God Created The Integers

Author : Stephen Hawking
Publisher : Running Press
Page : 256 pages
File Size : 55,6 Mb
Release : 2007-03-29
Category : Science
ISBN : 9780762432721

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God Created The Integers by Stephen Hawking Pdf

Bestselling author and physicist Stephen Hawking explores the "masterpieces" of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians, including Augustin Cauchy, Bernard Riemann, and Alan Turing. This extensive anthology allows readers to peer into the mind of genius by providing them with excerpts from the original mathematical proofs and results. It also helps them understand the progression of mathematical thought, and the very foundations of our present-day technologies. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication.

Author : Stephen Hawking
Publisher : Running Press Adult
Page : 1090 pages
File Size : 54,8 Mb
Release : 2011-10-25
Category : Science
ISBN : 9780762443741

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The Dreams That Stuff Is Made Of by Stephen Hawking Pdf

"God does not play dice with the universe." So said Albert Einstein in response to the first discoveries that launched quantum physics, as they suggested a random universe that seemed to violate the laws of common sense. This 20th-century scientific revolution completely shattered Newtonian laws, inciting a crisis of thought that challenged scientists to think differently about matter and subatomic particles.The Dreams That Stuff Is Made Of compiles the essential works from the scientists who sparked the paradigm shift that changed the face of physics forever, pushing our understanding of the universe on to an entirely new level of comprehension. Gathered in this anthology is the scholarship that shocked and befuddled the scientific world, including works by Niels Bohr, Max Planck, Werner Heisenberg, Max Born, Erwin Schrodinger, J. Robert Oppenheimer, Richard Feynman, as well as an introduction by today's most celebrated scientist, Stephen Hawking.

Author : Stephen W. Hawking,Stephen Hawking,Leonard Mlodinow
Publisher : Random House
Page : 258 pages
File Size : 51,9 Mb
Release : 2011
Category : Science
ISBN : 9780553819229

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The Grand Design by Stephen W. Hawking,Stephen Hawking,Leonard Mlodinow Pdf

Relativity physics.

Author : Ekkehard Kopp
Publisher : Open Book Publishers
Page : 280 pages
File Size : 41,9 Mb
Release : 2020-10-23
Category : Mathematics
ISBN : 9781800640979

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Making up Numbers: A History of Invention in Mathematics by Ekkehard Kopp Pdf

Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.

Author : L.E. Sigler
Publisher : Springer Science & Business Media
Page : 427 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461394105

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Algebra by L.E. Sigler Pdf

There is no one best way for an undergraduate student to learn elementary algebra. Some kinds of presentations will please some learners and will disenchant others. This text presents elementary algebra organized accord ing to some principles of universal algebra. Many students find such a presentation of algebra appealing and easier to comprehend. The approach emphasizes the similarities and common concepts of the many algebraic structures. Such an approach to learning algebra must necessarily have its formal aspects, but we have tried in this presentation not to make abstraction a goal in itself. We have made great efforts to render the algebraic concepts intuitive and understandable. We have not hesitated to deviate from the form of the text when we feel it advisable for the learner. Often the presenta tions are concrete and may be regarded by some as out of fashion. How to present a particular topic is a subjective one dictated by the author's estima tion of what the student can best handle at this level. We do strive for consistent unifying terminology and notation. This means abandoning terms peculiar to one branch of algebra when there is available a more general term applicable to all of algebra. We hope that this text is readable by the student as well as the instructor. It is a goal of ours to free the instructor for more creative endeavors than reading the text to the students.

Author : Mallik Asok Kumar
Publisher : #N/A
Page : 196 pages
File Size : 45,7 Mb
Release : 2017-07-27
Category : Juvenile Nonfiction
ISBN : 9789813222946

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The Story Of Numbers by Mallik Asok Kumar Pdf

This book is more than a mathematics textbook. It discusses various kinds of numbers and curious interconnections between them. Without getting into hardcore and difficult mathematical technicalities, the book lucidly introduces all kinds of numbers that mathematicians have created. Interesting anecdotes involving great mathematicians and their marvelous creations are included. The reader will get a glimpse of the thought process behind the invention of new mathematics. Starting from natural numbers, the book discusses integers, real numbers, imaginary and complex numbers and some special numbers like quaternions, dual numbers and p-adic numbers. Real numbers include rational, irrational and transcendental numbers. Iterations on real numbers are shown to throw up some unexpected behavior, which has given rise to the new science of "Chaos". Special numbers like e, pi, golden ratio, Euler's constant, Gauss's constant, amongst others, are discussed in great detail. The origin of imaginary numbers and the use of complex numbers constitute the next topic. It is shown why modern mathematics cannot even be imagined without imaginary numbers. Iterations on complex numbers are shown to generate a new mathematical object called 'Fractal', which is ubiquitous in nature. Finally, some very special numbers, not mentioned in the usual textbooks, and their applications, are introduced at an elementary level. The level of mathematics discussed in this book is easily accessible to young adults interested in mathematics, high school students, and adults having some interest in basic mathematics. The book concentrates more on the story than on rigorous mathematics.

