Combinatorial And Computational Algebra

Author : Raina Robeva,Matthew Macauley
Publisher : Academic Press
Page : 434 pages
File Size : 41,5 Mb
Release : 2018-10-08
Category : Mathematics
ISBN : 9780128140697

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Algebraic and Combinatorial Computational Biology by Raina Robeva,Matthew Macauley Pdf

Algebraic and Combinatorial Computational Biology introduces students and researchers to a panorama of powerful and current methods for mathematical problem-solving in modern computational biology. Presented in a modular format, each topic introduces the biological foundations of the field, covers specialized mathematical theory, and concludes by highlighting connections with ongoing research, particularly open questions. The work addresses problems from gene regulation, neuroscience, phylogenetics, molecular networks, assembly and folding of biomolecular structures, and the use of clustering methods in biology. A number of these chapters are surveys of new topics that have not been previously compiled into one unified source. These topics were selected because they highlight the use of technique from algebra and combinatorics that are becoming mainstream in the life sciences. Integrates a comprehensive selection of tools from computational biology into educational or research programs Emphasizes practical problem-solving through multiple exercises, projects and spinoff computational simulations Contains scalable material for use in undergraduate and graduate-level classes and research projects Introduces the reader to freely-available professional software Supported by illustrative datasets and adaptable computer code

Author : Ilias S. Kotsireas,Eugene V. Zima
Publisher : Springer Science & Business Media
Page : 174 pages
File Size : 55,9 Mb
Release : 2009-11-06
Category : Mathematics
ISBN : 9783642035623

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Advances in Combinatorial Mathematics by Ilias S. Kotsireas,Eugene V. Zima Pdf

The Second Waterloo Workshop on Computer Algebra was dedicated to the 70th birthday of combinatorics pioneer Georgy Egorychev. This book of formally-refereed papers submitted after that workshop covers topics closely related to Egorychev’s influential works.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 305 pages
File Size : 52,5 Mb
Release : 2000
Category : Algebra
ISBN : 0821856006

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Combinatorial and Computational Algebra by Anonim Pdf

Author : Kai-Yuen Chan,Alexander A. Mikhalev,Man-Keung Siu,Jie-Tai Yu,Efim I. Zelmanov
Publisher : American Mathematical Soc.
Page : 318 pages
File Size : 47,7 Mb
Release : 2000
Category : Algebra
ISBN : 9780821819845

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Combinatorial and Computational Algebra by Kai-Yuen Chan,Alexander A. Mikhalev,Man-Keung Siu,Jie-Tai Yu,Efim I. Zelmanov Pdf

This volume presents articles based on the talks at the International Conference on Combinatorial and Computational Algebra held at the University of Hong Kong (China). The conference was part of the Algebra Program at the Institute of Mathematical Research and the Mathematics Department at the University of Hong Kong. Topics include recent developments in the following areas: combinatorial and computational aspects of group theory, combinatorial and computational aspects of associative and nonassociative algebras, automorphisms of polynomial algebras and the Jacobian conjecture, and combinatorics and coding theory. This volume can serve as a solid introductory guide for advanced graduate students, as well as a rich and up-to-date reference source for contemporary researchers in the field.

Author : Dimitry Kozlov
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 48,5 Mb
Release : 2008-01-08
Category : Mathematics
ISBN : 3540730516

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Combinatorial Algebraic Topology by Dimitry Kozlov Pdf

This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.

Author : Veronika Pillwein,Carsten Schneider
Publisher : Springer Nature
Page : 415 pages
File Size : 52,8 Mb
Release : 2020-09-28
Category : Computers
ISBN : 9783030445591

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Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra by Veronika Pillwein,Carsten Schneider Pdf

The book is centered around the research areas of combinatorics, special functions, and computer algebra. What these research fields share is that many of their outstanding results do not only have applications in Mathematics, but also other disciplines, such as computer science, physics, chemistry, etc. A particular charm of these areas is how they interact and influence one another. For instance, combinatorial or special functions' techniques have motivated the development of new symbolic algorithms. In particular, first proofs of challenging problems in combinatorics and special functions were derived by making essential use of computer algebra. This book addresses these interdisciplinary aspects. Algorithmic aspects are emphasized and the corresponding software packages for concrete problem solving are introduced. Readers will range from graduate students, researchers to practitioners who are interested in solving concrete problems within mathematics and other research disciplines.

Author : Arjeh M. Cohen,Hans Cuypers,Hans Sterk
Publisher : Springer Science & Business Media
Page : 365 pages
File Size : 50,6 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9783662038918

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Some Tapas of Computer Algebra by Arjeh M. Cohen,Hans Cuypers,Hans Sterk Pdf

This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation. A wide range of topics are presented, including: Groebner bases, real algebraic geometry, lie algebras, factorization of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must read for anyone working in the area of computer algebra, symbolic computation, and computer science.

Author : G.M. Piacentini Cattaneo,Elisabetta Strickland
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401134248

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Topics in Computational Algebra by G.M. Piacentini Cattaneo,Elisabetta Strickland Pdf

The main purpose of these lectures is first to briefly survey the fundamental con nection between the representation theory of the symmetric group Sn and the theory of symmetric functions and second to show how combinatorial methods that arise naturally in the theory of symmetric functions lead to efficient algorithms to express various prod ucts of representations of Sn in terms of sums of irreducible representations. That is, there is a basic isometry which maps the center of the group algebra of Sn, Z(Sn), to the space of homogeneous symmetric functions of degree n, An. This basic isometry is known as the Frobenius map, F. The Frobenius map allows us to reduce calculations involving characters of the symmetric group to calculations involving Schur functions. Now there is a very rich and beautiful theory of the combinatorics of symmetric functions that has been developed in recent years. The combinatorics of symmetric functions, then leads to a number of very efficient algorithms for expanding various products of Schur functions into a sum of Schur functions. Such expansions of products of Schur functions correspond via the Frobenius map to decomposing various products of irreducible representations of Sn into their irreducible components. In addition, the Schur functions are also the characters of the irreducible polynomial representations of the general linear group over the complex numbers GLn(C).

