Author: Julian Havil Publisher: Princeton University Press ISBN: 0691247676 Category : Mathematics Languages : en Pages : 320
Book Description
An entertaining and enlightening history of irrational numbers, from ancient Greece to the twenty-first century The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define—and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.
Author: Ivan Niven Publisher: Cambridge University Press ISBN: 9780883850381 Category : Mathematics Languages : en Pages : 180
Book Description
In this monograph, Ivan Niven provides a masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments. The approximation of irrational numbers by rationals, up to such results as the best possible approximation of Hurwitz, is also given with elementary technique. The last third of the monograph treats normal and transcendental numbers, including the Lindemann theorem, and the Gelfond-Schneider theorem. The book is wholly self-contained. The results needed from analysis and algebra are central. Well-known theorems, and complete references to standard works are given to help the beginner. The chapters are for the most part independent. There are notes at the end of each chapter citing the main sources used by the author and suggesting further reading.
Author: Julian Havil Publisher: Princeton University Press ISBN: 1400841704 Category : Mathematics Languages : en Pages : 311
Book Description
The first popular history of irrational numbers and their discoverers, from ancient Greece to the twenty-first century The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define—and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.
Author: Eric R. Dodds Publisher: Univ of California Press ISBN: 0520242300 Category : History Languages : en Pages : 336
Book Description
In this philosophy classic, which was first published in 1951, E. R. Dodds takes on the traditional view of Greek culture as a triumph of rationalism. Using the analytical tools of modern anthropology and psychology, Dodds asks, "Why should we attribute to the ancient Greeks an immunity from 'primitive' modes of thought which we do not find in any society open to our direct observation?" Praised by reviewers as "an event in modern Greek scholarship" and "a book which it would be difficult to over-praise," The Greeks and the Irrational was Volume 25 of the Sather Classical Lectures series.
Author: Mike Ivsin Publisher: Lulu.com ISBN: 1847288480 Category : Science Languages : en Pages : 361
Book Description
Numbers, operators, and degrees of independence facilitate creation and organization of the real environment. The explanation and application of quantum mechanics on atomic and cosmic scales is suggested by the Pythagorean tradition
Author: D.G.H.B. Lloyd Publisher: Elsevier ISBN: 1483139808 Category : Mathematics Languages : en Pages : 247
Book Description
Modern Syllabus Algebra presents topics of traditional and modern algebra found in the Teachers Certificate and B.Ed, part I syllabuses of University Institutes of Education. It also contains additional exercises taken from examination papers of the University of London Institute of Education (the Teachers' Certificate). The book discusses several mathematical concepts such as sets, relations and functions, Boolean algebra, groups, and number systems. It also illustrates linear equations, matrices, and vector spaces and then demonstrates how to solve complex numbers and combine probabilities. Mathematics teachers will find this text a suitable and convenient way of bringing themselves up to date in what is now being taught in schools.
Author: William C. Bauldry Publisher: John Wiley & Sons ISBN: 0470371366 Category : Mathematics Languages : en Pages : 279
Book Description
An accessible introduction to real analysis and its connection to elementary calculus Bridging the gap between the development and history of real analysis, Introduction to Real Analysis: An Educational Approach presents a comprehensive introduction to real analysis while also offering a survey of the field. With its balance of historical background, key calculus methods, and hands-on applications, this book provides readers with a solid foundation and fundamental understanding of real analysis. The book begins with an outline of basic calculus, including a close examination of problems illustrating links and potential difficulties. Next, a fluid introduction to real analysis is presented, guiding readers through the basic topology of real numbers, limits, integration, and a series of functions in natural progression. The book moves on to analysis with more rigorous investigations, and the topology of the line is presented along with a discussion of limits and continuity that includes unusual examples in order to direct readers' thinking beyond intuitive reasoning and on to more complex understanding. The dichotomy of pointwise and uniform convergence is then addressed and is followed by differentiation and integration. Riemann-Stieltjes integrals and the Lebesgue measure are also introduced to broaden the presented perspective. The book concludes with a collection of advanced topics that are connected to elementary calculus, such as modeling with logistic functions, numerical quadrature, Fourier series, and special functions. Detailed appendices outline key definitions and theorems in elementary calculus and also present additional proofs, projects, and sets in real analysis. Each chapter references historical sources on real analysis while also providing proof-oriented exercises and examples that facilitate the development of computational skills. In addition, an extensive bibliography provides additional resources on the topic. Introduction to Real Analysis: An Educational Approach is an ideal book for upper- undergraduate and graduate-level real analysis courses in the areas of mathematics and education. It is also a valuable reference for educators in the field of applied mathematics.
Author: Charles Seife Publisher: Penguin ISBN: 9780140296471 Category : Mathematics Languages : en Pages : 260
Book Description
Popular math at its most entertaining and enlightening. "Zero is really something"-Washington Post A New York Times Notable Book. The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics. Now it threatens the foundations of modern physics. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything. In Zero, Science Journalist Charles Seife follows this innocent-looking number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe, its rise and transcendence in the West, and its ever-present threat to modern physics. Here are the legendary thinkers—from Pythagoras to Newton to Heisenberg, from the Kabalists to today's astrophysicists—who have tried to understand it and whose clashes shook the foundations of philosophy, science, mathematics, and religion. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything.
Author: Nathan Coombs Publisher: Edinburgh University Press ISBN: 0748699007 Category : Philosophy Languages : en Pages : 224
Book Description
Nathan Coombs demonstrates that the Marxist science of history has been reimagined by a strand of contemporary French theory after Louis Althusser. Taking a comparative approach, Coombs explores the technical details of both traditions' historical sciences.
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Author: Julian Havil
Author: Ivan Niven
Author: Julian Havil
Author: Eric R. Dodds
Author: Mike Ivsin
Author: D.G.H.B. Lloyd
Author: William C. Bauldry
Author: Charles Seife
Author: Peter G. Hinman
Author: Nathan Coombs