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Discrete Mathematics: Gary Chartrand and Ping Zhang – A Comprehensive Guide
Introduction:
Are you grappling with the intricacies of discrete mathematics? Finding the right textbook can make or break your understanding. For many students and professionals, the name Discrete Mathematics by Gary Chartrand and Ping Zhang immediately comes to mind. This comprehensive guide dives deep into this renowned textbook, exploring its strengths, weaknesses, and overall effectiveness in helping you master the core concepts of discrete mathematics. We’ll examine its approach, target audience, and ultimately, whether it's the right choice for your learning journey.
Understanding the Authors and their Approach (H2)
Gary Chartrand and Ping Zhang are highly respected figures in the field of mathematics, particularly graph theory. Their collaborative effort on Discrete Mathematics reflects their deep expertise and commitment to clear, accessible explanations. The book distinguishes itself from others through its:
Emphasis on clarity and readability: Chartrand and Zhang avoid overly dense mathematical notation where possible, prioritizing intuitive explanations and real-world examples to illustrate key concepts. This makes the material accessible to a wider audience, including those without a strong prior mathematical background.
Gradual progression of difficulty: The book carefully introduces concepts incrementally, building upon previously established knowledge. This scaffolded approach helps students develop a strong foundation before tackling more challenging topics.
Abundance of examples and exercises: The text is generously peppered with solved examples that demonstrate the application of theoretical concepts. Furthermore, a large number of practice exercises at the end of each chapter reinforce understanding and provide opportunities for self-assessment.
Key Topics Covered in Discrete Mathematics by Chartrand and Zhang (H2)
This textbook comprehensively covers the essential topics typically included in an introductory discrete mathematics course. These include:
#### Foundational Concepts (H3)
Logic and Proof Techniques: The book provides a solid grounding in propositional and predicate logic, crucial for formulating mathematical arguments and constructing rigorous proofs.
Set Theory: Fundamental set operations, relations, and functions are thoroughly explained, forming the basis for many subsequent chapters.
Number Theory: Divisibility, modular arithmetic, and the properties of prime numbers are explored in detail.
#### Core Areas of Discrete Mathematics (H3)
Graph Theory: A significant portion of the book is dedicated to graph theory, covering topics such as graph representations, trees, planar graphs, and graph coloring. This section is particularly strong, reflecting the authors' expertise in the area.
Combinatorics: This section delves into counting techniques, permutations, combinations, and the principle of inclusion-exclusion.
Recurrence Relations and Algorithm Analysis: The book introduces recurrence relations and techniques for solving them, essential for analyzing the efficiency of algorithms.
Boolean Algebra: The fundamentals of Boolean algebra and its applications in digital logic design are clearly explained.
Who is this Textbook For? (H2)
Discrete Mathematics by Chartrand and Zhang is ideally suited for:
Undergraduate students: It serves as an excellent textbook for introductory discrete mathematics courses at the undergraduate level in computer science, mathematics, and engineering.
Self-learners: The clear explanations and abundant examples make it a suitable resource for self-study, provided you have a basic mathematical background.
Professionals: The book can serve as a valuable reference for professionals working in fields requiring a solid understanding of discrete mathematical concepts.
Strengths and Weaknesses (H2)
Strengths:
Clarity and accessibility: The writing style is remarkably clear and easy to follow.
Comprehensive coverage: The book covers a broad range of topics in discrete mathematics.
Abundant examples and exercises: The numerous examples and exercises greatly aid in understanding the material.
Strong graph theory section: The in-depth coverage of graph theory is a significant advantage.
Weaknesses:
Potentially overwhelming for some: The sheer volume of material might be daunting for some students, particularly those with limited prior mathematical experience.
Lack of advanced topics: The book focuses on introductory concepts and does not delve into more advanced topics.