Author : Ilias S. Kotsireas,Eugene V. Zima
Publisher : Springer Science & Business Media
Page : 293 pages
File Size : 48,6 Mb
Release : 2013-08-04
Category : Mathematics
ISBN : 9783642309793

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Advances in Combinatorics by Ilias S. Kotsireas,Eugene V. Zima Pdf

This volume, as Andrew M. Odlzyko writes in the foreword, “commemorates and celebrates the life and achievements of an extraordinary person.” Originally conceived as an 80th birthday tribute to Herbert Wilf, the well-known combinatorialist, the book has evolved beyond the proceeds of the W80 tribute. Professor Wilf was an award-winning teacher, who was supportive of women mathematicians, and who had an unusually high proportion of women among his PhD candidates. He was Editor-in-chief of the American Mathematical Monthly and a founder of both the Journal of Algorithms and of the Electronic Journal of Combinatorics. But he was first a researcher, driven by his desire to know and explain the inner workings of the mathematical world. The book collects high-quality, refereed research contributions by some of Professor Wilf’s colleagues, students, and collaborators. Many of the papers presented here were featured in the Third Waterloo Workshop on Computer Algebra (WWCA 2011, W80), held May 26-29, 2011 at Wilfrid Laurier University, Waterloo, Canada. Others were included because of their relationship to his important work in combinatorics. All are presented as a tribute to Herb Wilf’s contributions to mathematics and mathematical life.

Author : Jacob E. Goodman,Janos Pach,Emo Welzl
Publisher : Cambridge University Press
Page : 640 pages
File Size : 43,5 Mb
Release : 2005-08-08
Category : Computers
ISBN : 0521848628

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Combinatorial and Computational Geometry by Jacob E. Goodman,Janos Pach,Emo Welzl Pdf

This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.

Author : George E. Andrews
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 46,8 Mb
Release : 1986-01-01
Category : Mathematics
ISBN : 0821889117

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Q-series by George E. Andrews Pdf

Author : Wieb Bosma,Alf van der Poorten
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 44,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401711081

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Computational Algebra and Number Theory by Wieb Bosma,Alf van der Poorten Pdf

Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few. Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed. Audience: Students, experts, and those performing current research in any of the topics mentioned above.

Author : Thomas Beth,Michael Clausen
Publisher : Springer Science & Business Media
Page : 228 pages
File Size : 48,5 Mb
Release : 1988-05-04
Category : Computers
ISBN : 354019200X

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Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra by Thomas Beth,Michael Clausen Pdf

This volume contains the proceedings of the 4th International Conference on Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra (AAECC-4), held in Karlsruhe, 23-26 September, 1986. Selected papers which were given at the conference have been reviewed a second time and are presented here.

Author : H. Crapo,D. Senato
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9788847021075

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Algebraic Combinatorics and Computer Science by H. Crapo,D. Senato Pdf

This book, dedicated to the memory of Gian-Carlo Rota, is the result of a collaborative effort by his friends, students and admirers. Rota was one of the great thinkers of our times, innovator in both mathematics and phenomenology. I feel moved, yet touched by a sense of sadness, in presenting this volume of work, despite the fear that I may be unworthy of the task that befalls me. Rota, both the scientist and the man, was marked by a generosity that knew no bounds. His ideas opened wide the horizons of fields of research, permitting an astonishing number of students from all over the globe to become enthusiastically involved. The contagious energy with which he demonstrated his tremendous mental capacity always proved fresh and inspiring. Beyond his renown as gifted scientist, what was particularly striking in Gian-Carlo Rota was his ability to appreciate the diverse intellectual capacities of those before him and to adapt his communications accordingly. This human sense, complemented by his acute appreciation of the importance of the individual, acted as a catalyst in bringing forth the very best in each one of his students. Whosoever was fortunate enough to enjoy Gian-Carlo Rota's longstanding friendship was most enriched by the experience, both mathematically and philosophically, and had occasion to appreciate son cote de bon vivant. The book opens with a heartfelt piece by Henry Crapo in which he meticulously pieces together what Gian-Carlo Rota's untimely demise has bequeathed to science.

Author : Viviana Ene,Ezra Miller
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 46,9 Mb
Release : 2009-11-25
Category : Mathematics
ISBN : 9780821847589

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Combinatorial Aspects of Commutative Algebra by Viviana Ene,Ezra Miller Pdf

This volume contains the proceedings of the Exploratory Workshop on Combinatorial Commutative Algebra and Computer Algebra, which took place in Mangalia, Romania on May 29-31, 2008. It includes research papers and surveys reflecting some of the current trends in the development of combinatorial commutative algebra and related fields. This volume focuses on the presentation of the newest research results in minimal resolutions of polynomial ideals (combinatorial techniques and applications), Stanley-Reisner theory and Alexander duality, and applications of commutative algebra and of combinatorial and computational techniques in algebraic geometry and topology. Both the algebraic and combinatorial perspectives are well represented and some open problems in the above directions have been included.