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How to Count: An Introduction to Combinatorics, Second Edition by Alan Slomson (-
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eBay-Artikelnr.:365722241666
Artikelmerkmale
- Artikelzustand
- ISBN-13
- 9781420082609
- Book Title
- How to Count
- ISBN
- 9781420082609
Über dieses Produkt
Product Identifiers
Publisher
CRC Press LLC
ISBN-10
1420082604
ISBN-13
9781420082609
eBay Product ID (ePID)
66543554
Product Key Features
Number of Pages
444 Pages
Language
English
Publication Name
How to Count : an Introduction to Combinatorics, Second Edition
Subject
Operating Systems / General, Algebra / General, Combinatorics
Publication Year
2010
Type
Textbook
Subject Area
Mathematics, Computers
Format
Hardcover
Dimensions
Item Height
0.8 in
Item Weight
36.1 Oz
Item Length
10.2 in
Item Width
7.3 in
Additional Product Features
Edition Number
2
Intended Audience
College Audience
LCCN
2010-024420
Reviews
The current edition is about 60% longer and represents an extensively updated collaboration coauthored with R.B.J.T. Allenby. Both authors have decades of experience teaching related material at the University of Leeds. ... The book is beautifully structured to facilitate both instruction in a classroom as well as self-instruction. ... Every section of the book has a number of [paired] exercises which are designed to solidify and build understanding of the topics in the section. ... This is exactly the kind of exercise regimen serious readers, instructors, and students need and are so rarely provided. ... Another pedagogical asset of the text is the extensive incorporation of historical anecdotes about the discoverers of the results. ... it fosters an admiration of the developers of the field, an attitude which is key to transforming students of mathematics into professional mathematicians. ... The authors have created an interesting, instructive, and remarkably usable text. The book clearly benefits instructors who need a solid, readable text for a course on discrete mathematics and counting. In fact, for any professional who wants an understandable text from which they can acquire a broad and mathematically solid view of many of the classic problems and results in counting theory, including their origin, proof, and application to other problems in combinatorics, this book is recommended. --James A. McHugh, SIAM Review, 54 (1), 2012 ... thoughtfully written, contain[s] plenty of material and exercises ... very readable and useful ... --MAA Reviews, February 2011 The reasons I adopted this book are simple: it's the best one-volume book on combinatorics for undergraduates. It begins slowly and gently, but does not avoid subtleties or difficulties. It includes the right mixture of topics without bloat, and always with an eye to good mathematical taste and coherence. Enumerative combinatorics is developed rather fully, through Stirling and Catalan numbers, for example, before generating functions are introduced. Thus this tool is very much appreciated and its 'naturalness' is easier to comprehend. Likewise, partitions are introduced in the absence of generating functions, and then later generating functions are applied to them: again, a wise pedagogical move. The ordering of chapters is nicely set up for two different single-semester courses: one that uses more algebra, culminating in Polya's counting theorem; the other concentrating on graph theory, ending with a variety of Ramsey theory topics. ... I was very much impressed with the first edition when I encountered it in 1994. I like the second edition even more. ... --Paul Zeitz, University of San Francisco, California, USA Completely revised, the book shows how to solve numerous classic and other interesting combinatorial problems. ... The reading list at the end of the book gives direction to exploring more complicated counting problems as well as other areas of combinatorics. --Zentralblatt MATH1197, The current edition is about 60% longer and represents an extensively updated collaboration coauthored with R.B.J.T. Allenby. Both authors have decades of experience teaching related material at the University of Leeds. ... The book is beautifully structured to facilitate both instruction in a classroom as well as self-instruction. ... Every section of the book has a number of [paired] exercises which are designed to solidify and build understanding of the topics in the section. ... This is exactly the kind of exercise regimen serious readers, instructors, and students need and are so rarely provided. ... Another pedagogical asset of the text is the extensive incorporation of historical anecdotes about the discoverers of the results. ... it fosters an admiration of the developers of the field, an attitude which is key to transforming students of mathematics into professional mathematicians. ... The authors have created an interesting, instructive, and remarkably usable text. The book clearly benefits instructors who need a solid, readable text for a course on discrete mathematics and counting. In fact, for any professional who wants an understandable text from which they can acquire a broad and mathematically solid view of many of the classic problems and