Author : Timothy Gowers
Publisher : Oxford Paperbacks
Page : 172 pages
File Size : 46,9 Mb
Release : 2002-08-22
Category : Mathematics
ISBN : 0192853619

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Mathematics: A Very Short Introduction by Timothy Gowers Pdf

The aim of this volume is to explain the differences between research-level mathematics and the maths taught at school. Most differences are philosophical and the first few chapters are about general aspects of mathematical thought.

Author : Patricia Anklam
Publisher : Unknown
Page : 296 pages
File Size : 53,8 Mb
Release : 1982
Category : Computers
ISBN : UOM:39015000507163

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Engineering a Compiler by Patricia Anklam Pdf

Author : G. Donald Allen,Amanda Ross
Publisher : Unknown
Page : 310 pages
File Size : 53,8 Mb
Release : 2017-10-13
Category : Mathematics
ISBN : 9463511369

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Pedagogy and Content in Middle and High School Mathematics by G. Donald Allen,Amanda Ross Pdf

The book provides an accumulation of articles, included in Focus on Mathematics Pedagogy and Content, a newsletter for teachers, published by Texas A&M University. Each article presents a discussion of a middle or high school mathematics topic. Many of the articles are written by professors at Texas A&M University. The book is broken into three parts, with the first part focusing on content and pedagogy, related to the NCTM content strands of Number, Algebra, Geometry, Measurement, and Statistics and Probability. Articles include an in-depth presentation of mathematical content, as well as suggested instructional strategies. Thus, the integration of content knowledge and pedagogical knowledge is emphasized. The second and third parts apply to assessments, mathematical games, teaching tips, and technological applications. While other pedagogical reference books may provide an in-depth look at how to teach a topic, this book includes articles that also explain a topic, in great length. Thus, teachers may develop content knowledge first and then re-read each article, in order to learn appropriate instructional strategies to use. Many articles include technological applications, which are interspersed throughout the book. In addition, a special section, which includes helpful information, available tools, training sessions, and other references, for using technology in mathematics, is also presented.

Author : Martin Aigner,Günter M. Ziegler
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 55,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662223437

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Proofs from THE BOOK by Martin Aigner,Günter M. Ziegler Pdf

According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Author : Mario Livio
Publisher : Simon and Schuster
Page : 320 pages
File Size : 43,9 Mb
Release : 2011-02-22
Category : Mathematics
ISBN : 9781416594437

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Is God a Mathematician? by Mario Livio Pdf

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 : Edward Nelson
Publisher : Princeton University Press
Page : 199 pages
File Size : 41,8 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400858927

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Predicative Arithmetic. (MN-32) by Edward Nelson Pdf

This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Noson S. Yanofsky
Publisher : MIT Press
Page : 419 pages
File Size : 42,7 Mb
Release : 2016-11-04
Category : Science
ISBN : 9780262529846

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The Outer Limits of Reason by Noson S. Yanofsky Pdf

This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve: • perfectly formed English sentences that make no sense • different levels of infinity • the bizarre world of the quantum • the relevance of relativity theory • the causes of chaos theory • math problems that cannot be solved by normal means • statements that are true but cannot be proven Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

Author : Thomas Crump
Publisher : Cambridge University Press
Page : 216 pages
File Size : 47,7 Mb
Release : 1992-10-15
Category : Mathematics
ISBN : 0521438071

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The Anthropology of Numbers by Thomas Crump Pdf

Numbers are an important feature of almost all known cultures. In this detailed anthropological study, Thomas Crump examines how people from a wide range of diverse cultures, and from different historical backgrounds, use and understand numbers. By looking at the logical, psychological and linguistic implications, he analyses how numbers operate within different contexts. The author goes on to consider the relationship of numbers to specific themes, such as ethnoscience, politics, measurement, time, money, music, games and architecture. The Anthropology of Numbers is an original contribution to scholarship, written in a clear and accessible style. It will be of interest to anthropologists who study cognition, symbolism, primitive thought and classification, and to those in adjacent disciplines of psychology, cognitive science and mathematical social science.

Author : John D. Barrow
Publisher : Oxford University Press, USA
Page : 344 pages
File Size : 53,8 Mb
Release : 1992
Category : Mathematics
ISBN : UOM:49015001378950

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Pi in the Sky by John D. Barrow Pdf

Famous cosmologist and prolific author John Barrow explores the origin and nature of mathematics and explains the important implications of the numerous unanswered questions in our search for a theory of everything. He weaves together a history of math that illuminates its far-reaching capabilities and its intrinsic limitations, its proven and unproven theories, and its pervasive impact on the way people think and live. Annotation copyrighted by Book News, Inc., Portland, OR