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Author: Jonathan Borwein Publisher: Cambridge University Press ISBN: 1139991396 Category : Mathematics Languages : en Pages : 223
Book Description
Despite their classical nature, continued fractions are a neverending research area, with a body of results accessible enough to suit a wide audience, from researchers to students and even amateur enthusiasts. Neverending Fractions brings these results together, offering fresh perspectives on a mature subject. Beginning with a standard introduction to continued fractions, the book covers a diverse range of topics, from elementary and metric properties, to quadratic irrationals, to more exotic topics such as folded continued fractions and Somos sequences. Along the way, the authors reveal some amazing applications of the theory to seemingly unrelated problems in number theory. Previously scattered throughout the literature, these applications are brought together in this volume for the first time. A wide variety of exercises guide readers through the material, which will be especially helpful to readers using the book for self-study, and the authors also provide many pointers to the literature.
Author: Jonathan Borwein Publisher: Cambridge University Press ISBN: 1139991396 Category : Mathematics Languages : en Pages : 223
Book Description
Despite their classical nature, continued fractions are a neverending research area, with a body of results accessible enough to suit a wide audience, from researchers to students and even amateur enthusiasts. Neverending Fractions brings these results together, offering fresh perspectives on a mature subject. Beginning with a standard introduction to continued fractions, the book covers a diverse range of topics, from elementary and metric properties, to quadratic irrationals, to more exotic topics such as folded continued fractions and Somos sequences. Along the way, the authors reveal some amazing applications of the theory to seemingly unrelated problems in number theory. Previously scattered throughout the literature, these applications are brought together in this volume for the first time. A wide variety of exercises guide readers through the material, which will be especially helpful to readers using the book for self-study, and the authors also provide many pointers to the literature.
Author: Walter Van Assche Publisher: Cambridge University Press ISBN: 1108441947 Category : Mathematics Languages : en Pages : 192
Book Description
There are a number of intriguing connections between Painlev equations and orthogonal polynomials, and this book is one of the first to provide an introduction to these. Researchers in integrable systems and non-linear equations will find the many explicit examples where Painlev equations appear in mathematical analysis very useful. Those interested in the asymptotic behavior of orthogonal polynomials will also find the description of Painlev transcendants and their use for local analysis near certain critical points helpful to their work. Rational solutions and special function solutions of Painlev equations are worked out in detail, with a survey of recent results and an outline of their close relationship with orthogonal polynomials. Exercises throughout the book help the reader to get to grips with the material. The author is a leading authority on orthogonal polynomials, giving this work a unique perspective on Painlev equations.
Author: Peter J. Cameron Publisher: Cambridge University Press ISBN: 1108417361 Category : Mathematics Languages : en Pages : 235
Book Description
An introduction to enumerative combinatorics, vital to many areas of mathematics. It is suitable as a class text or for individual study.
Author: Timothy C. Burness Publisher: Cambridge University Press ISBN: 131643267X Category : Mathematics Languages : en Pages : 365
Book Description
A classical theorem of Jordan states that every finite transitive permutation group contains a derangement. This existence result has interesting and unexpected applications in many areas of mathematics, including graph theory, number theory and topology. Various generalisations have been studied in more recent years, with a particular focus on the existence of derangements with special properties. Written for academic researchers and postgraduate students working in related areas of algebra, this introduction to the finite classical groups features a comprehensive account of the conjugacy and geometry of elements of prime order. The development is tailored towards the study of derangements in finite primitive classical groups; the basic problem is to determine when such a group G contains a derangement of prime order r, for each prime divisor r of the degree of G. This involves a detailed analysis of the conjugacy classes and subgroup structure of the finite classical groups.
Author: Norvin Pallas Publisher: Courier Corporation ISBN: 0486157326 Category : Juvenile Nonfiction Languages : en Pages : 113
Book Description
Perform amazing feats of mathematical magic, answer clever riddles, solve a baffling murder, and much more with this clever introduction to calculator games. Answers included.