results in counting theory, including their origin, proof, and application to other problems in combinatorics, this book is recommended. --James A. McHugh, SIAM Review, 54 (1), 2012 ... thoughtfully written, contain[s] plenty of material and exercises ... very readable and useful ... --MAA Reviews, February 2011 The reasons I adopted this book are simple: it's the best one-volume book on combinatorics for undergraduates. It begins slowly and gently, but does not avoid subtleties or difficulties. It includes the right mixture of topics without bloat, and always with an eye to good mathematical taste and coherence. Enumerative combinatorics is developed rather fully, through Stirling and Catalan numbers, for example, before generating functions are introduced. Thus this tool is very much appreciated and its 'naturalness' is easier to comprehend. Likewise, partitions are introduced in the absence of generating functions, and then later generating functions are applied to them: again, a wise pedagogical move. The ordering of chapters is nicely set up for two different single-semester courses: one that uses more algebra, culminating in Polya's counting theorem; the other concentrating on graph theory, ending with a variety of Ramsey theory topics. ... I was very much impressed with the first edition when I encountered it in 1994. I like the second edition even more. ... --Paul Zeitz, University of San Francisco, California, USA Completely revised, the book shows how to solve numerous classic and other interesting combinatorial problems. ... The reading list at the end of the book gives direction to exploring more complicated counting problems as well as other areas of combinatorics. --Zentralblatt MATH 1197, thoughtfully written, contain[s] plenty of material and exercises very readable and useful �MAA Reviews, February 2011 The reasons I adopted this book are simple: it "s the best one-volume book on combinatorics for undergraduates. It begins slowly and gently, but does not avoid subtleties or difficulties. It includes the right mixture of topics without bloat, and always with an eye to good mathematical taste and coherence. Enumerative combinatorics is developed rather fully, through Stirling and Catalan numbers, for example, before generating functions are introduced. Thus this tool is very much appreciated and its naturalness " is easier to comprehend. Likewise, partitions are introduced in the absence of generating functions, and then later generating functions are applied to them: again, a wise pedagogical move. The ordering of chapters is nicely set up for two different single-semester courses: one that uses more algebra, culminating in Polya "s counting theorem; the other concentrating on graph theory, ending with a variety of Ramsey theory topics. I was very much impressed with the first edition when I encountered it in 1994. I like the second edition even more. �Paul Zeitz, University of San Francisco, California, USA, … thoughtfully written, contain[s] plenty of material and exercises … very readable and useful … -MAA Reviews, February 2011 The reasons I adopted this book are simple: it's the best one-volume book on combinatorics for undergraduates. It begins slowly and gently, but does not avoid subtleties or difficulties. It includes the right mixture of topics without bloat, and always with an eye to good mathematical taste and coherence. Enumerative combinatorics is developed rather fully, through Stirling and Catalan numbers, for example, before generating functions are introduced. Thus this tool is very much appreciated and its 'naturalness' is easier to comprehend. Likewise, partitions are introduced in the absence of generating functions, and then later generating functions are applied to them: again, a wise pedagogical move. The ordering of chapters is nicely set up for two different single-semester courses: one that uses more algebra, culminating in Polya's counting theorem; the other concentrating on graph theory, ending with a variety of Ramsey theory topics. … I was very much impressed with the first edition when I encountered it in 1994. I like the second edition even more. … -Paul Zeitz, University of San Francisco, California, USA Completely revised, the book shows how to solve numerous classic and other interesting combinatorial problems. … The reading list at the end of the book gives direction to exploring more complicated counting problems as well as other areas of combinatorics. -Zentralblatt MATH1197, The current edition is about 60% longer and represents an extensively updated collaboration coauthored with R.B.J.T. Allenby. Both authors have decades of experience teaching related material at the University of Leeds. ... The book is beautifully structured to facilitate both instruction in a classroom as well as self-instruction. ... Every section of the book has a number of [paired] exercises which are designed to solidify and build understanding of the topics in the section. ... This is exactly the kind of exercise regimen serious readers, instructors, and students need and are so rarely provided. ... Another pedagogical asset of the text is the extensive incorporation of historical anecdotes about the discoverers