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Author: Dorin Andrica
Publisher: Springer Nature
ISBN: 3030515028
Category : Mathematics
Languages : en
Pages : 410
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Book Description
This self-contained text presents state-of-the-art results on recurrent sequences and their applications in algebra, number theory, geometry of the complex plane and discrete mathematics. It is designed to appeal to a wide readership, ranging from scholars and academics, to undergraduate students, or advanced high school and college students training for competitions. The content of the book is very recent, and focuses on areas where significant research is currently taking place. Among the new approaches promoted in this book, the authors highlight the visualization of some recurrences in the complex plane, the concurrent use of algebraic, arithmetic, and trigonometric perspectives on classical number sequences, and links to many applications. It contains techniques which are fundamental in other areas of math and encourages further research on the topic. The introductory chapters only require good understanding of college algebra, complex numbers, analysis and basic combinatorics. For Chapters 3, 4 and 6 the prerequisites include number theory, linear algebra and complex analysis. The first part of the book presents key theoretical elements required for a good understanding of the topic. The exposition moves on to to fundamental results and key examples of recurrences and their properties. The geometry of linear recurrences in the complex plane is presented in detail through numerous diagrams, which lead to often unexpected connections to combinatorics, number theory, integer sequences, and random number generation. The second part of the book presents a collection of 123 problems with full solutions, illustrating the wide range of topics where recurrent sequences can be found. This material is ideal for consolidating the theoretical knowledge and for preparing students for Olympiads.
Author: Dorin Andrica
Publisher: Springer Nature
ISBN: 3030515028
Category : Mathematics
Languages : en
Pages : 410
Get Book
Book Description
This self-contained text presents state-of-the-art results on recurrent sequences and their applications in algebra, number theory, geometry of the complex plane and discrete mathematics. It is designed to appeal to a wide readership, ranging from scholars and academics, to undergraduate students, or advanced high school and college students training for competitions. The content of the book is very recent, and focuses on areas where significant research is currently taking place. Among the new approaches promoted in this book, the authors highlight the visualization of some recurrences in the complex plane, the concurrent use of algebraic, arithmetic, and trigonometric perspectives on classical number sequences, and links to many applications. It contains techniques which are fundamental in other areas of math and encourages further research on the topic. The introductory chapters only require good understanding of college algebra, complex numbers, analysis and basic combinatorics. For Chapters 3, 4 and 6 the prerequisites include number theory, linear algebra and complex analysis. The first part of the book presents key theoretical elements required for a good understanding of the topic. The exposition moves on to to fundamental results and key examples of recurrences and their properties. The geometry of linear recurrences in the complex plane is presented in detail through numerous diagrams, which lead to often unexpected connections to combinatorics, number theory, integer sequences, and random number generation. The second part of the book presents a collection of 123 problems with full solutions, illustrating the wide range of topics where recurrent sequences can be found. This material is ideal for consolidating the theoretical knowledge and for preparing students for Olympiads.
Author: Graham Everest
Publisher: American Mathematical Soc.
ISBN: 1470423154
Category :
Languages : en
Pages : 318
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Book Description
Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
Author: Alex Graves
Publisher: Springer
ISBN: 3642247970
Category : Technology & Engineering
Languages : en
Pages : 148
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Book Description
Supervised sequence labelling is a vital area of machine learning, encompassing tasks such as speech, handwriting and gesture recognition, protein secondary structure prediction and part-of-speech tagging. Recurrent neural networks are powerful sequence learning tools—robust to input noise and distortion, able to exploit long-range contextual information—that would seem ideally suited to such problems. However their role in large-scale sequence labelling systems has so far been auxiliary. The goal of this book is a complete framework for classifying and transcribing sequential data with recurrent neural networks only. Three main innovations are introduced in order to realise this goal. Firstly, the connectionist temporal classification output layer allows the framework to be trained with unsegmented target sequences, such as phoneme-level speech transcriptions; this is in contrast to previous connectionist approaches, which were dependent on error-prone prior segmentation. Secondly, multidimensional recurrent neural networks extend the framework in a natural way to data with more than one spatio-temporal dimension, such as images and videos. Thirdly, the use of hierarchical subsampling makes it feasible to apply the framework to very large or high resolution sequences, such as raw audio or video. Experimental validation is provided by state-of-the-art results in speech and handwriting recognition.
