The Mathematics Of Chip Firing

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The Mathematics Of Chip Firing

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Author : Caroline J. Klivans
language : en
Publisher: CRC Press
Release Date : 2018-11-15

The Mathematics Of Chip Firing written by Caroline J. Klivans and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-15 with Computers categories.

The Mathematics of Chip-firing is a solid introduction and overview of the growing field of chip-firing. It offers an appreciation for the richness and diversity of the subject. Chip-firing refers to a discrete dynamical system — a commodity is exchanged between sites of a network according to very simple local rules. Although governed by local rules, the long-term global behavior of the system reveals fascinating properties. The Fundamental properties of chip-firing are covered from a variety of perspectives. This gives the reader both a broad context of the field and concrete entry points from different backgrounds. Broken into two sections, the first examines the fundamentals of chip-firing, while the second half presents more general frameworks for chip-firing. Instructors and students will discover that this book provides a comprehensive background to approaching original sources. Features: Provides a broad introduction for researchers interested in the subject of chip-firing The text includes historical and current perspectives Exercises included at the end of each chapter About the Author: Caroline J. Klivans received a BA degree in mathematics from Cornell University and a PhD in applied mathematics from MIT. Currently, she is an Associate Professor in the Division of Applied Mathematics at Brown University. She is also an Associate Director of ICERM (Institute for Computational and Experimental Research in Mathematics). Before coming to Brown she held positions at MSRI, Cornell and the University of Chicago. Her research is in algebraic, geometric and topological combinatorics.

The Mathematics Of Chip Firing

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Author : Caroline J. Klivans
language : en
Publisher:
Release Date : 2024

The Mathematics Of Chip Firing written by Caroline J. Klivans and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Abelian groups categories.

A Project Based Guide To Undergraduate Research In Mathematics

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Author : Pamela E. Harris
language : en
Publisher: Springer Nature
Release Date : 2020-04-17

A Project Based Guide To Undergraduate Research In Mathematics written by Pamela E. Harris and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-17 with Mathematics categories.

This volume provides accessible and self-contained research problems designed for undergraduate student projects, and simultaneously promotes the development of sustainable undergraduate research programs. The chapters in this work span a variety of topical areas of pure and applied mathematics and mathematics education. Each chapter gives a self-contained introduction on a research topic with an emphasis on the specific tools and knowledge needed to create and maintain fruitful research programs for undergraduates. Some of the topics discussed include:• Disease modeling• Tropical curves and surfaces• Numerical semigroups• Mathematics EducationThis volume will primarily appeal to undergraduate students interested in pursuing research projects and faculty members seeking to mentor them. It may also aid students and faculty participating in independent studies and capstone projects.

Abelian Networks Iv Dynamics Of Nonhalting Networks

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Author : Swee Hong Chan
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-08

Abelian Networks Iv Dynamics Of Nonhalting Networks written by Swee Hong Chan and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-08 with Mathematics categories.

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Illustrating Mathematics

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Author : Diana Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-16

Illustrating Mathematics written by Diana Davis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-16 with Education categories.

This book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it.

Introduction To Enumerative And Analytic Combinatorics

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Author : Miklos Bona
language : en
Publisher: CRC Press
Release Date : 2025-03-11

Introduction To Enumerative And Analytic Combinatorics written by Miklos Bona and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-11 with Mathematics categories.

This award-winning textbook targets the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The author’s goal is to make combinatorics more accessible to encourage student interest and to expand the number of students studying this rapidly expanding field. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares. Updates to the Third Edition include: Quick Check exercises at the end of each section, which are typically easier than the regular exercises at the end of each chapter. A new section discussing the Lagrange Inversion Formula and its applications, strengthening the analytic flavor of the book. An extended section on multivariate generating functions. Numerous exercises contain material not discussed in the text allowing instructors to extend the time they spend on a given topic. A chapter on analytic combinatorics and sections on advanced applications of generating functions, demonstrating powerful techniques that do not require the residue theorem or complex integration, and extending coverage of the given topics are highlights of the presentation. The second edition was recognized as an Outstanding Academic Title of the Year by Choice Magazine, published by the American Library Association.

Handbook Of The Tutte Polynomial And Related Topics

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Author : Joanna A. Ellis-Monaghan
language : en
Publisher: CRC Press
Release Date : 2022-07-06

Handbook Of The Tutte Polynomial And Related Topics written by Joanna A. Ellis-Monaghan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-06 with Computers categories.

