, enlightening drawings, and humor, Susskind and Friedman walk us through the complexities of waves, forces, and particles by exploring special relativity and electromagnetism. It's a must-read for both devotees of the series and any armchair physicist who wants to improve their knowledge of physics' deepest truths.

    In chapters that follow, detailed topic reviews cover polynomial, trigonometric, exponential, logarithmic, and rational functions; coordinate and three-dimensional geometry; numbers and operations; data analysis, statistics, and probability; and graphing calculators, their operations and applications. Six full-length model tests with answers, explanations, and self-evaluation charts conclude this manual.

    Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.

    With characteristic flair, insight and humor, Feynman discusses topics students struggle with and offers valuable tips on solving physics problems. An illuminating memoir by Matthew Sands who originally conceived The Feynman Lectures on Physics gives a fascinating insight into the history of Feynman’s lecture series and the books that followed. This book is rounded off by relevant exercises and answers by R. B. Leighton and R. E. Vogt, originally developed to accompany the Lectures on Physics.

    Dealing with measure theory and Lebesque integration, this is an introductory graduate text.

    A simple web search picks out a handful of relevant needles from the world's biggest haystack: the billions of pages on the World Wide Web. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers; and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? This is the first book to answer that question in language anyone can understand, revealing the extraordinary ideas that power our PCs, laptops, and smartphones. Using vivid examples, John MacCormick explains the fundamental "tricks" behind nine types of computer algorithms, including artificial intelligence (where we learn about the "nearest neighbor trick" and "twenty questions trick"), Google's famous PageRank algorithm (which uses the "random surfer trick"), data compression, error correction, and much more. These revolutionary algorithms have changed our world: this book unlocks their secrets, and lays bare the incredible ideas that our computers use every day.

    Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added, as well as commentary to the exercises explaining how they relate to the preceding section, and how they foreshadow later topics.

    I also hope that it will serve as a useful reference too for the many workers engaged in one type of solid state research activity or another, who may be without formal training in the subject.

    Early beginnings in antiquity, medieval contributions, and a century of anticipation lead up to a consideration of Newton and Leibniz, the period of indecison that followed them, and the final rigorous formulation that we know today.

    But was he right? Can the quantum theory of fields and Einstein's general theory of relativity, the two most accurate and successful theories in all of physics, be united in a single quantum theory of gravity? Can quantum and cosmos ever be combined? On this issue, two of the world's most famous physicists--Stephen Hawking ("A Brief History of Time") and Roger Penrose ("The Emperor's New Mind" and "Shadows of the Mind")--disagree. Here they explain their positions in a work based on six lectures with a final debate, all originally presented at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge.How could quantum gravity, a theory that could explain the earlier moments of the big bang and the physics of the enigmatic objects known as black holes, be constructed? Why does our patch of the universe look just as Einstein predicted, with no hint of quantum effects in sight? What strange quantum processes can cause black holes to evaporate, and what happens to all the information that they swallow? Why does time go forward, not backward?In this book, the two opponents touch on all these questions. Penrose, like Einstein, refuses to believe that quantum mechanics is a final theory. Hawking thinks otherwise, and argues that general relativity simply cannot account for how the universe began. Only a quantum theory of gravity, coupled with the no-boundary hypothesis, can ever hope to explain adequately what little we can observe about our universe. Penrose, playing the realist to Hawking's positivist, thinks that the universe is unbounded and will expand forever. The universe can be understood, he argues, in terms of the geometry of light cones, the compression and distortion of spacetime, and by the use of twistor theory. With the final debate, the reader will come to realize how much Hawking and Penrose diverge in their opinions of the ultimate quest to combine quantum mechanics and relativity, and how differently they have tried to comprehend the incomprehensible.

    By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist. Einstein endorsed this result reluctantly but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Godel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.