of the results. ... it fosters an admiration of the developers of the field, an attitude which is key to transforming students of mathematics into professional mathematicians. ... The authors have created an interesting, instructive, and remarkably usable text. The book clearly benefits instructors who need a solid, readable text for a course on discrete mathematics and counting. In fact, for any professional who wants an understandable text from which they can acquire a broad and mathematically solid view of many of the classic problems and results in counting theory, including their origin, proof, and application to other problems in combinatorics, this book is recommended. --James A. McHugh, SIAM Review, 54 (1), 2012 ... thoughtfully written, contain[s book is recommended. --James A. McHugh, SIAM Review, 54 (1), 2012 ... thoughtfully written, contain[s] plenty of material and exercises ... very readable and useful ... --MAA Reviews, February 2011 The reasons I adopted this book are simple: it's the best one-volume book on combinatorics for undergraduates. It begins slowly and gently, but does not avoid subtleties or difficulties. It includes the right mixture of topics without bloat, and always with an eye to good mathematical taste and coherence. Enumerative combinatorics is developed rather fully, through Stirling and Catalan numbers, for example, before generating functions are introduced. Thus this tool is very much appreciated and its 'naturalness' is easier to comprehend. Likewise, partitions are introduced in the absence of generating functions, and then later generating functions are applied to them: again, a wise pedagogical move. The ordering of chapters is nicely set up for two different single-semester courses: one that uses more algebra, culminating in Polya's counting theorem; the other concentrating on graph theory, ending with a variety of Ramsey theory topics. ... I was very much impressed with the first edition when I encountered it in 1994. I like the second edition even more. ... --Paul Zeitz, University of San Francisco, California, USA Completely revised, the book shows how to solve numerous classic and other interesting combinatorial problems. ... The reading list at the end of the book gives direction to exploring more complicated counting problems as well as other areas of combinatorics. --Zentralblatt MATH1197 centrating on graph theory, ending with a variety of Ramsey theory topics. ... I was very much impressed with the first edition when I encountered it in 1994. I like the second edition even more. ... --Paul Zeitz, University of San Francisco, California, USA Completely revised, the book shows how to solve numerous classic and other interesting combinatorial problems. ... The reading list at the end of the book gives direction to exploring more complicated counting problems as well as other areas of combinatorics. --Zentralblatt MATH1197, The current edition is about 60% longer and represents an extensively updated collaboration coauthored with R.B.J.T. Allenby. Both authors have decades of experience teaching related material at the University of Leeds. e The book is beautifully structured to facilitate both instruction in a classroom as well as self-instruction. e Every section of the book has a number of [paired] exercises which are designed to solidify and build understanding of the topics in the section. e This is exactly the kind of exercise regimen serious readers, instructors, and students need and are so rarely provided. e Another pedagogical asset of the text is the extensive incorporation of historical anecdotes about the discoverers of the results. e it fosters an admiration of the developers of the field, an attitude which is key to transforming students of mathematics into professional mathematicians. e The authors have created an interesting, instructive, and remarkably usable text. The book clearly benefits instructors who need a solid, readable text for a course on discrete mathematics and counting. In fact, for any professional who wants an understandable text from which they can acquire a broad and mathematically solid view of many of the classic problems and results in counting theory, including their origin, proof, and application to other problems in combinatorics, this book is recommended. e"James A. McHugh, SIAM Review, 54 (1), 2012 e thoughtfully written, contain[s] plenty of material and exercises e very readable and useful e e"MAA Reviews, February 2011 The reasons I adopted this book are simple: ite(tm)s the best one-volume book on combinatorics for undergraduates. It begins slowly and gently, but does not avoid subtleties or difficulties. It includes the right mixture of topics without bloat, and always with an eye to good mathematical taste and coherence. Enumerative combinatorics is developed rather fully, through Stirling and Catalan numbers, for example, before generating functions are introduced. Thus this tool is very much appreciated and its e~naturalnesse(tm) is easier to comprehend. Likewise, partitions are introduced in the absence of generating functions, and then later generating functions are applied to them: again, a wise pedagogical move. The ordering of chapters is nicely