Download or read book Mathematical Stories I Graphs Games and Proofs written by Susanne Schindler-Tschirner and published by Springer Nature. This book was released on 2021-06-04 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the help of tried and tested, carefully elaborated learning units, the authors convey fundamental mathematical techniques in this essential, which are important far beyond primary school. In the present volume I, path problems and word puzzles are modeled and solved using undirected and directed graphs. Simple math games are systematically analyzed and the optimal strategies are determined. Students learn to gradually reduce difficult problems to simpler ones and to provide evidence in different contexts. The tasks encourage mathematical thinking, imagination and creativity. The detailed sample solutions are designed for non-mathematicians. This book is a translation of the original German 1st edition Mathematische Geschichten I – Graphen, Spiele und Beweise by Susanne Schindler-Tschirner and Werner Schindler, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2019. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
Download or read book Mathematical Stories I Graphs Games and Proofs written by Susanne Schindler-Tschirner and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the help of tried and tested, carefully elaborated learning units, the authors convey fundamental mathematical techniques in this essential, which are important far beyond primary school. In the present volume I, path problems and word puzzles are modeled and solved using undirected and directed graphs. Simple math games are systematically analyzed and the optimal strategies are determined. Students learn to gradually reduce difficult problems to simpler ones and to provide evidence in different contexts. The tasks encourage mathematical thinking, imagination and creativity. The detailed sample solutions are designed for non-mathematicians. This book is a translation of the original German 1st edition Mathematische Geschichten I - Graphen, Spiele und Beweise by Susanne Schindler-Tschirner and Werner Schindler, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2019. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors. The content Mathematical techniques and tasks Detailed sample solutions The target groups Leaders of study groups as well as support courses for mathematically gifted students in grades 3 and 4, teachers who practice differentiated mathematics lessons Committed parents for extracurricular support The authors Susanne Schindler-Tschirner is a philologist and after studying to become a teacher, she was a project manager at a science publisher. She works in the field of student development and is the author of didactic-oriented publications. Werner Schindler has a PhD in mathematics. He is head of section at the Federal Office for Information Security (BSI) and an adjunct professor in the mathematics department at TU Darmstadt.
Download or read book Mathematical Stories II Recursion Divisibility and Proofs written by Susanne Schindler-Tschirner and published by Springer Nature. This book was released on 2023-04-13 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using field-tested, carefully crafted units of study, the authors in this essential teach fundamental mathematical techniques that are relevant well beyond the elementary school years. In this Volume II, the Gaussian summation formula and a recursion formula are derived and applied. Tasks on divisibility, prime factors and divisors follow. For calculating with remainders, the modulo calculation is introduced and applied. Students learn to perform proofs in a variety of contexts. As in Volume I, "Graphs, Games, and Proofs," the tasks encourage mathematical thinking skills, imagination, and creativity. The detailed sample solutions are designed for non-mathematicians. This book is a translation of the original German 1st edition Mathematische Geschichten II – Rekursion, Teilbarkeit und Beweise by Susanne Schindler-Tschirner and Werner Schindler, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2019. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
Download or read book The Mathematics of Various Entertaining Subjects written by Jennifer Beineke and published by Princeton University Press. This book was released on 2017-09-05 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects now returns with a brand-new compilation of fascinating problems and solutions in recreational mathematics. This latest volume gathers together the top experts in recreational math and presents a compelling look at board games, card games, dice, toys, computer games, and much more. The book is divided into five parts: puzzles and brainteasers, geometry and topology, graph theory, games of chance, and computational complexity. Readers will discover what origami, roulette wheels, and even the game of Trouble can teach about math. Essays contain new results, and the contributors include short expositions on their topic’s background, providing a framework for understanding the relationship between serious mathematics and recreational games. Mathematical areas explored include combinatorics, logic, graph theory, linear algebra, geometry, topology, computer science, operations research, probability, game theory, and music theory. Investigating an eclectic mix of games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.