Author: Benjamin Cornwell
Publisher: Cambridge University Press
ISBN: 1316368866
Category : Social Science
Languages : en
Pages : 339
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Book Description
Social sequence analysis includes a diverse and rapidly growing body of methods that social scientists have developed to help study complex ordered social processes, including chains of transitions, trajectories and other ordered phenomena. Social sequence analysis is not limited by content or time scale and can be used in many different fields, including sociology, communication, information science and psychology. Social Sequence Analysis aims to bring together both foundational and recent theoretical and methodological work on social sequences from the last thirty years. A unique reference book for a new generation of social scientists, this book will aid demographers who study life-course trajectories and family histories, sociologists who study career paths or work/family schedules, communication scholars and micro-sociologists who study conversation, interaction structures and small-group dynamics, as well as social epidemiologists.
Author: Library of Congress
Publisher:
ISBN:
Category : Subject headings, Library of Congress
Languages : en
Pages : 1432
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Book Description
Author: Colin Boyd
Publisher: Springer Science & Business Media
ISBN: 9783540606932
Category : Business & Economics
Languages : en
Pages : 308
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Book Description
This monograph provides a formal and systematic exposition of the main results on the existence and optimality of equilibria in economies with increasing returns to scale. For that, a general equilibrium model is carefully constructed first by means of a precise formalization of consumers and firms, and the proof of an abstract existence result. The analysis shifts then to the study of specific normative and positive models which are particularizations the general one, and to the study of the efficiency of equilibrium allocations. The book provides an unified approach of the topic, it maintains a relatively low mathematical complexity and offers a highly self-contained exposition.
Author: Mari Carmen Campoy
Publisher: Peter Lang
ISBN: 9783039112753
Category : Education
Languages : en
Pages : 288
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Book Description
This volume explores the opportunities that spoken corpora offer and the challenges of research with such corpora. The use and applications of spoken corpora are discussed from the perspective of both language analysis and language pedagogy. Twelve chapters written by corpus linguists analyse an extensive number of spoken corpora based on the oral production of speakers as varied as language learners, users of English as Lingua Franca, native speakers, or speakers of English in academic contexts. This book also highlights the growing emphasis on the use of corpus-based research by examining the implications of corpus findings in educational settings.
Author: Jonė Grigaliūnienė
Publisher: Cambridge Scholars Publishing
ISBN: 1443853852
Category : Language Arts & Disciplines
Languages : en
Pages : 284
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Book Description
This collection of papers offers diverse yet highly professional accounts of multiple cross-linguistic and cross-cultural aspects of English studies in Lithuania. It is valuable for the wide variety of empirical data presented, for the insights into both English and Lithuanian, which, when studied individually, sometimes cannot escape a narrower treatment. Most of the essays in this volume deal with semantics, pragmatics and grammar, while others focus on phonetics and language pedagogy. The collection is also notable for its use of various different methodologies, including triple CL – corpus linguistic, cognitive linguistic and contrastive linguistic – principles of investigation. A particular strength of the book is its focus on the contrastive aspect of study. Further, many of the contributions included here have profound implications for both translation and teaching.
Author: W. Narkiewicz
Publisher: Springer
ISBN: 3540390634
Category : Mathematics
Languages : en
Pages : 133
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Book Description
Author: Alekseĭ Ivanovich Markushevich
Publisher:
ISBN:
Category : Sequences (Mathematics).
Languages : en
Pages : 52
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Book Description
