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The Partition Method for a Power Series Expansion: Theory and Applications explores how the method known as 'the partition method for a power series expansion', which was developed by the author, can be applied to a host of previously intractable problems in mathematics and physics. In particular, this book describes how the method can be used to determine the Bernoulli, cosecant, and reciprocal logarithm numbers, which appear as the coefficients of the resulting power series expansions, then also extending the method to more complicated situations where the coefficients become polynomials or mathematical functions. From these examples, a general theory for the method is presented, which enables a programming methodology to be established. Finally, the programming techniques of previous chapters are used to derive power series expansions for complex generating functions arising in the theory of partitions and in lattice models of statistical mechanics. - Explains the partition method by presenting elementary applications involving the Bernoulli, cosecant, and reciprocal logarithm numbers - Compares generating partitions via the BRCP algorithm with the standard lexicographic approaches - Describes how to program the partition method for a power series expansion and the BRCP algorithm
The Art of Computer Programming, Volume 4A: Combinatorial Algorithms, Part 1 Knuth’s multivolume analysis of algorithms is widely recognized as the definitive description of classical computer science. The first three volumes of this work have long comprised a unique and invaluable resource in programming theory and practice. Scientists have marveled at the beauty and elegance of Knuth’s analysis, while practicing programmers have successfully applied his “cookbook” solutions to their day-to-day problems. The level of these first three volumes has remained so high, and they have displayed so wide and deep a familiarity with the art of computer programming, that a sufficient “review” of future volumes could almost be: “Knuth, Volume n has been published.” –Data Processing Digest Knuth, Volume n has been published, where n = 4A. In this long-awaited new volume, the old master turns his attention to some of his favorite topics in broadword computation and combinatorial generation (exhaustively listing fundamental combinatorial objects, such as permutations, partitions, and trees), as well as his more recent interests, such as binary decision diagrams. The hallmark qualities that distinguish his previous volumes are manifest here anew: detailed coverage of the basics, illustrated with well-chosen examples; occasional forays into more esoteric topics and problems at the frontiers of research; impeccable writing peppered with occasional bits of humor; extensive collections of exercises, all with solutions or helpful hints; a careful attention to history; implementations of many of the algorithms in his classic step-by-step form. There is an amazing amount of information on each page. Knuth has obviously thought long and hard about which topics and results are most central and important, and then, what are the most intuitive and succinct ways of presenting that material. Since the areas that he covers in this volume have exploded since he first envisioned writing about them, it is wonderful how he has managed to provide such thorough treatment in so few pages. –Frank Ruskey, Department of Computer Science, University of Victoria The book is Volume 4A, because Volume 4 has itself become a multivolume undertaking. Combinatorial searching is a rich and important topic, and Knuth has too much to say about it that is new, interesting, and useful to fit into a single volume, or two, or maybe even three. This book alone includes approximately 1500 exercises, with answers for self-study, plus hundreds of useful facts that cannot be found in any other publication. Volume 4A surely belongs beside the first three volumes of this classic work in every serious programmer’s library. Finally, after a wait of more than thirty-five years, the first part of Volume 4 is at last ready for publication. Check out the boxed set that brings together Volumes 1 - 4A in one elegant case, and offers the purchaser a $50 discount off the price of buying the four volumes individually. Ebook (PDF version) produced by Mathematical Sciences Publishers (MSP),http://msp.org The Art of Computer Programming, Volumes 1-4A Boxed Set, 3/e ISBN: 0321751043
This book constitutes the refereed proceedings of the 8th International Conference on Combinatorial Optimization and Applications, COCOA 2014, held on the island of Maui, Hawaii, USA, in December 2014. The 56 full papers included in the book were carefully reviewed and selected from 133 submissions. Topics covered include classic combinatorial optimization; geometric optimization; network optimization; optimization in graphs; applied optimization; CSoNet; and complexity, cryptography, and games.
With the encroachment of the Internet into nearly all aspects of work and life, it seems as though information is everywhere. However, there is information and then there is correct, appropriate, and timely information. While we might love being able to turn to Wikipedia for encyclopedia-like information or search Google for the thousands of links
This book presents extended versions of papers originally presented and discussed at the 3rd International Doctoral Symposium on Applied Computation and Security Systems (ACSS 2016) held from August 12 to 14, 2016 in Kolkata, India. The symposium was jointly organized by the AGH University of Science & Technology, Cracow, Poland; Ca’ Foscari University, Venice, Italy; and the University of Calcutta, India. The book is divided into two volumes, Volumes 3 and 4, and presents dissertation works in the areas of Image Processing, Biometrics-based Authentication, Soft Computing, Data Mining, Next-Generation Networking and Network Security, Remote Healthcare, Communications, Embedded Systems, Software Engineering and Service Engineering. The first two volumes of the book published the works presented at the ACSS 2015, which was held from May 23 to 25, 2015 in Kolkata, India.
Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.
This book contains revised and extended versions of selected papers from the 5th International Conference on Pattern Recognition, ICPRAM 2016, held in Rome, Italy, in February 2016. The 13 full papers were carefully reviewed and selected from 125 initial submissions and describe up-to-date applications of pattern recognition techniques to real-world problems, interdisciplinary research, experimental and/or theoretical studies yielding new insights that advance pattern recognition methods.
Python Algorithms explains the Python approach to algorithm analysis and design. Written by Magnus Lie Hetland, author of Beginning Python, this book is sharply focused on classical algorithms, but it also gives a solid understanding of fundamental algorithmic problem-solving techniques. The book deals with some of the most important and challenging areas of programming and computer science, but in a highly pedagogic and readable manner. The book covers both algorithmic theory and programming practice, demonstrating how theory is reflected in real Python programs. Well-known algorithms and data structures that are built into the Python language are explained, and the user is shown how to implement and evaluate others himself.
Founded in 1931 by Otto Neugebauer as the printed documentation service “Zentralblatt für Mathematik und ihre Grenzgebiete”, Zentralblatt MATH (ZBMATH) celebrates its 80th anniversary in 2011. Today it is the most comprehensive and active reference database in pure and applied mathematics worldwide. Many prominent mathematicians have been involved in this service as reviewers or editors and have, like all mathematicians, left their footprints in ZBMATH, in a long list of entries describing all of their research publications in mathematics. This book provides one review from each of the 80 years of ZBMATH. Names like Courant, Kolmogorov, Hardy, Hirzebruch, Faltings and many others can be found here. In addition to the original reviews, the book offers the authors' profiles indicating their co-authors, their favorite journals and the time span of their publication activities. In addition to this, a generously illustrated essay by Silke Göbel describes the history of ZBMATH.
This book constitutes the refereed proceedings of the International Conference on Intelligent Computer Mathematics, CICM 2015, held in Washington, DC, USA, in July 2015. The 16 full papers and 9 short papers presented together with two invited talks plus one abstract were carefully reviewed and selected from a total of 43 submissions. The papers are organized in topical sections following the tracks of the conference: Invited Talks; Calculemus; Digital Mathematics Libraries; Mathematical Knowledge Management; Projects and Surveys; Systems and Data.