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.

    This user-friendly self-study guide is aimed at the general reader who is motivated to tackle that not insignificant challenge. The book is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution (which gives a good approximation of the spacetime of our Solar System); simple black holes and relativistic cosmology. Following the historic 2015 LIGO (Laser Interferometer Gravitational-Wave Observatory) detection, there is now an additional chapter on gravitational waves, ripples in the fabric of spacetime that potentially provide a revolutionary new way to study the universe. Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes.Understand even the basics of Einstein's amazing theory and the world will never seem the same again. ContentsPrefaceIntroduction1 Foundation mathematics2 Newtonian mechanics3 Special relativity4 Introducing the manifold5 Scalars, vectors, one-forms and tensors6 More on curvature7 General relativity8 The Newtonian limit9 The Schwarzschild metric10 Schwarzschild black holes11 Cosmology12 Gravitational wavesAppendix: The Riemann curvature tensorBibliographyAcknowledgementsJanuary 2019. This third edition has been revised to make the material even more accessible to the enthusiastic general reader who seeks to understand the mathematics of relativity.

    Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

    If you like your science fun and unpredictable, don't miss this new addition to the Dr Karl library.

    Contemplation of time and the discoveries of modern science lead to the assertion that the mind is paramount and limitless.

    In the 14 billion years since, scientists have pointed their telescopes upward, peering outward in space and backward in time, developing and refining theories to explain the weird and wonderful phenomena they observed.Through these observations, we now understand concepts like the size of the universe (still expanding), the distance to the next-nearest star from earth (Alpha Centauri, 26 trillion miles) and what drives the formation of elements (nuclear fusion), planets and galaxies (gravity), and black holes (gravitational collapse). But are these cosmological questions definitively answered or is there more to discover?Oxford University astrophysicist and popular YouTube personality Dr. Becky Smethurst presents everything you need to know about the universe in 10 accessible and engaging lessons.In Space at the Speed of Light: The History of 14 Billion Years for People Short on Time, she guides you through fundamental questions, both answered and unanswered, posed by space scientists. Why does gravity matter? How do we know the big bang happened? What is dark matter? Do aliens exist? Why is the sky dark at night? If you have ever looked up at night and wondered how it all works, you will find answers - and many more questions - in this pocket-sized tour of the universe!

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

    Snyder exposes the political passions, religious impulses, friendships, rivalries, and love of knowledge—and power—that drove these extraordinary men.  Whewell (who not only invented the word “scientist,” but also founded the fields of crystallography, mathematical economics, and the science of tides), Babbage (a mathematical genius who invented the modern computer), Herschel (who mapped the skies of the Southern Hemisphere and contributed to the invention of photography), and Jones (a curate who shaped the science of economics) were at the vanguard of the modernization of science.  This absorbing narrative of people, science and ideas  chronicles the intellectual revolution inaugurated by these men, one that continues to mold our understanding of the world around us and of our place within it.  Drawing upon the voluminous correspondence between the four men over the fifty years of their work, Laura J. Snyder shows how friendship worked to spur the men on to greater accomplishments, and how it enabled them to transform science and help create the modern world.

    This book covers relevant geometric principles and how to represent objects algebraically so they can be computed and applied. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. Richard Hartley and Andrew Zisserman provide comprehensive background material and explain how to apply the methods and implement the algorithms. First Edition HB (2000): 0-521-62304-9

    In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.

    The book starts with a section on general cell structure and replication. Basic tissue types are covered in the following section, and the third section presents the microstructures of each of the major body systems. The highest -quality color light micrographs and electron micrograph images are accompanied by concise text and captions which explain the appearance, function, and clinical significance of each image. The accompanying website lets you view all the images from the atlas with a virtual microscope, allowing you to view the image at a variety of pre-set magnifications.Includes access to website containing book images and additional material, extra illustrations, self tests, and more. Utilizes virtual microscope function on the website, allowing you to see images first in low-powered and then in high powered magnification. Incorporates new information on histology of bone marrow, male reproductive system, respiratory system, pancreas, blood, cartilage, muscle types, staining methods, and more. Uses Color coding at the side of each page to make it easier to access information quickly and efficiently. Includes access to www.studentconsult.com - where you'll find the complete text and illustrations of the book online, fully searchable - Integration Links to bonus content in other STUDENT CONSULT titles - 300 new USMLE-style review questions, with answers and rationales - content clipping for handheld devices - an interactive community center with a wealth of additional resources - and much more!

    The text converts all programming code into the C++ language.

    This guidebook is aimed clearly at the needs of the student, with a thorough understanding of, and provision for, the potential conceptual difficulties he or she is likely to encounter.

    In the book, Sagan explores 15 billion years of cosmic evolution and the development of science and civilization. Cosmos traces the origins of knowledge and the scientific method, mixing science and philosophy, and speculates to the future of science. The book also discusses the underlying premises of science by providing biographical anecdotes about many prominent scientists throughout history, placing their contributions into the broader context of the development of modern science.The book covers a broad range of topics, comprising Sagan's reflections on anthropological, cosmological, biological, historical, and astronomical matters from antiquity to contemporary times. Sagan reiterates his position on extraterrestrial life—that the magnitude of the universe permits the existence of thousands of alien civilizations, but no credible evidence exists to demonstrate that such life has ever visited earth.

    No graduate student of quantum theory should leave it unread"--W.C Schieve, University of Texas