Conclusion:
Discrete Mathematics by Gary Chartrand and Ping Zhang is a highly respected and widely used textbook that provides a comprehensive introduction to the subject. Its strength lies in its clarity, accessibility, and comprehensive coverage of fundamental concepts. While the sheer volume of material might be challenging for some, the book’s well-structured approach and abundant examples make it a valuable resource for students and professionals alike seeking a solid understanding of discrete mathematics. If you're searching for a reliable and effective textbook for an introductory course or self-study, this book is certainly worth considering.
FAQs
1. Is this book suitable for a high school student? While possible for a highly motivated student with a strong mathematical background, it is generally more appropriate for undergraduate-level study.
2. Does the book include solutions to all the exercises? No, solutions are typically provided for selected exercises, encouraging active learning and self-assessment.
3. Are there any online resources to supplement the book? While not officially associated, many online resources and tutorials covering discrete mathematics concepts exist and can complement the textbook's content.
4. What software or tools are needed to use this book effectively? No specialized software is required. Basic mathematical notation understanding and perhaps a good calculator will be beneficial.
5. Can this book be used for advanced discrete math courses? No, this textbook focuses on introductory concepts. For advanced topics, you'll need more specialized texts.
| discrete mathematics gary chartrand ping zhang: Discrete Mathematics Gary Chartrand, Ping Zhang, 2011 |
| discrete mathematics gary chartrand ping zhang: Discrete Mathematics (Classic Version) John Dossey, Albert Otto, Lawrence Spence, Charles Vanden Eynden, 2017-03-07 This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. An ever-increasing percentage of mathematic applications involve discrete rather than continuous models. Driving this trend is the integration of the computer into virtually every aspect of modern society. Intended for a one-semester introductory course, the strong algorithmic emphasis of Discrete Mathematics is independent of a specific programming language, allowing students to concentrate on foundational problem-solving and analytical skills. Instructors get the topical breadth and organizational flexibility to tailor the course to the level and interests of their students. |
| discrete mathematics gary chartrand ping zhang: Chromatic Graph Theory Gary Chartrand, Ping Zhang, 2019-11-28 With Chromatic Graph Theory, Second Edition, the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings. Features of the Second Edition: The book can be used for a first course in graph theory as well as a graduate course The primary topic in the book is graph coloring The book begins with an introduction to graph theory so assumes no previous course The authors are the most widely-published team on graph theory Many new examples and exercises enhance the new edition |
| discrete mathematics gary chartrand ping zhang: A First Course in Graph Theory Gary Chartrand, Ping Zhang, 2013-05-20 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. |
| discrete mathematics gary chartrand ping zhang: Mathematical Proofs Gary Chartrand, Albert D. Polimeni, Ping Zhang, 2013 This book prepares students for the more abstract mathematics courses that follow calculus. The author introduces students to proof techniques, analyzing proofs, and writing proofs of their own. It also provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. |
| discrete mathematics gary chartrand ping zhang: Graphs & Digraphs, Fourth Edition Gary Chartrand, Linda Lesniak, Ping Zhang, 1996-08-01 This is the third edition of the popular text on graph theory. As in previous editions, the text presents graph theory as a mathematical discipline and emphasizes clear exposition and well-written proofs. New in this edition are expanded treatments of graph decomposition and external graph theory, a study of graph vulnerability and domination, and introductions to voltage graphs, graph labelings, and the probabilistic method in graph theory. |
| discrete mathematics gary chartrand ping zhang: The Fascinating World of Graph Theory Arthur Benjamin, Gary Chartrand, Ping Zhang, 2017-06-06 The history, formulas, and most famous puzzles of graph theory Graph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics—and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, and each chapter contains math exercises for readers to savor. An eye-opening journey into the world of graphs, The Fascinating World of Graph Theory offers exciting problem-solving possibilities for mathematics and beyond. |