Download or read book Game of Nim Graph Theory written by Rebecca Rapoport and published by Math Lab for Kids. This book was released on 2018-08 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Math Lab for Kids proves that math is more than just numbers--the hands-on activities in this book make learning math fun! With Game of Nim and Graph Theory, kids learn winning strategies for Nim, a game first played in China more than 1,000 years ago, and explore the famous Bridges of Königsberg problem that spawned an entire field of mathematics. No expensive supplies are required! Everything needed to complete the activities are included or can be found around the house. Math Lab for Kids: Game of Nim and Graph Theory will give kids a great experience and a solid foundation in a subject that's more important than ever.
Download or read book Graph Theory written by Karin R Saoub and published by CRC Press. This book was released on 2021-03-17 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph Theory: An Introduction to Proofs, Algorithms, and Applications Graph theory is the study of interactions, conflicts, and connections. The relationship between collections of discrete objects can inform us about the overall network in which they reside, and graph theory can provide an avenue for analysis. This text, for the first undergraduate course, will explore major topics in graph theory from both a theoretical and applied viewpoint. Topics will progress from understanding basic terminology, to addressing computational questions, and finally ending with broad theoretical results. Examples and exercises will guide the reader through this progression, with particular care in strengthening proof techniques and written mathematical explanations. Current applications and exploratory exercises are provided to further the reader’s mathematical reasoning and understanding of the relevance of graph theory to the modern world. Features The first chapter introduces graph terminology, mathematical modeling using graphs, and a review of proof techniques featured throughout the book The second chapter investigates three major route problems: eulerian circuits, hamiltonian cycles, and shortest paths. The third chapter focuses entirely on trees – terminology, applications, and theory. Four additional chapters focus around a major graph concept: connectivity, matching, coloring, and planarity. Each chapter brings in a modern application or approach. Hints and Solutions to selected exercises provided at the back of the book. Author Karin R. Saoub is an Associate Professor of Mathematics at Roanoke College in Salem, Virginia. She earned her PhD in mathematics from Arizona State University and BA from Wellesley College. Her research focuses on graph coloring and on-line algorithms applied to tolerance graphs. She is also the author of A Tour Through Graph Theory, published by CRC Press.
Download or read book Introduction to Graph Theory written by Richard J. Trudeau and published by Courier Corporation. This book was released on 2013-04-15 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.
Download or read book Graph Theory As I Have Known It written by W. T. Tutte and published by Clarendon Press. This book was released on 2012-05-24 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unique and unusual introduction to graph theory by one of the founding fathers, and will be of interest to all researchers in the subject. It is not intended as a comprehensive treatise, but rather as an account of those parts of the theory that have been of special interest to the author. Professor Tutte details his experience in the area, and provides a fascinating insight into how he was led to his theorems and the proofs he used. As well as being of historical interest it provides a useful starting point for research, with references to further suggested books as well as the original papers. The book starts by detailing the first problems worked on by Professor Tutte and his colleagues during his days as an undergraduate member of the Trinity Mathematical Society in Cambridge. It covers subjects such as comnbinatorial problems in chess, the algebraicization of graph theory, reconstruction of graphs, and the chromatic eigenvalues. In each case fascinating historical and biographical information about the author's research is provided.