set up for two different single-semester courses: one that uses more algebra, culminating in Polyae(tm)s counting theorem; the other concentrating on graph theory, ending with a variety of Ramsey theory topics. e I was very much impressed with the first edition when I encountered it in 1994. I like the second edition even more. e e"Paul Zeitz, University of San Francisco, California, USA Completely revised, the book shows how to solve numerous classic and other interesting combinatorial problems. e The reading list at the end of the book gives direction to exploring more complicated counting problems as well as other areas of combinatorics. e"Zentralblatt MATH 1197, The current edition is about 60% longer and represents an extensively updated collaboration coauthored with R.B.J.T. Allenby. Both authors have decades of experience teaching related material at the University of Leeds. … The book is beautifully structured to facilitate both instruction in a classroom as well as self-instruction. … Every section of the book has a number of [paired] exercises which are designed to solidify and build understanding of the topics in the section. … This is exactly the kind of exercise regimen serious readers, instructors, and students need and are so rarely provided. … Another pedagogical asset of the text is the extensive incorporation of historical anecdotes about the discoverers of the results. … it fosters an admiration of the developers of the field, an attitude which is key to transforming students of mathematics into professional mathematicians. … The authors have created an interesting, instructive, and remarkably usable text. The book clearly benefits instructors who need a solid, readable text for a course on discrete mathematics and counting. In fact, for any professional who wants an understandable text from which they can acquire a broad and mathematically solid view of many of the classic problems and results in counting theory, including their origin, proof, and application to other problems in combinatorics, this book is recommended. -James A. McHugh, SIAM Review, 54 (1), 2012 … thoughtfully written, contain[s] plenty of material and exercises … very readable and useful … -MAA Reviews, February 2011 The reasons I adopted this book are simple: it's the best one-volume book on combinatorics for undergraduates. It begins slowly and gently, but does not avoid subtleties or difficulties. It includes the right mixture of topics without bloat, and always with an eye to good mathematical taste and coherence. Enumerative combinatorics is developed rather fully, through Stirling and Catalan numbers, for example, before generating functions are introduced. Thus this tool is very much appreciated and its 'naturalness' is easier to comprehend. Likewise, partitions are introduced in the absence of generating functions, and then later generating functions are applied to them: again, a wise pedagogical move. The ordering of chapters is nicely set up for two different single-semester courses: one that uses more algebra, culminating in Polya's counting theorem; the other concentrating on graph theory, ending with a variety of Ramsey theory topics. … I was very much impressed with the first edition when I encountered it in 1994. I like the second edition even more. … -Paul Zeitz, University of San Francisco, California, USA Completely revised, the book shows how to solve numerous classic and other interesting combinatorial problems. … The reading list at the end of the book gives direction to exploring more complicated counting problems as well as other areas of combinatorics. -Zentralblatt MATH1197
Illustrated
Yes
Edition Description
New Edition,Revised edition
Table Of Content
What's It All About? What Is Combinatorics? Classic Problems What You Need to Know Are You Sitting Comfortably? Permutations and Combinations The Combinatorial Approach Permutations Combinations Applications to Probability Problems The Multinomial Theorem Permutations and Cycles Occupancy Problems Counting the Solutions of Equations New Problems from Old A "Reduction" Theorem for the Stirling Numbers The Inclusion-Exclusion Principle Double Counting Derangements A Formula for the Stirling Numbers Stirling and Catalan Numbers Stirling Numbers Permutations and Stirling Numbers Catalan Numbers Partitions and Dot Diagrams Partitions Dot Diagrams A Bit of Speculation More Proofs Using Dot Diagrams Generating Functions and Recurrence Relations Functions and Power Series Generating Functions What Is a Recurrence Relation? Fibonacci Numbers Solving Homogeneous Linear Recurrence Relations Nonhomogeneous Linear Recurrence Relations The Theory of Linear Recurrence Relations Some Nonlinear Recurrence Relations Partitions and Generating Functions The Generating Function for the Partition Numbers A Quick(ish) Way of Finding p(n) An Upper Bound for the Partition Numbers The Hardy-Ramanujan Formula The Story of Hardy and Ramanujan Introduction to Graphs Graphs and Pictures Graphs: A Picture-Free Definition Isomorphism of Graphs Paths and Connected Graphs Planar Graphs Eulerian Graphs Hamiltonian Graphs The Four-Color Theorem Trees What Is a Tree? Labeled Trees Spanning Trees and Minimal Connectors