Download or read book Farey Sequences written by Andrey O. Matveev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-11-07 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a first comprehensive overview on Farey sequences and subsequences, this monograph is intended as a reference for anyone looking for specific material or formulas related to the subject. Duality of subsequences and maps between them are discussed and explicit proofs are shown in detail. From the Content Basic structural and enumerative properties of Farey sequences, Collective decision making, Committee methods in pattern recognition, Farey duality, Farey sequence, Fundamental Farey subsequences, Monotone bijections between Farey subsequences

Download or read book Algorithms ESA 2007 written by Lars Arge and published by Springer. This book was released on 2007-09-17 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th Annual European Symposium on Algorithms, ESA 2007, held in Eilat, Israel, in October 2007 in the context of the combined conference ALGO 2007. The 63 revised full papers presented together with abstracts of three invited lectures address all current subjects in algorithmics reaching from design and analysis issues of algorithms over to real-world applications and engineering of algorithms in various fields.

Download or read book Mathematical Diamonds written by Ross Honsberger and published by Cambridge University Press. This book was released on 2003-05-15 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collection of elementary mathematical problems with solutions. Ideal for students, teachers and general readers.

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 Computational Models of Rhythm and Meter written by Georg Boenn and published by Springer. This book was released on 2018-06-20 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the latest computational models of rhythm and meter that are based on number theory, combinatorics and pattern matching. Two computational models of rhythm and meter are evaluated: The first one explores a relatively new field in Mathematics, namely Combinatorics on Words, specifically Christoffel Words and the Burrows-Wheeler Transform, together with integer partitions. The second model uses filtered Farey Sequences in combination with specific weights that are assigned to inter-onset ratios. This work is assessed within the context of the current state of the art of tempo tracking and computational music transcription. Furthermore, the author discusses various representations of musical rhythm, which lead to the development of a new shorthand notation that will be useful for musicologists and composers. Computational Models of Rhythm and Meter also contains numerous investigations into the timing structures of human rhythm and metre perception carried out within the last decade. Our solution to the transcription problem has been tested using a wide range of musical styles, and in particular using two recordings of J.S. Bach's Goldberg Variations by Glenn Gould. The technology is capable of modelling musical rhythm and meter by using Farey Sequences, and by detecting duration classes in a windowed analysis, which also detects the underlying tempo. The outcomes represent human performances of music as accurate as possible within Western score notation.

Download or read book Geometry of Lengths Areas and Volumes written by James W. Cannon and published by American Mathematical Soc.. This book was released on 2017-11-16 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the Bolyai-Gerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straight-edge and compass constructions, giving complete proofs, including the transcendence of and , of the impossibility of squaring the circle, duplicating the cube, and trisecting the angle; and finally to a construction of the Hausdorff-Banach-Tarski paradox that shows some spherical sets are too complicated and cloudy to admit a well-defined notion of area.

Download or read book Continuous And Discontinuous Piecewise smooth One dimensional Maps Invariant Sets And Bifurcation Structures written by Viktor Avrutin and published by World Scientific. This book was released on 2019-05-28 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.

Download or read book Measurement Modelling and Evaluation of Computing Systems written by Holger Hermanns and published by Springer Nature. This book was released on 2020-03-09 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 20th International GI/ITG Conference on Measurement, Modelling and Evaluation of Computing Systems, MMB 2020, held in Saarbrücken, Germany, in March 2020. The 16 full papers presented in this volume were carefully reviewed and selected from 32 submissions. They are dealing with scientific aspects of measurement, modelling and evaluation of intelligent systems including computer architectures, communication networks, distributed systems and software, autonomous systems, workflow systems, cyber-physical systems and networks, Internet-of-Things, as well as highly dependable, highly performant and highly secure systems.

Download or read book Geometry of Continued Fractions written by Oleg N. Karpenkov and published by Springer Nature. This book was released on 2022-05-28 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects. 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. 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 An Invitation to Real Analysis written by Luis F. Moreno and published by The Mathematical Association of America. This book was released on 2015-05-17 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Invitation to Real Analysis is written both as a stepping stone to higher calculus and analysis courses, and as foundation for deeper reasoning in applied mathematics. This book also provides a broader foundation in real analysis than is typical for future teachers of secondary mathematics. In connection with this, within the chapters, students are pointed to numerous articles from The College Mathematics Journal and The American Mathematical Monthly. These articles are inviting in their level of exposition and their wide-ranging content. Axioms are presented with an emphasis on the distinguishing characteristics that new ones bring, culminating with the axioms that define the reals. Set theory is another theme found in this book, beginning with what students are familiar with from basic calculus. This theme runs underneath the rigorous development of functions, sequences, and series, and then ends with a chapter on transfinite cardinal numbers and with chapters on basic point-set topology. Differentiation and integration are developed with the standard level of rigor, but always with the goal of forming a firm foundation for the student who desires to pursue deeper study. A historical theme interweaves throughout the book, with many quotes and accounts of interest to all readers. Over 600 exercises and dozens of figures help the learning process. Several topics (continued fractions, for example), are included in the appendices as enrichment material. An annotated bibliography is included.

