* Enhanced sections throughout text provide much firmer foundation than the first edition. * Literature citations are given throughout for reference to additional material.

    His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order—a language Hogben shows one can both master and enjoy.

    Frank Wilczek has played a lead role in establishing the new paradigms. Transcending the clash and mismatch of older ideas about what matter is, and what space is, Wilczek presents here some brilliant and clear syntheses. Space is a dynamic material, the engine of reality; matter is a subtle pattern of disturbance in that material.Extraordinarily readable and authoritative, The Lightness of Being is the first book to unwrap these exciting new ideas for the general public. It explores their implications for basic questions about space, mass, energy, and the longed-for possibility of a fully unified theory of Nature. Along the way, Wilczek presents new perspectives on many strange aspects of our fantastic universe. Pointing toward new directions where the great discoveries in fundamental physics are likely to come, he envisions a new Golden Age in physics.

    

    . .he believes these ideas to be accessible to the audience he wantsto reach, and he writes so that they are. -- NatureIf you want to encourage anyone's interest in math, get them TheMathematical Universe. * New Scientist

    Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

    More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge--from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool--the general principle--from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

    Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics.In this follow-up to The Theoretical Minimum, Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic objects through mathematical abstractions. Unlike other popularizations that shy away from quantum mechanics’ weirdness, Quantum Mechanics embraces the utter strangeness of quantum logic. The authors offer crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics, and each chapter includes exercises to ensure mastery of each area. Like The Theoretical Minimum, this volume runs parallel to Susskind’s eponymous Stanford University-hosted continuing education course.An approachable yet rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.

    And she can't concentrate on her tennis matches when she's worried about the questions she missed on the big test! Luckily for her, she befriends Ryota, a patient physics geek who uses real-world examples to help her understand classical mechanics-and improve her tennis game in the process!In The Manga Guide to Physics, you'll follow alongside Megumi as she learns about the physics of everyday objects like roller skates, slingshots, braking cars, and tennis serves. In no time, you'll master tough concepts like momentum and impulse, parabolic motion, and the relationship between force, mass, and acceleration.You'll also learn how to:Apply Newton's three laws of motion to real-life problems Determine how objects will move after a collision Draw vector diagrams and simplify complex problems using trigonometry Calculate how an object's kinetic energy changes as its potential energy increases If you're mystified by the basics of physics or you just need a refresher, The Manga Guide to Physics will get you up to speed in a lively, quirky, and practical way.

    In this book, Chris Bernhardt offers an introduction to quantum computing that is accessible to anyone who is comfortable with high school mathematics. He explains qubits, entanglement, quantum teleportation, quantum algorithms, and other quantum-related topics as clearly as possible for the general reader. Bernhardt, a mathematician himself, simplifies the mathematics as much as he can and provides elementary examples that illustrate both how the math works and what it means.Bernhardt introduces the basic unit of quantum computing, the qubit, and explains how the qubit can be measured; discusses entanglement--which, he says, is easier to describe mathematically than verbally--and what it means when two qubits are entangled (citing Einstein's characterization of what happens when the measurement of one entangled qubit affects the second as "spooky action at a distance"); and introduces quantum cryptography. He recaps standard topics in classical computing--bits, gates, and logic--and describes Edward Fredkin's ingenious billiard ball computer. He defines quantum gates, considers the speed of quantum algorithms, and describes the building of quantum computers. By the end of the book, readers understand that quantum computing and classical computing are not two distinct disciplines, and that quantum computing is the fundamental form of computing. The basic unit of computation is the qubit, not the bit.

    Although deeply influenced by Einstein, he was also, more unusually for a scientist, inspired by mysticism. Indeed, in the 1970s and 1980s he made contact with both J. Krishnamurti and the Dalai Lama whose teachings helped shape his work. In both science and philosophy, Bohm's main concern was with understanding the nature of reality in general and of consciousness in particular. In this classic work he develops a theory of quantum physics which treats the totality of existence as an unbroken whole. Writing clearly and without technical jargon, he makes complex ideas accessible to anyone interested in the nature of reality.

    String Theory For Dummies offers an accessible introduction to this highly mathematical "theory of everything," which posits ten or more dimensions in an attempt to explain the basic nature of matter and energy. Written for both students and people interested in science, this guide explains concepts, discusses the string theory's hypotheses and predictions, and presents the math in an approachable manner. It features in-depth examples and an easy-to-understand style so that readers can understand this controversial, cutting-edge theory.

    People go to temples, churches, mosques, and synagogues to pray to their divine incarnation of Oneness. Following a surprisingly similar notion, scientists have long asserted that under Nature’s apparent complexity there is a simpler underlying reality. In its modern incarnation, this Theory of Everything would unite the physical laws governing very large bodies (Einstein’s theory of relativity) and those governing tiny ones (quantum mechanics) into a single framework. But despite the brave efforts of many powerful minds, the Theory of Everything remains elusive. It turns out that the universe is not elegant. It is gloriously messy. Overturning more than twenty-five centuries of scientific thought, award-winning physicist Marcelo Gleiser argues that this quest for a Theory of Everything is fundamentally misguided, and he explains the volcanic implications this ideological shift has for humankind. All the evidence points to a scenario in which everything emerges from fundamental imperfections, primordial asymmetries in matter and time, cataclysmic accidents in Earth’s early life, and duplication errors in the genetic code. Imbalance spurs creation. Without asymmetries and imperfections, the universe would be filled with nothing but smooth radiation.A Tear at the Edge of Creation calls for nothing less than a new "humancentrism" to reflect our position in the universal order. All life, but intelligent life in particular, is a rare and precious accident. Our presence here has no meaning outside of itself, but it does have meaning. The unplanned complexity of humankind is all the more beautiful for its improbability. It’s time for science to let go of the old aesthetic that labels perfection beautiful and holds that "beauty is truth." It’s time to look at the evidence without centuries of monotheistic baggage. In this lucid, down-to-earth narrative, Gleiser walks us through the basic and cutting-edge science that fueled his own transformation from unifier to doubter—a fascinating scientific quest that led him to a new understanding of what it is to be human.

    William H. Cropper vividly portrays the life and accomplishments of such giants as Galileo and Isaac Newton, Marie Curie and Ernest Rutherford, Albert Einstein and NielsBohr, right up to contemporary figures such as Richard Feynman, Murray Gell-Mann, and Stephen Hawking. We meet scientists--all geniuses--who could be gregarious, aloof, unpretentious, friendly, dogged, imperious, generous to colleagues or contentious rivals. As Cropper captures their personalities, he also offers vivid portraits of their great moments of discovery, their bitter feuds, their relations with family and friends, their religious beliefs and education. In addition, Cropper has grouped these biographies by discipline--mechanics, thermodynamics, particle physics, and others--eachsection beginning with a historical overview. Thus in the section on quantum mechanics, readers can see how the work of Max Planck influenced Niels Bohr, and how Bohr in turn influenced Werner Heisenberg.Our understanding of the physical world has increased dramatically in the last four centuries. With Great Physicists, readers can retrace the footsteps of the men and women who led the way.