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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: 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: 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: 0520931270 Category : Philosophy 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: Ivan Niven Publisher: American Mathematical Soc. ISBN: 1614440115 Category : Irrational numbers Languages : en Pages : 164
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 techniques. The last third of the monograph treats normal and transcendental numbers, including the transcendence of p and its generalization in the Lindermann theorem, and the Gelfond-Schneider theorem. Most of the material in the first two thirds of the book presupposes only calculus and beginning number theory. The book is almost wholly self-contained. The results needed from analysis and algebra are central and well-known theorems, and complete references to standard works are given to help the beginner. The chapters are, for the most part, independent. There is a set of 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: 0691247668 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: Dan Ariely Publisher: Harper Collins ISBN: 006135323X Category : Business & Economics Languages : en Pages : 310
Book Description
Intelligent, lively, humorous, and thoroughly engaging, "The Predictably Irrational" explains why people often make bad decisions and what can be done about it.
Author: Franz Halter-Koch Publisher: CRC Press ISBN: 1466591846 Category : Mathematics Languages : en Pages : 431
Book Description
Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms, and class groups.T
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: Mari Fitzduff Publisher: Bloomsbury Publishing USA ISBN: Category : Political Science Languages : en Pages : 249
Book Description
The 2016 election has inspired millions of U.S. citizens-and struck panic in the hearts of millions more. This book explains the allure of Trump, examines how Trump's success ties into the hopes and fears of many Americans, and calls into question the limitations of our democratic system. Across the United States and around the world, people are struggling to understand why so many turned to Donald Trump-an individual described as rude and insensitive at best, and as racist, hateful, and ignorant at worst-as their champion. Trump's nomination as the Republican presidential candidate, and his subsequent election to president of the United States, upended many long-held assumptions and beliefs about politics, such as the inevitable power of superfunding election syndicates and the need for presidential candidates to have governance experience and broad knowledge of domestic and foreign affairs. Why Irrational Politics Appeals: Understanding the Allure of Trump takes a serious, scientific look at Trump and his politics against the backdrop of modern American society. It brings together experts from a variety of psychological and political science fields to answer the mystifying question of why people by the millions would follow a leader who to so many others seems unqualified, undiplomatic, and in opposition to previously established standards for a national leader. Readers will gain an understanding of how little a role rationality plays in political choices, particularly-but not always-among citizens of certain socioeconomic backgrounds; and why Trump's apparently divisive attitudes and prejudices, his lack of "political correctness," and his hubris appeal to so many voters. The book also raises questions about our democratic processes, and our need for more thoughtful political cultures to ensure that citizens are adequately prepared to make important leadership decisions that will affect the future of our nation's economy, social norms, and global safety.
Author: Julian Havil
Author: Julian Havil
Author: Julian Havil
Author: Eric R. Dodds
Author: Ivan Niven
Author: Julian Havil
Author: Dan Ariely
Author: Franz Halter-Koch
Author: William C. Bauldry
Author: Mari Fitzduff
Author: Euclid