An Invitation To Pursuit Evasion Games And Graph Theory
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An Invitation To Pursuit Evasion Games And Graph Theory
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Author : Anthony Bonato
language : en
Publisher: American Mathematical Society
Release Date : 2022-06-16
An Invitation To Pursuit Evasion Games And Graph Theory written by Anthony Bonato 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 2022-06-16 with Mathematics categories.
Graphs measure interactions between objects such as friendship links on Twitter, transactions between Bitcoin users, and the flow of energy in a food chain. While graphs statically represent interacting systems, they may also be used to model dynamic interactions. For example, imagine an invisible evader loose on a graph, leaving only behind breadcrumb clues to their whereabouts. You set out with pursuers of your own, seeking out the evader's location. Would you be able to detect their location? If so, then how many resources are needed for detection, and how fast can that happen? These basic-seeming questions point towards the broad conceptual framework of pursuit-evasion games played on graphs. Central to pursuit-evasion games on graphs is the idea of optimizing certain parameters, whether they are the cop number, burning number, or localization number, for example. This book would be excellent for a second course in graph theory at the undergraduate or graduate level. It surveys different areas in graph searching and highlights many fascinating topics intersecting classical graph theory, geometry, and combinatorial designs. Each chapter ends with approximately twenty exercises and five larger scale projects.
Dots And Lines
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Author : Anthony Bonato
language : en
Publisher: JHU Press
Release Date : 2025-05-13
Dots And Lines written by Anthony Bonato and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-13 with Computers categories.
Can networks unlock secrets of AI or make sense of a social media mess? A behind-the-scenes look at how networks reveal reality. According to mathematician Anthony Bonato, the hidden world of networks permeates our lives in astounding ways. From Bitcoin transactions to neural connections, his book explains how networks shape everything from political landscapes to climate patterns and how deceptively simple dots and lines can unveil the wonders of technology, society, and even nature. From a fresh and startling look at the true impact of clever keywords in politicians' social media posts to a fun breakdown of survival strategies in reality TV shows, Bonato shows us how network theory operates everywhere. Each chapter focuses on a unique aspect of networks to reveal how they provide a captivating lens for bringing diverse phenomena into clearer focus. The book offers an accessible snapshot of networks for anyone curious about what makes the modern world tick. Bonato's insights will give readers a deeper appreciation and understanding of networks and their relevance to our everyday lives.
Graph Theoretic Concepts In Computer Science
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Author : Daniël Paulusma
language : en
Publisher: Springer Nature
Release Date : 2023-09-22
Graph Theoretic Concepts In Computer Science written by Daniël Paulusma and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-22 with Mathematics categories.
This volume constitutes the thoroughly refereed proceedings of the 49th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2023. The 33 full papers presented in this volume were carefully reviewed and selected from a total of 116 submissions. The WG 2022 workshop aims to merge theory and practice by demonstrating how concepts from graph theory can be applied to various areas in computer science, or by extracting new graph theoretic problems from applications.
Glimpses Of Soliton Theory
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Author : Alex Kasman
language : en
Publisher: American Mathematical Society
Release Date : 2023-03-30
Glimpses Of Soliton Theory written by Alex Kasman 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 2023-03-30 with Mathematics categories.
This book challenges and intrigues from beginning to end. It would be a treat to use for a capstone course or senior seminar. —William J. Satzer, MAA Reviews on Glimpses of Soliton Theory (First Edition) Solitons are nonlinear waves which behave like interacting particles. When first proposed in the 19th century, leading mathematical physicists denied that such a thing could exist. Now they are regularly observed in nature, shedding light on phenomena like rogue waves and DNA transcription. Solitons of light are even used by engineers for data transmission and optical switches. Furthermore, unlike most nonlinear partial differential equations, soliton equations have the remarkable property of being exactly solvable. Explicit solutions to those equations provide a rare window into what is possible in the realm of nonlinearity. Glimpses of Soliton Theory reveals the hidden connections discovered over the last half-century that explain the existence of these mysterious mathematical objects. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra, the book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass $wp$-functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Hierarchy, and Sato's theory relating the Bilinear KP Equation to the geometry of Grassmannians. Notable features of the book include: careful selection of topics and detailed explanations to make the subject accessible to undergraduates, numerous worked examples and thought-provoking exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of Mathematica® to facilitate computation and animate solutions. The second edition refines the exposition in every chapter, adds more homework exercises and projects, updates references, and includes new examples involving non-commutative integrable systems. Moreover, the chapter on KdV multisolitons has been greatly expanded with new theorems providing a thorough analysis of their behavior and decomposition.
Modelling And Mining Networks
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Author : Megan Dewar
language : en
Publisher: Springer Nature
Release Date : 2024-04-28
Modelling And Mining Networks written by Megan Dewar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-28 with Computers categories.
This book constitutes the refereed proceedings of the 19th International Workshop on Modelling and Mining Networks, WAW 2024, held in Warsaw, Poland, during June 3–6, 2024. The 12 full papers presented in this book were carefully reviewed and selected from 19 submissions. The aim of this workshop was to further the understanding of networks that arise in theoretical as well as applied domains. The goal was also to stimulate the development of high-performance and scalable algorithms that exploit these networks.