Download or read book Infinite Ergodic Theory of Numbers written by Marc Kesseböhmer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-10-10 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: By connecting dynamical systems and number theory, this graduate textbook on ergodic theory acts as an introduction to a highly active area of mathematics, where a variety of strands of research open up. The text explores various concepts in infinite ergodic theory, always using continued fractions and other number-theoretic dynamical systems as illustrative examples. Contents: Preface Mathematical symbols Number-theoretical dynamical systems Basic ergodic theory Renewal theory and α-sum-level sets Infinite ergodic theory Applications of infinite ergodic theory Bibliography Index

Download or read book All the Math That s Fit to Print written by Keith Devlin and published by Cambridge University Press. This book was released on 1994 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects many of the columns Keith Devlin wrote for The Guardian.

Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1951 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Compendium Of Musical Mathematics written by Franck Jedrzejewski and published by World Scientific. This book was released on 2024-02-28 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide a concise introduction to the mathematical theory of music, opening each chapter to the most recent research. Despite the complexity of some sections, the book can be read by a large audience. Many examples illustrate the concepts introduced. The book is divided into 9 chapters.In the first chapter, we tackle the question of the classification of chords and scales. Chapter 2 is a mathematical presentation of David Lewin's Generalized Interval Systems. Chapter 3 offers a new theory of diatonicity in equal-tempered universes. Chapter 4 presents the Neo-Riemannian theories based on the work of David Lewin, Richard Cohn and Henry Klumpenhouwer. Chapter 5 is devoted to the application of word combinatorics to music. Chapter 6 studies the rhythmic canons and the tessellation of the line. Chapter 7 is devoted to serial knots. Chapter 8 presents combinatorial designs and their applications to music. The last chapter, chapter 9, is dedicated to the study of tuning systems.

Download or read book Combinatorial Image Analysis written by Reinhard Klette and published by Springer. This book was released on 2004-11-03 with total page 771 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the 10th International Workshop on Combinatorial Image Analysis, held December 1–3, 2004, in Auckland, New Zealand. Prior meetings took place in Paris (France, 1991), Ube (Japan, 1992), Washington DC (USA, 1994), Lyon (France, 1995), Hiroshima (Japan, 1997), Madras (India, 1999), Caen (France, 2000), Philadelphia (USA, 2001), and - lermo (Italy, 2003). For this workshop we received 86 submitted papers from 23 countries. Each paper was evaluated by at least two independent referees. We selected 55 papers for the conference. Three invited lectures by Vladimir Kovalevsky (Berlin), Akira Nakamura (Hiroshima), and Maurice Nivat (Paris) completed the program. Conference papers are presented in this volume under the following topical part titles: discrete tomography (3 papers), combinatorics and computational models (6), combinatorial algorithms (6), combinatorial mathematics (4), d- ital topology (7), digital geometry (7), approximation of digital sets by curves and surfaces (5), algebraic approaches (5), fuzzy image analysis (2), image s- mentation (6), and matching and recognition (7). These subjects are dealt with in the context of digital image analysis or computer vision.

Download or read book A Pathway Into Number Theory written by R. P. Burn and published by Cambridge University Press. This book was released on 1996-11-28 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory is concerned with the properties of the natural numbers: 1, 2, 3 ... During the seventeenth and eighteenth centuries, number theory became established through the work of Fermat, Euler and Gauss. With the hand calculators and computers of today the results of extensive numerical work are instantly available and the road leading to their discoveries may be traversed with comparative care. Now in its second edition, this book consists of a sequence of exercises that will lead readers from quite simple number work to the point where they can prove algebraically the classical results of elementary number theory for themselves. A modern secondary school course in mathematics is sufficient background for the whole book which is designed to be used as an undergraduate course in number theory to be pursued by independent study without supporting lectures.

Download or read book Number Theory written by Tristin Cleveland and published by Scientific e-Resources. This book was released on 2018-04-11 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: In spite of the fact that arithmetic majors are generally familiar with number hypothesis when they have finished a course in conceptual polynomial math, different students, particularly those in training and the human sciences, regularly require a more essential prologue to the theme. In this book the writer takes care of the issue of keeping up the enthusiasm of understudies at the two levels by offering a combinatorial way to deal with basic number hypothesis. In concentrate number hypothesis from such a point of view, arithmetic majors are saved reiteration and furnished with new bits of knowledge, while different understudies advantage from the subsequent effortlessness of the verifications for some hypotheses. Of specific significance in this content is the creator's accentuation on the estimation of numerical cases in number hypothesis and the part of PCs in getting such illustrations. The point of this book is to acquaint the reader with essential subjects in number hypothesis: hypothesis of distinctness, arithmetrical capacities, prime numbers, geometry of numbers, added substance number hypothesis, probabilistic number hypothesis, hypothesis of Diophantine approximations and logarithmic number hypothesis.