The Shortest-Path Problem Groups of Permutations Permutations as Groups Symmetry Groups Subgroups and Lagrange's Theorem Orders of Group Elements The Orders of Permutations Group Actions Colorings The Axioms for Group Actions Orbits Stabilizers Counting Patterns Frobenius's Counting Theorem Applications of Frobenius's Counting Theorem Pólya Counting Colorings and Group Actions Pattern Inventories The Cycle Index of a Group Pólya's Counting Theorem: Statement and Examples Pólya's Counting Theorem: The Proof Counting Simple Graphs Dirichlet's Pigeonhole Principle The Origin of the Principle The Pigeonhole Principle More Applications of the Pigeonhole Principle Ramsey Theory What Is Ramsey's Theorem? Three Lovely Theorems Graphs of Many Colors Euclidean Ramsey Theory Rook Polynomials and Matchings How Rook Polynomials Are Defined Matchings and Marriages Solutions to the A Exercises Books for Further Reading Index
Synopsis
Emphasizes a Problem Solving Approach A first course in combinatorics Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics. New to the Second Edition This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet's pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises. Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and P lya's counting theorem., Emphasizes a Problem Solving Approach A first course in combinatorics Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics. New to the Second Edition This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet's pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises. Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya's counting theorem.
LC Classification Number
QA164
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- r***r (2961)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufBook arrived today, 2 days before deadline given by the seller. Well-packaged & in good condition. Price was very competitive, & the book was accurately listed. Great communication. I appreciate the seller getting back to me when I was having trouble tracking the book's delivery progress. Apparently there were 2 different tracking numbers - one in Canada & the other in the U.S., since it was initially shipped from Canada. Thank you very much for your quick response & helpful information.Rethinking Investing: A Very Short Guide to Very Long-Term Investing by Charles (Nr. 396183075510)
- e***_ (14)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufSeller handles a massive inventory so I give them grace on the slow processing and shipping. They were very communicative and prompt with their response when I messaged in asking about it. Book was in good condition as described. Small ding on the page edges which wasn't mentioned, but that's fairly common even at your typical book store. Still a good value and I'd buy from them again.
- 0***i (5)- Bewertung vom Käufer.Letzter MonatBestätigter KaufThe first item arrived with some damage to the inside back cover, but the seller responded immediately, assuring me they’d provide a replacement, and even told me I could keep the original. They were upfront about a short delay, and gave a clear estimated ship date, and followed up right on time once it shipped. The replacement arrived in perfect condition and exactly as described. I really appreciated their transparency and professionalism. Would definitely buy from them again!
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grandeagleretail
98,3% positive Bewertungen•2,8 Mio. Artikel verkauft
Angemeldet als gewerblicher Verkäufer
Verkäuferbewertungen (1.054.155)
- r***r (2961)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufBook arrived today, 2 days before deadline given by the seller. Well-packaged & in good condition. Price was very competitive, & the book was accurately listed. Great communication. I appreciate the seller getting back to me when I was having trouble tracking the book's delivery progress. Apparently there were 2 different tracking numbers - one in Canada & the other in the U.S., since it was initially shipped from Canada. Thank you very much for your quick response & helpful information.Rethinking Investing: A Very Short Guide to Very Long-Term Investing by Charles (Nr. 396183075510)
- e***_ (14)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufSeller handles a massive inventory so I give them grace on the slow processing and shipping. They were very communicative and prompt with their response when I messaged in asking about it. Book was in good condition as described. Small ding on the page edges which wasn't mentioned, but that's fairly common even at your typical book store. Still a good value and I'd buy from them again.
- 0***i (5)- Bewertung vom Käufer.Letzter MonatBestätigter KaufThe first item arrived with some damage to the inside back cover, but the seller responded immediately, assuring me they’d provide a replacement, and even told me I could keep the original. They were upfront about a short delay, and gave a clear estimated ship date, and followed up right on time once it shipped. The replacement arrived in perfect condition and exactly as described. I really appreciated their transparency and professionalism. Would definitely buy from them again!