The Tutte Polynomial touches on nearly every area of combinatorics as well as many other fields, including statistical mechanics, coding theory, and DNA sequencing. It is one of the most studied graph polynomials. Handbook of the Tutte Polynomial and Related Topics is the first handbook published on the Tutte Polynomial. It consists of thirty-four chapters written by experts in the field, which collectively offer a concise overview of the polynomial’s many properties and applications. Each chapter covers a different aspect of the Tutte polynomial and contains the central results and references for its topic. The chapters are organized into six parts. Part I describes the fundamental properties of the Tutte polynomial, providing an overview of the Tutte polynomial and the necessary background for the rest of the handbook. Part II is concerned with questions of computation, complexity, and approximation for the Tutte polynomial; Part III covers a selection of related graph polynomials; Part IV discusses a range of applications of the Tutte polynomial to mathematics, physics, and biology; Part V includes various extensions and generalizations of the Tutte polynomial; and Part VI provides a history of the development of the Tutte polynomial. Features Written in an accessible style for non-experts, yet extensive enough for experts Serves as a comprehensive and accessible introduction to the theory of graph polynomials for researchers in mathematics, physics, and computer science Provides an extensive reference volume for the evaluations, theorems, and properties of the Tutte polynomial and related graph, matroid, and knot invariants Offers broad coverage, touching on the wide range of applications of the Tutte polynomial and its various specializations

The Lambert W Function

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Author : Istvan Mezo
language : en
Publisher: CRC Press
Release Date : 2022-04-10

The Lambert W Function written by Istvan Mezo and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-10 with Mathematics categories.

This book is the very first one in the English language entirely dedicated to the Lambert W function, its generalizations, and its applications. One goal is to promote future research on the topic. The book contains all the information one needs when trying to find a result. The most important formulas and results are framed. The Lambert W function is a multi-valued inverse function with plenty of applications in areas like molecular physics, relativity theory, fuel consumption models, plasma physics, analysis of epidemics, bacterial growth models, delay differential equations, fluid mechanics, game theory, statistics, study of magnetic materials, and so on. The first part of the book gives a full treatise of the W function from theoretical point of view. The second part presents generalizations of this function which have been introduced by the need of applications where the classical W function is insufficient. The third part presents a large number of applications from physics, biology, game theory, bacterial cell growth models, and so on. The second part presents the generalized Lambert functions based on the tools we had developed in the first part. In the third part familiarity with Newtonian physics will be useful. The text is written to be accessible for everyone with only basic knowledge on calculus and complex numbers. Additional features include the Further Notes sections offering interesting research problems and information for further studies. Mathematica codes are included. The Lambert function is arguably the simplest non-elementary transcendental function out of the standard set of sin, cos, log, etc., therefore students who would like to deepen their understanding of real and complex analysis can see a new “almost elementary” function on which they can practice their knowledge.

Methods For The Summation Of Series

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Author : Tian-Xiao He
language : en
Publisher: CRC Press
Release Date : 2022-01-25

Methods For The Summation Of Series written by Tian-Xiao He and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-25 with Mathematics categories.

This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author’s focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding. Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in this field, while some materials of the book can be used as a portal for further research.

Combinatorics Of Permutations

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Author : Miklos Bona
language : en
Publisher: CRC Press
Release Date : 2022-05-09

Combinatorics Of Permutations written by Miklos Bona and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-09 with Computers categories.

A CHOICE "Outstanding Academic Title," the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a one-semester course, Combinatorics of Permutations, third edition continues to clearly show the usefulness of this subject for both students and researchers. The research in combinatorics of permutations has advanced rapidly since this book was published in a first edition. Now the third edition offers not only updated results, it remains the leading textbook for a course on the topic. Coverage is mostly enumerative, but there are algebraic, analytic, and topological parts as well, and applications. Since the publication of the second edition, there is tremendous progress in pattern avoidance (Chapters 4 and 5). There is also significant progress in the analytic combinatorics of permutations, which will be incorporated. •A completely new technique from extremal combinatorics disproved a long-standing conjecture, and this is presented in Chapter 4. •The area of universal permutations has undergone a lot of very recent progress, and that has been noticed outside the academic community as well. This also influenced the revision of Chapter 5. •New results in stack sorting are added to Chapter 8. •Chapter 9 applications to biology has been revised. The author’s other works include Introduction to Enumerative and Analytic Combinatorics, second edition (CHOICE "Outstanding Academic Title") and Handbook of Enumerative Combinatorics, published by CRC Press. The author also serves as Series Editor for CRC’s Discrete Mathematics and Its Applications.