| discrete mathematics gary chartrand ping zhang: Combinatorics of Train Tracks R. C. Penner, John L. Harer, 1992 Measured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry, and dynamical systems. This book presents a self-contained and comprehensive treatment of the rich combinatorial structure of the space of measured geodesic laminations in a fixed surface. Families of measured geodesic laminations are described by specifying a train track in the surface, and the space of measured geodesic laminations is analyzed by studying properties of train tracks in the surface. The material is developed from first principles, the techniques employed are essentially combinatorial, and only a minimal background is required on the part of the reader. Specifically, familiarity with elementary differential topology and hyperbolic geometry is assumed. The first chapter treats the basic theory of train tracks as discovered by W. P. Thurston, including recurrence, transverse recurrence, and the explicit construction of a measured geodesic lamination from a measured train track. The subsequent chapters develop certain material from R. C. Penner's thesis, including a natural equivalence relation on measured train tracks and standard models for the equivalence classes (which are used to analyze the topology and geometry of the space of measured geodesic laminations), a duality between transverse and tangential structures on a train track, and the explicit computation of the action of the mapping class group on the space of measured geodesic laminations in the surface. |
| discrete mathematics gary chartrand ping zhang: Graphs & Digraphs Gary Chartrand, Linda Lesniak, Ping Zhang, 2010-10-19 Continuing to provide a carefully written, thorough introduction, Graphs & Digraphs, Fifth Edition expertly describes the concepts, theorems, history, and applications of graph theory. Nearly 50 percent longer than its bestselling predecessor, this edition reorganizes the material and presents many new topics. New to the Fifth Edition New or expanded coverage of graph minors, perfect graphs, chromatic polynomials, nowhere-zero flows, flows in networks, degree sequences, toughness, list colorings, and list edge colorings New examples, figures, and applications to illustrate concepts and theorems Expanded historical discussions of well-known mathematicians and problems More than 300 new exercises, along with hints and solutions to odd-numbered exercises at the back of the book Reorganization of sections into subsections to make the material easier to read Bolded definitions of terms, making them easier to locate Despite a field that has evolved over the years, this student-friendly, classroom-tested text remains the consummate introduction to graph theory. It explores the subject’s fascinating history and presents a host of interesting problems and diverse applications. |
| discrete mathematics gary chartrand ping zhang: Essential Discrete Mathematics for Computer Science Harry Lewis, Rachel Zax, 2019-03-19 Discrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and graph theory. Essential Discrete Mathematics for Computer Science aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof. It is fully illustrated in color, and each chapter includes a concise summary as well as a set of exercises. |
| discrete mathematics gary chartrand ping zhang: Discrete Orthogonal Polynomials. (AM-164) Jinho Baik, 2007 Publisher description |
| discrete mathematics gary chartrand ping zhang: Isoperimetric Inequalities in Mathematical Physics. (AM-27), Volume 27 G. Polya, G. Szegö, 2016-03-02 The description for this book, Isoperimetric Inequalities in Mathematical Physics. (AM-27), Volume 27, will be forthcoming. |
| discrete mathematics gary chartrand ping zhang: Frontiers in Complex Dynamics Araceli Bonifant, Misha Lyubich, Scott Sutherland, 2014-03-16 John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, Tien-Cuong Dinh, Romain Dujardin, Hugo García-Compeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, Viet-Anh Nguyên, Lex Oversteegen, Ricardo Pérez-Marco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto Santos-Silva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky. |
| discrete mathematics gary chartrand ping zhang: Distance In Graphs Fred Buckley, Frank Harary, 1990-01-21 |
| discrete mathematics gary chartrand ping zhang: Bipartite Graphs and Their Applications Armen S. Asratian, Tristan M. J. Denley, Roland Häggkvist, 1998-07-13 This is the first book which deals solely with bipartite graphs. Together with traditional material, the reader will also find many new and unusual results. Essentially all proofs are given in full; many of these have been streamlined specifically for this text. Numerous exercises of all standards have also been included. The theory is illustrated with many applications especially to problems in timetabling, Chemistry, Communication Networks and Computer Science. For the most part the material is accessible to any reader with a graduate understanding of mathematics. However, the book contains advanced sections requiring much more specialized knowledge, which will be of interest to specialists in combinatorics and graph theory. |