Download or read book Domination Games Played on Graphs written by Boštjan Brešar and published by Springer Nature. This book was released on 2021-04-15 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise monograph present the complete history of the domination game and its variants up to the most recent developments and will stimulate research on closely related topics, establishing a key reference for future developments. The crux of the discussion surrounds new methods and ideas that were developed within the theory, led by the imagination strategy, the Continuation Principle, and the discharging method of Bujtás, to prove results about domination game invariants. A toolbox of proof techniques is provided for the reader to obtain results on the domination game and its variants. Powerful proof methods such as the imagination strategy are presented. The Continuation Principle is developed, which provides a much-used monotonicity property of the game domination number. In addition, the reader is exposed to the discharging method of Bujtás. The power of this method was shown by improving the known upper bound, in terms of a graph's order, on the (ordinary) domination number of graphs with minimum degree between 5 and 50. The book is intended primarily for students in graph theory as well as established graph theorists and it can be enjoyed by anyone with a modicum of mathematical maturity. The authors include exact results for several families of graphs, present what is known about the domination game played on subgraphs and trees, and provide the reader with the computational complexity aspects of domination games. Versions of the games which involve only the “slow” player yield the Grundy domination numbers, which connect the topic of the book with some concepts from linear algebra such as zero-forcing sets and minimum rank. More than a dozen other related games on graphs and hypergraphs are presented in the book. In all these games there are problems waiting to be solved, so the area is rich for further research. The domination game belongs to the growing family of competitive optimization graph games. The game is played by two competitors who take turns adding a vertex to a set of chosen vertices. They collaboratively produce a special structure in the underlying host graph, namely a dominating set. The two players have complementary goals: one seeks to minimize the size of the chosen set while the other player tries to make it as large as possible. The game is not one that is either won or lost. Instead, if both players employ an optimal strategy that is consistent with their goals, the cardinality of the chosen set is a graphical invariant, called the game domination number of the graph. To demonstrate that this is indeed a graphical invariant, the game tree of a domination game played on a graph is presented for the first time in the literature.
Download or read book Combinatorics and Graph Theory written by John Harris and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.
Download or read book Graph Theory written by Bela Bollobas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Béla Bollobás introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject. ... The book has chapters on electrical networks, flows, connectivity and matchings, extremal problems, colouring, Ramsey theory, random graphs, and graphs and groups. Each chapter starts at a measured and gentle pace. Classical results are proved and new insight is provided, with the examples at the end of each chapter fully supplementing the text... Even so this allows an introduction not only to some of the deeper results but, more vitally, provides outlines of, and firm insights into, their proofs. Thus in an elementary text book, we gain an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject. It is this aspect of the book which should guarantee it a permanent place in the literature." #Bulletin of the London Mathematical Society#1
Download or read book Hex written by Ryan B. Hayward and published by CRC Press. This book was released on 2019-01-30 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hex is the subject of books by Martin Gardner and Cameron Browne. Hex theory touches on graph theory, game theory and combinatorial game theory, with elegant proofs that the game has no draws and that the first player can win. From machines built by Claude Shannon to agents using Monte Carlo Tree Search, Hex is often used in the study of artificial intelligence. Written for a wide audience, this is the full story of Hex, inside and out, with all its twists and turns: Hein’s creation, Lindhard’s puzzles, Nash’s proofs, Gale’s Bridg-it, the game of Rex, Shannon’s machines, Bridg-it’s fall, Hex’s resilience, Hex theory, the hunt for winning strategies, and the rise of Hexbots.
Download or read book Pearls in Graph Theory written by Nora Hartsfield and published by Courier Corporation. This book was released on 2013-04-15 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stimulating and accessible, this undergraduate-level text covers basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 edition.
Download or read book The Countingbury Tales written by Miguel de Guzm n and published by World Scientific. This book was released on 2000 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents mathematical concepts through stories and games, including "The Mathematics of a Sandwich," "The Jumping Frog," and "The Secret of the Oval Hall."
Download or read book A First Course in Graph Theory written by Gary Chartrand and published by Courier Corporation. This book was released on 2013-05-20 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by two prominent figures in the field, this comprehensive text provides a remarkably student-friendly approach. Its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.
Download or read book Introductory Graph Theory written by Gary Chartrand and published by Courier Corporation. This book was released on 2012-04-30 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear, lively style covers all basics of theory and application, including mathematical models, elementary graph theory, transportation problems, connection problems, party problems, diagraphs and mathematical models, games and puzzles, more.
Download or read book An Invitation to Pursuit Evasion Games and Graph Theory written by Anthony Bonato and published by American Mathematical Society. This book was released on 2022-06-16 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
