Gary Chartrand – författare

For courses in Transition to Advanced Mathematics or Introduction to Proof.

Meticulously crafted, student-friendly text that helps build mathematical maturity

Mathematical Proofs: A Transition to Advanced Mathematics, 4th Edition introduces students to proof techniques, analyzing proofs, and writing proofs of their own that are not only mathematically correct but clearly written. Written in a student-friendly manner, it provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as optional excursions into fields such as number theory, combinatorics, and calculus. The exercises receive consistent praise from users for their thoughtfulness and creativity.  They help students progress from understanding and analyzing proofs and techniques to producing well-constructed proofs independently. This book is also an excellent reference for students to use in future courses when writing or reading proofs.

0134746759 / 9780134746753 Chartrand/Polimeni/Zhang, Mathematical Proofs: A Transition to Advanced Mathematics, 4/e

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:

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:

Graphs & Digraphs, Seventh Edition masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory. This classic text, widely popular among students and instructors alike for decades, is thoroughly streamlined in this new, seventh edition, to present a text consistent with contemporary expectations.

Changes and updates to this edition include:

The text remains the consummate choice for an advanced undergraduate level or introductory graduate-level course exploring the subject’s fascinating history, while covering a host of interesting problems and diverse applications. Our major objective is to introduce and treat graph theory as the beautiful area of mathematics we have always found it to be. We have striven to produce a reader-friendly, carefully written book that emphasizes the mathematical theory of graphs, in all their forms. While a certain amount of mathematical maturity, including a solid understanding of proof, is required to appreciate the material, with a small number of exceptions this is the only pre-requisite.

In addition, owing to the exhilarating pace of progress in the field, there have been countless developments in fundamental graph theory ever since the previous edition, and many of these discoveries have been incorporated into the book. Of course, some of the proofs of these results are beyond the scope of the book, in which cases we have only included their statements. In other cases, however, these new results have led us to completely reorganize our presentation. Two examples are the chapters on coloring and extremal graph theory.

Graphs & Digraphs, Seventh Edition masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory. This classic text, widely popular among students and instructors alike for decades, is thoroughly streamlined in this new, seventh edition, to present a text consistent with contemporary expectations.

Changes and updates to this edition include:

The text remains the consummate choice for an advanced undergraduate level or introductory graduate-level course exploring the subject’s fascinating history, while covering a host of interesting problems and diverse applications. Our major objective is to introduce and treat graph theory as the beautiful area of mathematics we have always found it to be. We have striven to produce a reader-friendly, carefully written book that emphasizes the mathematical theory of graphs, in all their forms. While a certain amount of mathematical maturity, including a solid understanding of proof, is required to appreciate the material, with a small number of exceptions this is the only pre-requisite.

In addition, owing to the exhilarating pace of progress in the field, there have been countless developments in fundamental graph theory ever since the previous edition, and many of these discoveries have been incorporated into the book. Of course, some of the proofs of these results are beyond the scope of the book, in which cases we have only included their statements. In other cases, however, these new results have led us to completely reorganize our presentation. Two examples are the chapters on coloring and extremal graph theory.

The history, formulas, and most famous puzzles of graph theoryGraph 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.

This book depicts graph labelings that have led to thought-provoking problems and conjectures. Problems and conjectures in graceful labelings, harmonious labelings, prime labelings, additive labelings, and zonal labelings are introduced with fundamentals, examples, and illustrations. A new labeling with a connection to the four color theorem is described to aid mathematicians to initiate new methods and techniques to study classical coloring problems from a new perspective. Researchers and graduate students interested in graph labelings will find the concepts and problems featured in this book valuable for finding new areas of research.