| discrete mathematics gary chartrand ping zhang: Modern Graph Theory Bela Bollobas, 2013-12-01 An in-depth account of graph theory, written for serious students of mathematics and computer science. It reflects the current state of the subject and emphasises connections with other branches of pure mathematics. Recognising that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory, the book presents a detailed account of newer topics, including Szemerédis Regularity Lemma and its use, Shelahs extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader. |
| discrete mathematics gary chartrand ping zhang: Handbook of Graph Theory Jonathan L. Gross, Jay Yellen, 2003-12-29 The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approach |
| discrete mathematics gary chartrand ping zhang: Introduction to Graph Theory Gary Chartrand, Ping Zhang, 2005 Economic applications of graphs ands equations, differnetiation rules for exponentiation of exponentials ... |
| discrete mathematics gary chartrand ping zhang: Graph Theory Ronald Gould, 2013-10-03 An introductory text in graph theory, this treatment covers primary techniques and includes both algorithmic and theoretical problems. Algorithms are presented with a minimum of advanced data structures and programming details. 1988 edition. |
| discrete mathematics gary chartrand ping zhang: Graphic Discovery Howard Wainer, 2013-10-24 Good graphs make complex problems clear. From the weather forecast to the Dow Jones average, graphs are so ubiquitous today that it is hard to imagine a world without them. Yet they are a modern invention. This book is the first to comprehensively plot humankind's fascinating efforts to visualize data, from a key seventeenth-century precursor--England's plague-driven initiative to register vital statistics--right up to the latest advances. In a highly readable, richly illustrated story of invention and inventor that mixes science and politics, intrigue and scandal, revolution and shopping, Howard Wainer validates Thoreau's observation that circumstantial evidence can be quite convincing, as when you find a trout in the milk. The story really begins with the eighteenth-century origins of the art, logic, and methods of data display, which emerged, full-grown, in William Playfair's landmark 1786 trade atlas of England and Wales. The remarkable Scot singlehandedly popularized the atheoretical plotting of data to reveal suggestive patterns--an achievement that foretold the graphic explosion of the nineteenth century, with atlases published across the observational sciences as the language of science moved from words to pictures. Next come succinct chapters illustrating the uses and abuses of this marvelous invention more recently, from a murder trial in Connecticut to the Vietnam War's effect on college admissions. Finally Wainer examines the great twentieth-century polymath John Wilder Tukey's vision of future graphic displays and the resultant methods--methods poised to help us make sense of the torrent of data in our information-laden world. |
| discrete mathematics gary chartrand ping zhang: An Introduction to Abstract Mathematics Robert J. Bond, William J. Keane, 2007-08-24 Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant disciplineits long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher- level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1-5 introduce the fundamentals of abstract mathematics and chapters 6-8 apply the ideas and techniques, placing the earlier material in a real context. Readers interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments. |
| discrete mathematics gary chartrand ping zhang: Graph Theory in America Robin Wilson, John J. Watkins, David J. Parks, 2023-01-17 How a new mathematical field grew and matured in America Graph Theory in America focuses on the development of graph theory in North America from 1876 to 1976. At the beginning of this period, James Joseph Sylvester, perhaps the finest mathematician in the English-speaking world, took up his appointment as the first professor of mathematics at the Johns Hopkins University, where his inaugural lecture outlined connections between graph theory, algebra, and chemistry—shortly after, he introduced the word graph in our modern sense. A hundred years later, in 1976, graph theory witnessed the solution of the long-standing four color problem by Kenneth Appel and Wolfgang Haken of the University of Illinois. Tracing graph theory’s trajectory across its first