Knots Links And Their Invariants
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Author : A. B. Sossinsky
language : en
Publisher: American Mathematical Society
Release Date : 2023-05-22
Knots Links And Their Invariants written by A. B. Sossinsky 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 2023-05-22 with Mathematics categories.
This book is an elementary introduction to knot theory. Unlike many other books on knot theory, this book has practically no prerequisites; it requires only basic plane and spatial Euclidean geometry but no knowledge of topology or group theory. It contains the first elementary proof of the existence of the Alexander polynomial of a knot or a link based on the Conway axioms, particularly the Conway skein relation. The book also contains an elementary exposition of the Jones polynomial, HOMFLY polynomial and Vassiliev knot invariants constructed using the Kontsevich integral. Additionally, there is a lecture introducing the braid group and shows its connection with knots and links. Other important features of the book are the large number of original illustrations, numerous exercises and the absence of any references in the first eleven lectures. The last two lectures differ from the first eleven: they comprise a sketch of non-elementary topics and a brief history of the subject, including many references.
Numbers And Figures
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Author : Giancarlo Travaglini
language : en
Publisher: American Mathematical Society
Release Date : 2023-05-31
Numbers And Figures written by Giancarlo Travaglini 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 2023-05-31 with Mathematics categories.
One of the great charms of mathematics is uncovering unexpected connections. In Numbers and Figures, Giancarlo Travaglini provides six conversations that do exactly that by talking about several topics in elementary number theory and some of their connections to geometry, calculus, and real-life problems such as COVID-19 vaccines or fiscal frauds. Each conversation is in two parts—an introductory essay which provides a gentle introduction to the topic and a second section that delves deeper and requires study by the reader. The topics themselves are extremely appealing and include, for example, Pick's theorem, Simpson's paradox, Farey sequences, the Frobenius problem, and Benford's Law. Numbers and Figures will be a useful resource for college faculty teaching Elementary Number Theory or Calculus. The chapters are largely independent and could make for nice course-ending projects or even lead-ins to high school or undergraduate research projects. The whole book would make for an enjoyable semester-long independent reading course. Faculty will find it entertaining bedtime reading and, last but not least, readers more generally will be interested in this book if they miss the accuracy and imagination found in their high school and college math courses.
Finite Fields With Applications To Combinatorics
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Author : Kannan Soundararajan
language : en
Publisher: American Mathematical Society
Release Date : 2022-11-09
Finite Fields With Applications To Combinatorics written by Kannan Soundararajan 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 2022-11-09 with Mathematics categories.
This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.
An Introduction To The Circle Method
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Author : M. Ram Murty
language : en
Publisher: American Mathematical Society
Release Date : 2023-06-15
An Introduction To The Circle Method written by M. Ram Murty 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 2023-06-15 with Mathematics categories.
The circle method, pioneered by Ramanujan and Hardy in the early 20th century, has over the past 100 years become part of the standard tool chest of analytic number theory. Its scope of applications is ever-expanding, and the subject continues to see important breakthroughs. This book provides an introduction to the circle method that is accessible to undergraduate students with no background in number theory. The authors' goal is to show the students the elegance of the circle method and at the same time give a complete solution of the famous Waring problem as an illustration of the method. The first half of this book is a curated introduction to elementary number theory with an emphasis on topics needed for the second half. The second half showcases the two most “classic” applications of the circle method, to Waring's problem (following Hardy–Littlewood–Hua) and to Goldbach's conjectures (following Vinogradov, with improvements by Vaughan). This text is suitable for a one-semester undergraduate course or for independent study and will be a great entry point into this fascinating area of research.
Random Explorations
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Author : Gregory F. Lawler
language : en
Publisher: American Mathematical Society
Release Date : 2022-12-06
Random Explorations written by Gregory F. Lawler 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 2022-12-06 with Mathematics categories.
The title “Random Explorations” has two meanings. First, a few topics of advanced probability are deeply explored. Second, there is a recurring theme of analyzing a random object by exploring a random path. This book is an outgrowth of lectures by the author in the University of Chicago Research Experiences for Undergraduate (REU) program in 2020. The idea of the course was to expose advanced undergraduates to ideas in probability research. The book begins with Markov chains with an emphasis on transient or killed chains that have finite Green's function. This function, and its inverse called the Laplacian, is discussed next to relate two objects that arise in statistical physics, the loop-erased random walk (LERW) and the uniform spanning tree (UST). A modern approach is used including loop measures and soups. Understanding these approaches as the system size goes to infinity requires a deep understanding of the simple random walk so that is studied next, followed by a look at the infinite LERW and UST. Another model, the Gaussian free field (GFF), is introduced and related to loop measure. The emphasis in the book is on discrete models, but the final chapter gives an introduction to the continuous objects: Brownian motion, Brownian loop measures and soups, Schramm-Loewner evolution (SLE), and the continuous Gaussian free field. A number of exercises scattered throughout the text will help a serious reader gain better understanding of the material.