Author: Chrystine Skelly Publisher: S.E. Burr ISBN: Category : Juvenile Nonfiction Languages : en Pages : 28
Book Description
Poetry and rhymes have been shown to be an important and valuable part of literacy education, and kids love them! 11 authors and illustrators collaborated to create this book: Chrystine Skelly Elizabeth Burr Emily Mah Heather Cardon Matt Burr Melinda Burr Nathan Nichols S.E. Burr Shad Wilde Zel Hartman Zerin Nichols
Author: Pierre Dardot Publisher: Verso Books ISBN: 1786634740 Category : Political Science Languages : en Pages : 209
Book Description
Neoliberalism's war against democracy and how to resist it How do we explain the strange survival of the forces responsible for the 2008 economic crisis, one of the worst since 1929? How do we explain the fact that neoliberalism has emerged from the crisis strengthened? When it broke, a number of the most prominent economists hastened to announce the 'death' of neoliberalism. They regarded the pursuit of neoliberal policy as the fruit of dogmatism. For Pierre Dardot and Christian Laval, neoliberalism is no mere dogma. Supported by powerful oligarchies, it is a veritable politico-institutional system that obeys a logic of self-reinforcement. Far from representing a break, crisis has become a formidably effective mode of government. In showing how this system crystallized and solidified, the book explains that the neoliberal straitjacket has succeeded in preventing any course correction by progressively deactivating democracy. Increasing the disarray and demobilization, the so-called 'governmental' Left has actively helped strengthen this oligarchical logic. The latter could lead to a definitive exit from democracy in favour of expertocratic governance, free of any control. However, nothing has been decided yet. The revival of democratic activity, which we see emerging in the political movements and experiments of recent years, is a sign that the political confrontation with the neoliberal system and the oligarchical bloc has already begun.
Author: Egmont Colerus Publisher: Courier Corporation ISBN: 0486170330 Category : Mathematics Languages : en Pages : 274
Book Description
This witty and engaging stylebook presents the fundamentals of mathematical operations: number systems, first steps in algebra and algebraic notation, common fractions and equations, and much more. 1958 edition.
Author: Mohammad H. Tamdgidi Publisher: Ahead Publishing House (imprint: Okcir Press) ISBN: 1640980334 Category : Science Languages : en Pages : 799
Book Description
Omar Khayyam’s Secret: Hermeneutics of the Robaiyat in Quantum Sociological Imagination, by Mohammad H. Tamdgidi, is a twelve-book series of which this book is the sixth volume, subtitled Khayyami Science: The Methodological Structures of the Robaiyat in All the Scientific Works of Omar Khayyam. Each book, independently readable, can be best understood as a part of the whole series. In Book 6, Tamdgidi shares the Arabic texts, his new English translations (based on others’ or his new Persian translations, also included in the volume), and hermeneutic analyses of five extant scientific writings of Khayyam: a treatise in music on tetrachords; a treatise on balance to measure the weights of precious metals in a body composed of them; a treatise on dividing a circle quadrant to achieve a certain proportionality; a treatise on classifying and solving all cubic (and lower degree) algebraic equations using geometric methods; and a treatise on explaining three postulation problems in Euclid’s book Elements. Khayyam wrote three other non-extant scientific treatises on nature, geography, and music, while a treatise in arithmetic is differently extant since it influenced the work of later Islamic and Western scientists. His work in astronomy on solar calendar reform is also differently extant in the calendar used in Iran today. A short tract on astrology attributed to him has been neglected. Tamdgidi studies the scientific works in relation to Khayyam’s own theological, philosophical, and astronomical views. The study reveals that Khayyam’s science was informed by a unifying methodological attention to ratios and proportionality. So, likewise, any quatrain he wrote cannot be adequately