century, this book looks at influential figures in the field, both familiar and less known. Whereas many of the featured mathematicians spent their entire careers working on problems in graph theory, a few such as Hassler Whitney started there and then moved to work in other areas. Others, such as C. S. Peirce, Oswald Veblen, and George Birkhoff, made excursions into graph theory while continuing their focus elsewhere. Between the main chapters, the book provides short contextual interludes, describing how the American university system developed and how graph theory was progressing in Europe. Brief summaries of specific publications that influenced the subject’s development are also included. Graph Theory in America tells how a remarkable area of mathematics landed on American soil, took root, and flourished. |
| discrete mathematics gary chartrand ping zhang: Graph Theory and Complex Networks Maarten van Steen, 2010 This book aims to explain the basics of graph theory that are needed at an introductory level for students in computer or information sciences. To motivate students and to show that even these basic notions can be extremely useful, the book also aims to provide an introduction to the modern field of network science. Mathematics is often unnecessarily difficult for students, at times even intimidating. For this reason, explicit attention is paid in the first chapters to mathematical notations and proof techniques, emphasizing that the notations form the biggest obstacle, not the mathematical concepts themselves. This approach allows to gradually prepare students for using tools that are necessary to put graph theory to work: complex networks. In the second part of the book the student learns about random networks, small worlds, the structure of the Internet and the Web, peer-to-peer systems, and social networks. Again, everything is discussed at an elementary level, but such that in the end students indeed have the feeling that they: 1.Have learned how to read and understand the basic mathematics related to graph theory. 2.Understand how basic graph theory can be applied to optimization problems such as routing in communication networks. 3.Know a bit more about this sometimes mystical field of small worlds and random networks. There is an accompanying web site www.distributed-systems.net/gtcn from where supplementary material can be obtained, including exercises, Mathematica notebooks, data for analyzing graphs, and generators for various complex networks. |
| discrete mathematics gary chartrand ping zhang: Geodesic Convexity in Graphs Ignacio M. Pelayo, 2013-09-06 Geodesic Convexity in Graphs is devoted to the study of the geodesic convexity on finite, simple, connected graphs. The first chapter includes the main definitions and results on graph theory, metric graph theory and graph path convexities. The following chapters focus exclusively on the geodesic convexity, including motivation and background, specific definitions, discussion and examples, results, proofs, exercises and open problems. The main and most studied parameters involving geodesic convexity in graphs are both the geodetic and the hull number which are defined as the cardinality of minimum geodetic and hull set, respectively. This text reviews various results, obtained during the last one and a half decade, relating these two invariants and some others such as convexity number, Steiner number, geodetic iteration number, Helly number, and Caratheodory number to a wide range a contexts, including products, boundary-type vertex sets, and perfect graph families. This monograph can serve as a supplement to a half-semester graduate course in geodesic convexity but is primarily a guide for postgraduates and researchers interested in topics related to metric graph theory and graph convexity theory. |
| discrete mathematics gary chartrand ping zhang: Mathematical Writing Donald E. Knuth, Tracy Larrabee, Paul M. Roberts, 1989 This book will help those wishing to teach a course in technical writing, or who wish to write themselves. |
| discrete mathematics gary chartrand ping zhang: Domination in Graphs TeresaW. Haynes, 2017-11-22 Presents the latest in graph domination by leading researchers from around the world-furnishing known results, open research problems, and proof techniques. Maintains standardized terminology and notation throughout for greater accessibility. Covers recent developments in domination in graphs and digraphs, dominating functions, combinatorial problems on chessboards, and more. |
| discrete mathematics gary chartrand ping zhang: A Transition to Advanced Mathematics Douglas Smith, Maurice Eggen, Richard St. Andre, 2010-06-01 A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. |
