KARIN R SAOUB - Böcker

This booknbspintroduces graph theory to students who are not mathematics majors. Instead of featuring formal mathematical proofs, it focuses on explanations and logical reasoning. It also includes discussions of historical problems and modern questions.nbsp

Graph Theory: An Introduction to Proofs, Algorithms, and ApplicationsGraph 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.FeaturesThe 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.AuthorKarin 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.

Graph theory is an area of mathematics that can challenge one's notions of what mathematics is and can be. The author discovered this as a student, as her discovery led her to pursue an advanced degree in mathematics. In A Tour through Graph Theory, Second Edition, the author shares her enthusiasm for the topic with students assuming only high school mathematics experience.The book introduces graph theory to students who are not mathematics majors. To distinguish itself from others covering the same topic, the book: Employs graph theory to teach mathematical reasoningPromotes critical thinking and problem solvingProvides rich examples and clear explanations without using proofsIncludes thoughtful discussions of historical problems and modern questionsNew to this edition, the author offers more explanation for concepts or adds more context for the topics. Significant care was taken in modifying the description and examples for the more complex algorithms and theoretical discussions. More than 40 new exercises have been added, and 50 additional graphs have been added to existing exercises to provide more options for homework or quiz problems.This book is intended to strike a balance between focusing on the theory and exploration of proof techniques and the algorithmic aspect of graph theory. Explanations and logical reasoning for solutions, but no formal mathematical proofs, are provided. Each chapter includes problems to test understanding of the material and can be used for homework, quiz problems, or self-study.

Graph theory is an area of mathematics that can challenge one's notions of what mathematics is and can be. The author discovered this as a student, as her discovery led her to pursue an advanced degree in mathematics. In A Tour through Graph Theory, Second Edition, the author shares her enthusiasm for the topic with students assuming only high school mathematics experience.The book introduces graph theory to students who are not mathematics majors. To distinguish itself from others covering the same topic, the book: Employs graph theory to teach mathematical reasoningPromotes critical thinking and problem solvingProvides rich examples and clear explanations without using proofsIncludes thoughtful discussions of historical problems and modern questionsNew to this edition, the author offers more explanation for concepts or adds more context for the topics. Significant care was taken in modifying the description and examples for the more complex algorithms and theoretical discussions. More than 40 new exercises have been added, and 50 additional graphs have been added to existing exercises to provide more options for homework or quiz problems.This book is intended to strike a balance between focusing on the theory and exploration of proof techniques and the algorithmic aspect of graph theory. Explanations and logical reasoning for solutions, but no formal mathematical proofs, are provided. Each chapter includes problems to test understanding of the material and can be used for homework, quiz problems, or self-study.

A Tour Through Graph Theory introduces graph theory to students who are not mathematics majors. Rather than featuring formal mathematical proofs, the book focuses on explanations and logical reasoning. It also includes thoughtful discussions of historical problems and modern questions. The book inspires readers to learn by working through examples, drawing graphs and exploring concepts. This book distinguishes itself from others covering the same topic. It strikes a balance of focusing on accessible problems for non-mathematical students while providing enough material for a semester-long course. Employs graph theory to teach mathematical reasoning Expressly written for non-mathematical students Promotes critical thinking and problem solving Provides rich examples and clear explanations without using proofs

A Tour Through Graph Theory introduces graph theory to students who are not mathematics majors. Rather than featuring formal mathematical proofs, the book focuses on explanations and logical reasoning. It also includes thoughtful discussions of historical problems and modern questions. The book inspires readers to learn by working through examples, drawing graphs and exploring concepts. This book distinguishes itself from others covering the same topic. It strikes a balance of focusing on accessible problems for non-mathematical students while providing enough material for a semester-long course. Employs graph theory to teach mathematical reasoning Expressly written for non-mathematical students Promotes critical thinking and problem solving Provides rich examples and clear explanations without using proofs