Combinatorics And Reasoning
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Combinatorics And Reasoning
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Author : Carolyn A. Maher
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-29
Combinatorics And Reasoning written by Carolyn A. Maher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-29 with Education categories.
Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level. This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.
Combinatorial Reasoning
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Author : Duane DeTemple
language : en
Publisher: John Wiley & Sons
Release Date : 2014-04-08
Combinatorial Reasoning written by Duane DeTemple and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-08 with Mathematics categories.
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.
Combinatorics And Reasoning
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Author : Carolyn A. Maher
language : en
Publisher: Springer
Release Date : 2011-01-14
Combinatorics And Reasoning written by Carolyn A. Maher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-14 with Education categories.
Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level. This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.
Solutions Manual To Accompany Combinatorial Reasoning An Introduction To The Art Of Counting
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Author : Duane DeTemple
language : en
Publisher: John Wiley & Sons
Release Date : 2014-09-29
Solutions Manual To Accompany Combinatorial Reasoning An Introduction To The Art Of Counting written by Duane DeTemple and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-29 with Mathematics categories.
COMBINATORIAL REASONING Showcases the interdisciplinary aspects of combinatorics and illustrates how to problem solve with a multitude of exercises 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.
Well Quasi Orders In Computation Logic Language And Reasoning
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Author : Peter M. Schuster
language : en
Publisher: Springer Nature
Release Date : 2020-01-01
Well Quasi Orders In Computation Logic Language And Reasoning written by Peter M. Schuster and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-01 with Philosophy categories.
This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.
Probabilistic Reasoning In Combinatorics
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Author : Matthew Kwan
language : en
Publisher:
Release Date : 2018
Probabilistic Reasoning In Combinatorics written by Matthew Kwan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
An Introduction To Mathematical Reasoning
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Author : Peter J. Eccles
language : en
Publisher: Cambridge University Press
Release Date : 2013-06-26
An Introduction To Mathematical Reasoning written by Peter J. Eccles and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-26 with Mathematics categories.
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.
Applied Combinatorics
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Author : Alan Tucker
language : en
Publisher:
Release Date : 1984
Applied Combinatorics written by Alan Tucker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Combinatorial analysis categories.
This revision of a survey of combinatorial analysis and graph theory is designed for students specializing in mathematics and computer science. Three principal aspects of combinatorial reasoning are emphasized in the book: the systematic analysis of different possibilities, the exploration of the logical structure of a problem, and ingenuity. Keeping theory to a minimum, it uses numerical examples to demonstrate the combinatorial reasoning involved in computer science, operations research and finite probability.
An Introduction To Mathematical Reasoning
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Author : Peter Eccles
language : en
Publisher:
Release Date : 1997
An Introduction To Mathematical Reasoning written by Peter Eccles and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. 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 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. Over 250 problems include questions to interest and challenge the most able student as well as plenty of routine exercises to help familiarize the reader with the basic ideas.
Discrete Mathematics
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Author : Douglas E. Ensley
language : en
Publisher: John Wiley & Sons
Release Date : 2005-10-07
Discrete Mathematics written by Douglas E. Ensley and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-07 with Mathematics categories.
Did you know that games and puzzles have given birth to many of today's deepest mathematical subjects? Now, with Douglas Ensley and Winston Crawley's Introduction to Discrete Mathematics, you can explore mathematical writing, abstract structures, counting, discrete probability, and graph theory, through games, puzzles, patterns, magic tricks, and real-world problems. You will discover how new mathematical topics can be applied to everyday situations, learn how to work with proofs, and develop your problem-solving skills along the way. Online applications help improve your mathematical reasoning. Highly intriguing, interactive Flash-based applications illustrate key mathematical concepts and help you develop your ability to reason mathematically, solve problems, and work with proofs. Explore More icons in the text direct you to online activities at www.wiley.com/college/ensley. Improve your grade with the Student Solutions Manual. A supplementary Student Solutions Manual contains more detailed solutions to selected exercises in the text.