| discrete mathematics gary chartrand ping zhang: Topics in Chromatic Graph Theory Lowell W. Beineke, Robin J. Wilson, 2015-05-07 Chromatic graph theory is a thriving area that uses various ideas of 'colouring' (of vertices, edges, and so on) to explore aspects of graph theory. It has links with other areas of mathematics, including topology, algebra and geometry, and is increasingly used in such areas as computer networks, where colouring algorithms form an important feature. While other books cover portions of the material, no other title has such a wide scope as this one, in which acknowledged international experts in the field provide a broad survey of the subject. All fifteen chapters have been carefully edited, with uniform notation and terminology applied throughout. Bjarne Toft (Odense, Denmark), widely recognized for his substantial contributions to the area, acted as academic consultant. The book serves as a valuable reference for researchers and graduate students in graph theory and combinatorics and as a useful introduction to the topic for mathematicians in related fields. |
| discrete mathematics gary chartrand ping zhang: Graph Theory Ralucca Gera, Stephen Hedetniemi, Craig Larson, 2016-10-19 This is the first in a series of volumes, which provide an extensive overview of conjectures and open problems in graph theory. The readership of each volume is geared toward graduate students who may be searching for research ideas. However, the well-established mathematician will find the overall exposition engaging and enlightening. Each chapter, presented in a story-telling style, includes more than a simple collection of results on a particular topic. Each contribution conveys the history, evolution, and techniques used to solve the authors’ favorite conjectures and open problems, enhancing the reader’s overall comprehension and enthusiasm. The editors were inspired to create these volumes by the popular and well attended special sessions, entitled “My Favorite Graph Theory Conjectures, which were held at the winter AMS/MAA Joint Meeting in Boston (January, 2012), the SIAM Conference on Discrete Mathematics in Halifax (June,2012) and the winter AMS/MAA Joint meeting in Baltimore(January, 2014). In an effort to aid in the creation and dissemination of open problems, which is crucial to the growth and development of a field, the editors requested the speakers, as well as notable experts in graph theory, to contribute to these volumes. |
| discrete mathematics gary chartrand ping zhang: Discrete Mathematics with Ducks Sarah-marie Belcastro, 2018-11-15 Discrete Mathematics with Ducks, Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first edition was widely well received, with its whimsical writing style and numerous exercises and materials that engaged students at all levels. The new, expanded edition continues to facilitate effective and active learning. It is designed to help students learn about discrete mathematics through problem-based activities. These are created to inspire students to understand mathematics by actively practicing and doing, which helps students better retain what they’ve learned. As such, each chapter contains a mixture of discovery-based activities, projects, expository text, in-class exercises, and homework problems. The author’s lively and friendly writing style is appealing to both instructors and students alike and encourages readers to learn. The book’s light-hearted approach to the subject is a guiding principle and helps students learn mathematical abstraction. Features: The book’s Try This! sections encourage students to construct components of discussed concepts, theorems, and proofs Provided sets of discovery problems and illustrative examples reinforce learning Bonus sections can be used by instructors as part of their regular curriculum, for projects, or for further study |
| discrete mathematics gary chartrand ping zhang: Introduction to Topology Theodore W. Gamelin, Robert Everist Greene, 2013-04-22 This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition. |
| discrete mathematics gary chartrand ping zhang: An Introduction to Mathematical Reasoning Peter J. Eccles, 2013-06-26 This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas. |