understood without considering its place in the relational whole of its parent collection. Khayyam’s Robaiyat is found to be, as a critique of fatalistic astrology, his most important scientific work in astronomy rendered in poetic form. Studying Khayyam’s scientific works in relation to those of other scientists out of the context of his own philosophical, theological, and astronomical views, would be like comparing the roundness of two fruits while ignoring that they are apples and oranges. Khayyam was a relational, holistic, and self-including objective thinker, being systems and causal-chains discerning, creative, transdisciplinary, transcultural, and applied in method. He applied a poetic geometric imagination to solving algebraic problems and his logically methodical thinking did not spare even Euclid of criticism. His treatise on Euclid unified numerical and magnitudinal notions of ratio and proportionality by way of broadening the notion of number to include both rational and irrational numbers, transcending its Greek atomistic tradition. Khayyam’s classification of algebraic equations, being capped at cubic types, tells of his applied scientific intentions that can be interpreted, in the context of his own Islamic philosophy and theology, as an effort in building an algebraic and numerical theory of everything that is not only symbolic of body’s three dimensions, but also of the three-foldness of intellect, soul, and body as essential types of a unitary substance created by God to evolve relatively on its own in a two-fold succession order of coming from and going to its Source. Although the succession order poses limits, as captured in the astrological imagination, existence is not fatalistic. Khayyam’s conceptualist view of the human subject as an objective creative force in a participatory universe allows for the possibility of human self-determination and freedom depending on his or her self-awakening, a cause for which the Robaiyat was intended. Its collection would be a balanced unity of wisdom gems ascending from multiplicity toward unity using Wine and various astrological, geometrical, numerical, calendrical, and musical tropes in relationally classified quatrains that follow a logical succession order. CONTENTS About OKCIR—i Published to Date in the Series—ii About this Book—iv About the Author—viii Notes on Transliteration—xvii Acknowledgments—xix Preface to Book 6: Recap from Prior Books of the Series—1 Introduction to Book 6: Exploring the Methodology of the Robaiyat in Omar Khayyam’s Scientific Works—9 CHAPTER I—Omar Khayyam’s Treatise in Music on Tetrachords: The Arabic Text and New Persian and English Translations, Followed by Textual Analysis—19 CHAPTER II—Omar Khayyam’s Treatises on the Straight Balance and on How to Use a Water Balance to Measure the Weights of Gold and Silver in a Body Composed of Them: The Arabic Texts and New Persian and English Translations, Followed by Textual Analysis—61 CHAPTER III—Omar Khayyam’s Treatise on Dividing A Circle Quadrant: The Arabic Text, the Persian Translation by Gholamhossein Mosaheb, and Its New English Translation, Followed by Textual Analysis—119 CHAPTER IV—Omar Khayyam’s Treatise on the Proofs of Problems in Algebra and Equations: The Arabic Text, the Persian Translation by Gholamhossein Mosaheb, and Its New English Translation, Followed by Textual Analysis—203 CHAPTER V—Omar Khayyam’s Treatise on the Explanation of Postulation Problems in Euclid’s Work: The Arabic Text, the Persian Translation by Jalaleddin Homaei, and Its New English Translation, Followed by Textual Analysis—439 CHAPTER VI—The Robaiyat as a Critique of Fatalistic Astrology: Understanding Omar Khayyam’s Astronomy in Light of His Own Philosophical, Theological, and Scientific Outlook—623 Conclusion to Book 6: Summary of Findings—677 Appendix: Transliteration System and Glossary—717 Cumulative Glossary of Transliterations (Books 1-5)—730 Book 6 References—739 Book 6 Index—751
Author: Jonathan Borwein
Author: Jonathan Borwein
Author: Jonathan Borwein
Author: Walter Van Assche
Author: Peter J. Cameron
Author: Timothy C. Burness
Author: Norvin Pallas
Author: Chrystine Skelly
Author: Pierre Dardot
Author: Egmont Colerus
Author: Mohammad H. Tamdgidi