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9781118652183 English 1118652185 With a focus on beginning combinatorics, this book features complete exposition of the discussed topics and over 700 exercises that illustrate the presented concepts and methodology. The book covers fundamental topics in enumeration, all of which are explored in great depth. The authors' approach is very reader-friendly and avoids the "scholarly tone" found in many other related books. Abstract ideas are grounded in familiar concrete settings, and there are far more diagrams within the book than are found in most other related texts. In addition, simple cases are treated first before general and advanced cases, and the notations are kept simple and helpful. To help readers learn how combinatorics interacts with other subjects as a tool or as an application, the book provides brief summaries of basic concepts from probability, power series, and group theory. Each chapter begins with an introduction to the topics covered within the chapter, followed by sections that are each accompanied by a large number of exercises that range from basic calculations to more challenging problems. The exercises are carefully structured to range from the routine to the more advanced. The beginning level problems are designed to confirm and develop students' understanding of the fundamental concepts and calculations, where a calculation is most often based on combinatorial reasoning rather than algebraic manipulation. More advanced exercises allow students to explore and more deeply understand the topics in the chapter and apply the techniques to more complex combinatorial situations. Each chapter also contains a brief summary of the most important concepts covered. Finally, each chapter ends with a few additional problems that further synthesize the ideas that were presented in the chapter. Chapter coverage includes: Initial EnCOUNTers with Combinatorial Reasoning; Arrangements, Selections, and Distributions; Binomial Series and Generating Functions; Alternating Sums, Inclusion-Exclusion, and Rook Polynomials; Recurrence Relations; Special Numbers; Linear Spaces and Recurrences Sequences; and Counting Symmetric Arrangements., Written by two well-known scholars in the field, Combinatorial Reasoning: An Introduction to the Art of Counting presents a clear and comprehensive introduction to the concepts and methodology of beginning combinatorics. Focusing on modern techniques and applications, the book develops a variety of effective approaches to solving counting problems. Balancing abstract ideas with specific topical coverage, the book utilizes real world examples with problems ranging from basic calculations that are designed to develop fundamental concepts to more challenging exercises that allow for a deeper exploration of complex combinatorial situations. Simple cases are treated first before moving on to general and more advanced cases. Additional features of the book include: * Approximately 700 carefully structured problems designed for readers at multiple levels, many with hints and/or short answers * Numerous examples that illustrate problem solving using both combinatorial reasoning and sophisticated algorithmic methods * A novel approach to the study of recurrence sequences, which simplifies many proofs and calculations * Concrete examples and diagrams interspersed throughout to further aid comprehension of abstract concepts * A chapter-by-chapter review to clarify the most crucial concepts covered Combinatorial Reasoning: An Introduction to the Art of Counting is an excellent textbook for upper-undergraduate and beginning graduate-level courses on introductory combinatorics and discrete mathematics., Written by well-known scholars in the field, this book introduces combinatorics alongside modern techniques, showcases the interdisciplinary aspects of the topic, and illustrates how to problem solve with a multitude of exercises throughout. The authors approach is very reader-friendly and avoids the "scholarly tone" found in many books on this topic. Combinatorial Reasoning: An Introduction to the Art of Counting : Focuses on enumeration and combinatorial thinking as a way to develop a variety of effective approaches to solving counting problems Includes brief summaries of basic concepts from probability, power series, and group theory to show how combinatorics interacts with other fields Provides abstract ideas that are grounded in familiar concrete settings and features plentiful diagrams throughout to further add in reader understanding Presents simple and helpful notations as needed, and simple cases are treated first before more general and/or advanced cases Contains over 700 exercise sets, ranging from the routine to the advanced, with either hints, short answers, or complete solutions for odd numbered problems. An Instructors Manual (available via request to the Publisher) provides complete solutions for all exercises
9781118652183 English 1118652185 With a focus on beginning combinatorics, this book features complete exposition of the discussed topics and over 700 exercises that illustrate the presented concepts and methodology. The book covers fundamental topics in enumeration, all of which are explored in great depth. The authors' approach is very reader-friendly and avoids the "scholarly tone" found in many other related books. Abstract ideas are grounded in familiar concrete settings, and there are far more diagrams within the book than are found in most other related texts. In addition, simple cases are treated first before general and advanced cases, and the notations are kept simple and helpful. To help readers learn how combinatorics interacts with other subjects as a tool or as an application, the book provides brief summaries of basic concepts from probability, power series, and group theory. Each chapter begins with an introduction to the topics covered within the chapter, followed by sections that are each accompanied by a large number of exercises that range from basic calculations to more challenging problems. The exercises are carefully structured to range from the routine to the more advanced. The beginning level problems are designed to confirm and develop students' understanding of the fundamental concepts and calculations, where a calculation is most often based on combinatorial reasoning rather than algebraic manipulation. More advanced exercises allow students to explore and more deeply understand the topics in the chapter and apply the techniques to more complex combinatorial situations. Each chapter also contains a brief summary of the most important concepts covered. Finally, each chapter ends with a few additional problems that further synthesize the ideas that were presented in the chapter. Chapter coverage includes: Initial EnCOUNTers with Combinatorial Reasoning; Arrangements, Selections, and Distributions; Binomial Series and Generating Functions; Alternating Sums, Inclusion-Exclusion, and Rook Polynomials; Recurrence Relations; Special Numbers; Linear Spaces and Recurrences Sequences; and Counting Symmetric Arrangements., Written by two well-known scholars in the field, Combinatorial Reasoning: An Introduction to the Art of Counting presents a clear and comprehensive introduction to the concepts and methodology of beginning combinatorics. Focusing on modern techniques and applications, the book develops a variety of effective approaches to solving counting problems. Balancing abstract ideas with specific topical coverage, the book utilizes real world examples with problems ranging from basic calculations that are designed to develop fundamental concepts to more challenging exercises that allow for a deeper exploration of complex combinatorial situations. Simple cases are treated first before moving on to general and more advanced cases. Additional features of the book include: * Approximately 700 carefully structured problems designed for readers at multiple levels, many with hints and/or short answers * Numerous examples that illustrate problem solving using both combinatorial reasoning and sophisticated algorithmic methods * A novel approach to the study of recurrence sequences, which simplifies many proofs and calculations * Concrete examples and diagrams interspersed throughout to further aid comprehension of abstract concepts * A chapter-by-chapter review to clarify the most crucial concepts covered Combinatorial Reasoning: An Introduction to the Art of Counting is an excellent textbook for upper-undergraduate and beginning graduate-level courses on introductory combinatorics and discrete mathematics., Written by well-known scholars in the field, this book introduces combinatorics alongside modern techniques, showcases the interdisciplinary aspects of the topic, and illustrates how to problem solve with a multitude of exercises throughout. The authors approach is very reader-friendly and avoids the "scholarly tone" found in many books on this topic. Combinatorial Reasoning: An Introduction to the Art of Counting : Focuses on enumeration and combinatorial thinking as a way to develop a variety of effective approaches to solving counting problems Includes brief summaries of basic concepts from probability, power series, and group theory to show how combinatorics interacts with other fields Provides abstract ideas that are grounded in familiar concrete settings and features plentiful diagrams throughout to further add in reader understanding Presents simple and helpful notations as needed, and simple cases are treated first before more general and/or advanced cases Contains over 700 exercise sets, ranging from the routine to the advanced, with either hints, short answers, or complete solutions for odd numbered problems. An Instructors Manual (available via request to the Publisher) provides complete solutions for all exercises