| discrete mathematics gary chartrand ping zhang: Graph Theory with Applications to Engineering and Computer Science Narsingh Deo, 1974 Because of its inherent simplicity, graph theory has a wide range of applications in engineering, and in physical sciences. It has of course uses in social sciences, in linguistics and in numerous other areas. In fact, a graph can be used to represent almost any physical situation involving discrete objects and the relationship among them. Now with the solutions to engineering and other problems becoming so complex leading to larger graphs, it is virtually difficult to analyze without the use of computers. This book is recommended in IIT Kharagpur, West Bengal for B.Tech Computer Science, NIT Arunachal Pradesh, NIT Nagaland, NIT Agartala, NIT Silchar, Gauhati University, Dibrugarh University, North Eastern Regional Institute of Management, Assam Engineering College, West Bengal Univerity of Technology (WBUT) for B.Tech, M.Tech Computer Science, University of Burdwan, West Bengal for B.Tech. Computer Science, Jadavpur University, West Bengal for M.Sc. Computer Science, Kalyani College of Engineering, West Bengal for B.Tech. Computer Science. Key Features: This book provides a rigorous yet informal treatment of graph theory with an emphasis on computational aspects of graph theory and graph-theoretic algorithms. Numerous applications to actual engineering problems are incorpo-rated with software design and optimization topics. |
| discrete mathematics gary chartrand ping zhang: Graphs and Matrices Ravindra B. Bapat, 2014-09-19 This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering. |
| discrete mathematics gary chartrand ping zhang: Distance-Regular Graphs Andries E. Brouwer, Arjeh M. Cohen, Arnold Neumaier, 2012-12-06 Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as a common setting for regular graphs which are extremal in one sense or another. Several other important regular combinatorial structures are then shown to be equivalent to special families of distance-regular graphs. Other subjects of more general interest, such as regularity and extremal properties in graphs, association schemes, representations of graphs in euclidean space, groups and geometries of Lie type, groups acting on graphs, and codes are covered independently. Many new results and proofs and more than 750 references increase the encyclopaedic value of this book. |
| discrete mathematics gary chartrand ping zhang: Mississippi Noir Ace Atkins, Jimmy Cajoleas, RaShell R. Smith-Spears, 2016-07-11 This anthology of Mississippi crime fiction “has produced a unique, delicious flavor of noir” with stories by Ace Atkins, Megan Abott and more (New York Daily News). From poverty to state corruption, Mississippi has a well-deserved reputation for trouble. Could there be a connection between its many misfortunes and its rich literary legacy? Mississippians from Tennessee Williams and Eudora Welty to Richard Ford and John Grisham certainly know how to tell a good story. Now Mississippi Noir offers “a devilishly wrought introduction” to a new generation of “writers with a feel for Mississippi who are pursuing lonely, haunting paths of the imagination” (Associated Press). Mississippi Noir includes brand-new stories by Ace Atkins, William Boyle, Megan Abbott, Jack Pendarvis, Dominiqua Dickey, Michael Kardos, Jamie Paige, Jimmy Cajoleas, Chris Offutt, Michael Farris Smith, Andrew Paul, Lee Durkee, Robert Busby, John M. Floyd, RaShell R. Smith-Spears, and Mary Miller. |
| discrete mathematics gary chartrand ping zhang: Introduction to Graph Theory Richard J. Trudeau, 2013-04-15 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. |
| discrete mathematics gary chartrand ping zhang: Rainbow Connections of Graphs Xueliang Li, Yuefang Sun, 2012-02-23 Rainbow connections are natural combinatorial measures that are used in applications to secure the transfer of classified information between agencies in communication networks. Rainbow Connections of Graphs covers this new and emerging topic in graph theory and brings together a majority of the results that deal with the concept of rainbow connections, first introduced by Chartrand et al. in 2006. The authors begin with an introduction to rainbow connectedness, rainbow coloring, and rainbow connection number. The work is organized into the following categories, computation of the exact values of the rainbow connection numbers for some special graphs, algorithms and complexity analysis, upper bounds in terms of other graph parameters, rainbow connection for dense and sparse graphs, for some graph classes and graph products, rainbow k-connectivity and k-rainbow index, and, rainbow vertex-connection number. Rainbow Connections of Graphs appeals to researchers and graduate students in the field of graph theory. Conjectures, open problems and questions are given throughout the text with the hope for motivating young graph theorists and graduate students to do further study in this subject. |
| discrete mathematics gary chartrand ping zhang: Foundations of Discrete Mathematics Albert D. Polimeni, H. Joseph Straight, 1985 |
| discrete mathematics gary chartrand ping zhang: Weyl Group Multiple Dirichlet Series Ben Brubaker, Daniel Bump, Solomon Friedberg, 2011 Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics. These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished. The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation. |
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