Download or read book Solving the Pell Equation written by Michael Jacobson and published by Springer Science & Business Media. This book was released on 2008-12-04 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pell’s Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very active, as can be seen by the publication of at least 150 articles related to this equation over the past decade. However, very few modern books have been published on Pell’s Equation, and this will be the first to give a historical development of the equation, as well as to develop the necessary tools for solving the equation. The authors provide a friendly introduction for advanced undergraduates to the delights of algebraic number theory via Pell’s Equation. The only prerequisites are a basic knowledge of elementary number theory and abstract algebra. There are also numerous references and notes for those who wish to follow up on various topics.

Download or read book Pell s Equation written by Edward J. Barbeau and published by Springer Science & Business Media. This book was released on 2006-05-04 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pell's equation is part of a central area of algebraic number theory that treats quadratic forms and the structure of the rings of integers in algebraic number fields. It is an ideal topic to lead college students, as well as some talented and motivated high school students, to a better appreciation of the power of mathematical technique. Even at the specific level of quadratic diophantine equations, there are unsolved problems, and the higher degree analogues of Pell's equation, particularly beyond the third, do not appear to have been well studied. In this focused exercise book, the topic is motivated and developed through sections of exercises which will allow the readers to recreate known theory and provide a focus for their algebraic practice. There are several explorations that encourage the reader to embark on their own research. A high school background in mathematics is all that is needed to get into this book, and teachers and others interested in mathematics who do not have (or have forgotten) a background in advanced mathematics may find that it is a suitable vehicle for keeping up an independent interest in the subject.

Download or read book Solving Pell s Equation Using Continued Fraction written by Yee Shyuan Lee and published by . This book was released on 2007 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Continued Fractions written by Carl Douglas Olds and published by Mathematical Association of America (MAA). This book was released on 1963 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Continued Fractions written by A. M. Rockett and published by World Scientific. This book was released on 1992-08-01 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.

Download or read book The Pell Equation written by Edward Everett Whitford and published by . This book was released on 1912 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematics and Its History written by John Stillwell and published by Springer Nature. This book was released on 2020-11-07 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course. The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed. From reviews of previous editions: “Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel.... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition

Download or read book Continued Fractions written by Source Wikipedia and published by University-Press.org. This book was released on 2013-09 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 50. Chapters: Continued fraction, Pell's equation, Mathematical constants, Mobius transformation, Generalized continued fraction, Incomplete gamma function, Gauss's continued fraction, Pade table, Stern-Brocot tree, Silver ratio, Minkowski's question mark function, Solving quadratic equations with continued fractions, Convergence problem, Periodic continued fraction, Khinchin's constant, Gauss-Kuzmin-Wirsing operator, Pade approximant, Engel expansion, Euler's continued fraction formula, Complete quotient, Restricted partial quotients, Rogers-Ramanujan continued fraction, Gauss-Kuzmin distribution, Convergent, Stieltjes transformation, Fundamental recurrence formulas, Chain sequence, Levy's constant, Lochs' theorem.

Download or read book An Introduction to Diophantine Equations written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2010-09-02 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

Download or read book Continued Fractions written by Eric Skouson and published by . This book was released on 2001 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Certain subsets of continued fractions correspond exactly with certain subsets of real numbers. Finite simple continued fractions correspond exactly to rational numbers. Infinite simple continued fractions correspond to irrational numbers, and periodic simple continued fractions to quadratic irrationals. We also show that continued fractions provide the best rational approximations to irrational numbers. The properties of continued fractions make them useful for many applications. They can be used to solve Pell's equations, and all solutions to a given Pell equation can be described as powers of a fundamental unit generated by a continued fraction. Graphs of some Pell equations can also used to demonstrate some of the properties of continued fractions. Using continued fractions one can establish sequences of natural triangles approaching certain classic right triangle shapes, and this procedure can sometimes be extended to other triangles. Continued fractions also have an interesting relationship with certain 2x2 matrices. For example matrices can be used to more quickly calculate the value of a periodic irrational. This relationship can also be used to develop a semi-group of 2x2 matrices. Properties of continued fractions and their relationship to these matrices can be used to show that all elements of the semi- group have a unique factorization, and that symmetric elements have a palindromic factorization"--Document.

Download or read book An Introduction to Continued Fractions written by Charles Godat Moore and published by . This book was released on 1964 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Pell Equation and Continued Fraction Expansion written by Hideo Wada and published by . This book was released on 1978 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Continued Fractions and Pell s Equation written by Shari Harris and published by . This book was released on 1991 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometry of Continued Fractions written by Oleg Karpenkov and published by Springer Science & Business Media. This book was released on 2013-08-15 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.

Download or read book Solutions to a Generalized Pell Equation written by Kyle Christopher Castro and published by . This book was released on 2012 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study aims to extend the notion of continued fractions to a new field Q ( x )*, in order to find solutions to generalized Pell's Equations in Q [ x ] . The investigation of these new solutions to Pell's Equation will begin with the necessary extensions of theorems as they apply to polynomials with rational coefficients and fractions of such polynomials in order to describe each "family" of solutions.

Download or read book Neverending Fractions written by Jonathan Borwein and published by Cambridge University Press. This book was released on 2014-07-03 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text covers a variety of applications to interest every reader, from researchers to amateur mathematicians.

Download or read book On Problems Related to Multiple Solutions of Pell s Equation and Continued Fractions Over Function Fields written by Nikoleta Dianova Kalaydzhieva and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: