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Author: Mario Livio Publisher: Simon and Schuster ISBN: 0743274628 Category : Mathematics Languages : en Pages : 367
Book Description
The author of The Golden Ratio tells the “lively and fascinating” story of two nineteenth-century mathematicians whose work revealed the laws of symmetry (Nature). What do Bach’s compositions, Rubik’s Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry—known as group theory—did not emerge from the study of symmetry at all, but from an equation that couldn’t be solved. For three centuries, the quintic equation resisted efforts by mathematicians to find a solution. Working independently, two great prodigies ultimately proved that it couldn’t be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn’t Be Solved is told not through abstract formulas but in a dramatic account of the lives and work of some of the greatest mathematicians in history.
Author: Mario Livio Publisher: Simon and Schuster ISBN: 0743274628 Category : Mathematics Languages : en Pages : 367
Book Description
The author of The Golden Ratio tells the “lively and fascinating” story of two nineteenth-century mathematicians whose work revealed the laws of symmetry (Nature). What do Bach’s compositions, Rubik’s Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry—known as group theory—did not emerge from the study of symmetry at all, but from an equation that couldn’t be solved. For three centuries, the quintic equation resisted efforts by mathematicians to find a solution. Working independently, two great prodigies ultimately proved that it couldn’t be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn’t Be Solved is told not through abstract formulas but in a dramatic account of the lives and work of some of the greatest mathematicians in history.
Author: Mario Livio Publisher: Simon and Schuster ISBN: 1416594434 Category : Mathematics Languages : en Pages : 320
Book Description
Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
Author: Mario Livio Publisher: Simon and Schuster ISBN: 1439192375 Category : Biography & Autobiography Languages : en Pages : 352
Book Description
"Drawing on the lives of five great scientists -- Charles Darwin, William Thomson (Lord Kelvin), Linus Pauling, Fred Hoyle and Albert Einstein -- scientist/author Mario Livio shows how even the greatest scientists made major mistakes and how science built on these errors to achieve breakthroughs, especially into the evolution of life and the universe"--
Author: Peter Pesic Publisher: MIT Press ISBN: 9780262661829 Category : Technology & Engineering Languages : en Pages : 242
Book Description
The intellectual and human story of a mathematical proof that transformed our ideas about mathematics. In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancé. But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the "real" world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra—which even Newton resisted—and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof.
Author: Jordan Ellenberg Publisher: Penguin Press ISBN: 1594205221 Category : Mathematics Languages : en Pages : 480
Book Description
A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.
Author: Christopher G. Small Publisher: Springer Science & Business Media ISBN: 0387489010 Category : Mathematics Languages : en Pages : 139
Book Description
Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. Each chapter includes a list of problems associated with the covered material. These vary in difficulty, with the easiest being accessible to any high school student who has read the chapter carefully. The most difficult will challenge students studying for the International Mathematical Olympiad or the Putnam Competition. An appendix provides a springboard for further investigation of the concepts of limits, infinite series and continuity.
Author: Phil Chambers Publisher: LTL Training Ltd ISBN: 1904906044 Category : Self-Help Languages : en Pages : 125
Book Description
At last! The book that all maths and physics students have been waiting for - "How To Remember Equations And Formulae" “If you need to remember formulae of any length, for study or work, and you’d like your hand held while you master this skill effortlessly in a fun way, you should buy this book today.” Amanda Ollier, author of the Self Help Bible and The Mindset Shift Never forget an equation or formula ever again Save time in exams, get the results you really deserve Impress your tutors and potential employers Stand out against others in the job market Enhance your earning potential Perfect for anyone studying or teaching maths, physics, accountancy, economics, engineering or the sciences, from A levels right through to postgraduate. What the experts say... “This is an outstanding and comprehensive book that delivers on every promise! All memory strategies including mind mapping and the journey system are here for you to depend on and you’ll quickly realize this is your most treasured memory resource.” Pat Wyman, founder HowToLearn.com and author, Amazing Grades “I am delighted to recommend this book to students. Phil’s and James’ work is based on a sound application of the fundamental principles of memory training, namely the use of imagination, association, and location.” Dominic O’Brien, Eight times World Memory Champion, Author and Media Personality “Explains the techniques in a beautifully simple and eloquent manner.” David Thomas GMM. International speaker, Sunday Times No.1 bestselling author, media personality “What James Smith and Phil Chambers offer their readers here is a thoroughly researched and simple system, which combines mnemonics and mind mapping in a unique and interesting way. As well as covering just about every mathematical equation you can think of, James and Phil offer solutions for the English, Greek and Roman alphabets and all with a splash of humour and encouraging examples to get you started. I wish this has existed when I was at school, I will certainly be introducing this to my students and I am confident their results will improve as a direct result.” Amanda Ollier, author of The Self Help Bible and The Mindset Shift
Author: John N. Crossley Publisher: World Scientific ISBN: 9789971504144 Category : Mathematics Languages : en Pages : 240
Book Description
This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of Gdel's theorem. The second part is concerned with the development of complex numbers and tries to answer the question as to why complex numbers were not introduced before the 16th century and then, by looking at the original materials, shows how they were introduced as a pragmatic device which was only subsequently shown to be theoretically justifiable. The third part concerns the real numbers and examines the distinction that the Greeks made between number and magnitude. It then traces the gradual development of a theory of real numbers up to the precise formulations in the nineteeth century. The importance of the Greek distinction between the number line and the geometric line is brought into sharp focus.This is an new edition of the book which first appeared privately published in 1980 and is now out of print. Substantial revisions have been made throughout the text, incorporating new material which has recently come to light and correcting a few relatively minor errors. The third part on real numbers has been very extensively revised and indeed the last chapter has been almost completely rewritten. Many revisions are the results of comments from earlier readers of the book.
Author: Lawrence M. Krauss Publisher: Penguin ISBN: 1440627339 Category : Science Languages : en Pages : 289
Book Description
An exploration of mankind's fascination with worlds beyond our own-by the bestselling author of The Physics of Star Trek Lawrence Krauss -an international leader in physics and cosmology-examines our long and ardent romance with parallel universes, veiled dimensions, and regions of being that may extend tantalizingly beyond the limits of our perception. Krauss examines popular culture's current embrace (and frequent misunderstanding) of such topics as black holes, life in other dimensions, strings, and some of the more extraordinary new theories that propose the existence of vast extra dimensions alongside our own. BACKCOVER: "An astonishing and brilliantly written work of popular science." -Science a GoGo "A brilliant, thrilling book . . . You'll have so much fun reading that you'll hardly notice you're getting a primer on contemporary physics and cosmology." -Walter Isaacson, author of Benjamin Franklin: An American Life
Author: Barry Cipra Publisher: American Mathematical Soc. ISBN: 9780821890431 Category : Science Languages : en Pages : 108
Book Description
Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.
Author: Mario Livio
Author: Mario Livio
Author: Mario Livio
Author: Mario Livio
Author: Peter Pesic
Author: Jordan Ellenberg
Author: Christopher G. Small
Author: Phil Chambers
Author: John N. Crossley
Author: Lawrence M. Krauss
Author: Barry Cipra