Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of a missionary with the rigor of a purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.

    In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

    Together, they explain virtually everything about the world we live in. But, almost a century after their advent, most people haven't the slightest clue what either is about. Did you know that there's so much empty space inside matter that the entire human race could be squeezed into the volume of a sugar cube? Or that you grow old more quickly on the top floor of a building than on the ground floor? And did you realize that 1 per cent of the static on a TV tuned between stations is the relic of the Big Bang? These and many other remarkable facts about the world are direct consequences of quantum physics and relativity. Quantum theory has literally made the modern world possible. Not only has it given us lasers, computers, and nuclear reactors, but it has provided an explanation of why the sun shines and why the ground beneath our feet is solid. Despite this, however, quantum theory and relativity remain a patchwork of fragmented ideas, vaguely understood at best and often utterly mysterious. average person. Author Marcus Chown emphatically disagrees. As Einstein himself said, Most of the fundamental ideas of science are essentially simple and may, as a rule, be expressed in a language comprehensible to everyone. If you think that the marvels of modern physics have passed you by, it is not too late. In Chown's capable hands, quantum physics and relativity are not only painless but downright fun. So sit back, relax, and get comfortable as an adept and experienced science communicator brings you quickly up to speed on some of the greatest ideas in the history of human thought.

      “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.”—Nina MacLaughlin, Boston Globe “Engaging, eminently readable . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.”—Judith Goodstein, American Scientist  Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers readers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.

    

    In recent years, however, the concept of information has gained importance. Why? In this book, eminent scientists, philosophers and theologians chart various aspects of information, from quantum information to biological and digital information, in order to understand how nature works. Beginning with a historical treatment of the topic, the book also examines physical and biological approaches to information, and its philosophical, theological and ethical implications.

    Be prepared to question the world you live in and everything you thought you knew about the universe, human origins, and the lost civilizations of the past. Discover thought-bending evidence from some of the oldest text ever written and learn the reasons why their content eventually became suppressed and hidden from most of society. Conspiracy theories or conspiracy facts, you decide what's real based on the evidence. Once you read The Stage of Time, your perspective on reality may never be quite the same way again. This book includes: -Details about the ancient civilizations that once existed around the world and the events which led to their disappearance. -Translations from ancient texts that include: The Atrahasis, Enuma Elish, Sumerian King List, Eridu Genesis, Code of Hammurabi, Emerald Tablets, and more. -The eagle and the serpent, cataclysms during the last ice age, and the influences of the Anunnaki. -Secrets of consciousness, reincarnation, spirituality, and sentient life in the universe.

    A team of fossil hunters... A desperate fight to survive.... In book 5, Hannah and the other survivors arrive in the ice world of the Pleistocene, bare of trees and with almost no animal life. Starving, with no other game to hunt, they must take on the mighty Mammoth and his wicked tusks. Can they survive the freeze long enough to jump back to modern times?

    Highly recommended for graduate-level libraries.' ChoiceThis highly successful text, which first appeared in the year 1972 and has continued to be popular ever since, has now been brought up-to-date by incorporating the remarkable developments in the field of 'phase transitions and critical phenomena' that took place over the intervening years. This has been done by adding three new chapters (comprising over 150 pages and containing over 60 homework problems) which should enhance the usefulness of the book for both students and instructors. We trust that this classic text, which has been widely acclaimed for its clean derivations and clear explanations, will continue to provide further generations of students a sound training in the methods of statistical physics.

    Here are Einstein, Fleming, Bohr, McClintock, Paul ing, Watson and Crick, Heisenberg and many others. With remarkable insight, Lightman charts the intellectual and emotional landscape of the time, portrays the human drama of discovery, and explains the significance and impact of the work. Finally he includes a fascinating and unique guided tour through the original papers in which the discoveries were revealed. Here is science writing at its best–beautiful, lyrical and completely accessible. It brings the process of discovery to life before our very eyes.

    In this comprehensive and practical guide, you will learn how to make and activate Crystal Grids for yourself, others and your home. Explore the fascinating history and symbolism behind Crystal Grids. Learn how and why Crystal Grids work. Ethan Lazzerini uses over 20 years experience with crystals to formulate 34 intention based Crystal Grids for every purpose. No more secrets, this No.1 Amazon Bestselling book will demystify the world of Crystal Grids. Learn exactly why each different crystal is used and the reason every geometric shape was chosen for each grid. Crystal Grids Power is filled with tips and techniques to supercharge your grids. Access simple to advanced Crystal Grids and learn how to create your own. Includes Powerful Crystal Grids for: Abundance & Prosperity, Psychic Protection, Personal & Distant Healing, Success, Relationships, Increased Energy, Motivation, Angels, Confidence, Better Sleep, Karma Releasing, Life Purpose, Stress Relief, Earth Healing, Overcoming Obstacles, Aura Clearing, Peace & Harmony, Home Protection, New Beginnings and many more... Contains 34 Crystal Grids for all areas of your life Clearly illustrated with diagrams and step-by-step instructions The meaning of Sacred Geometry shapes and symbols explained Learn three different ways to activate your Crystal Grids Helpful substitute crystals are given for every grid Includes FREE Printable Crystal Grid Templates to download Crystal Grids Power is an indispensable guide to the magical world of Crystal Grids. This enlightening book contains EVERYTHING you need to know about Crystal Grids and how to use them. Take a look inside, download a sample or buy your copy today!

    Part One presents the general principles of pathophysiology and discusses the influence of the environment and the role of genetics in the development of disease. Part Two, organized by body system, examines normal anatomy and physiology, alterations of function in adults, and alterations of function in children.

    This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.

    It covers all relevant areas, including molecular spectroscopy, electronic structure computations, molecular beam methods and time-resolved measurements of chemical systems.

    New BIG IDEAs help all students focus on the most important concepts. Students explore concepts through engaging narrative, frequent use of analogies, familiar examples, and clear and instructional graphics. Now, with Success Tracker™ online, teachers can choose from a variety of diagnostic and benchmark tests to gauge student comprehension. Targeted remediation is available too! Whether using the text alone or in tandem with exceptional ancillaries and technology, teachers can meet the needs of every student at every learning level.With unparalleled reading support, resources to reach every student, and a proven research-based approach, authors Kenneth Miller and Joseph Levine continue to set the standard.Prentice Hall Biology delivers:-Clear, accessible writing-Up-to-date content-A student friendly approach-A powerful framework for connecting key concepts