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Counting: The Art of Enumerative Combinatorics 2001 ed. [Kõva köide]

4.17/5 (11 hinnangut Goodreads-ist)
  • Formaat: Hardback, 252 pages, kõrgus x laius: 234x156 mm, kaal: 1220 g, XII, 252 p., 1 Hardback
  • Sari: Undergraduate Texts in Mathematics
  • Ilmumisaeg: 21-Jun-2001
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 038795225X
  • ISBN-13: 9780387952253
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Counting: The Art of Enumerative Combinatorics 2001 ed.Suurem pilt
  • Formaat: Hardback, 252 pages, kõrgus x laius: 234x156 mm, kaal: 1220 g, XII, 252 p., 1 Hardback
  • Sari: Undergraduate Texts in Mathematics
  • Ilmumisaeg: 21-Jun-2001
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 038795225X
  • ISBN-13: 9780387952253
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780387952253.html
Märksõnad:
Counting is hard. "Counting" is short for "Enumerative Combinatorics," which certainly doesn't sound easy. This book provides an introduction to discrete mathematics that addresses questions that begin, How many ways are there to... . At the end of the book the reader should be able to answer such nontrivial counting questions as, How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? There are no prerequisites for this course beyond mathematical maturity. The book can be used for a semester course at the sophomore level as introduction to discrete mathematics for mathematics, computer science, and statistics students. The first five chapters can also serve as a basis for a graduate course for in-service teachers.

Arvustused

From the reviews:



"Much of Martins charming and accessible text could be used with bright school students. The book is rounded off by a section called The back of the book which includes solutions and discussion of many exercises. George E. Martin is a remarkable writer who brings combinatorics alive. He has written a splendid introduction that requires very few prerequisites, yet soon delivers the reader into some highly effective methods of counting. The book is highly recommended." (S. C. Russen, The Mathematical Gazette, Vol. 88 (551), 2004)



"This truly is an undergraduate mathematics text; parts of it could be the text for a high school combinatorics course. The author has made a successful effort to illuminate and teach the elementary parts of combinatorics. He uses examples and problems to teach; there are 245 problems in Chapter 1! If I were not retired and had been asked to teach an undergraduate course in combinatorics, I would have liked to use this book." (W. Moser, Mathematical Reviews, Issue 2002 g)



"This book is a nice textbook on enumerative combinatorics to undergraduates. It introduces the most important ideas . A lot of easy applications are given and homework is listed (with hints). The book also touches some elementary graph enumeration problems. The text is clear and easy to follow. It is even suitable to learn it alone, which is also aided by nice exam problems." (Péter L. Erdös, Zentralblatt MATH, Vol. 968, 2001)



"The teaching of topics in discrete mathematics is becoming increasingly popular and this text contains chapters on a number of pertinent areas for exposure at an elementary level. The author uses non-worked discovery-type examples to lead into observations about the material. There are many interesting exercises for the student to attempt. These are spread throughout the various chapters and are effective in developing interest in the topics. The book contains aBack of the Book section rather than an Answers section." (M. J. Williams, The Australian Mathematical Society Gazette, Vol. 29 (1), 2002)

Preface vii
Elementary Enumeration
Counting Is Hard
1(1)
Conventions
2(1)
Permutations
3(1)
A Discussion Question
4(1)
The Pigeonhole Principle
4(1)
n Chose r by Way of Mississippi
5(2)
The Round Table
7(3)
The Birthday Problem
10(1)
n Chose r with Repetition
11(6)
Ice Cream Cones---The Double Dip
17(1)
Block Walking
18(1)
Quickies and Knights
19(3)
The Binomial Theorem
22(1)
Homework for a Week
23(1)
Three Hour Exams
24(3)
The Principle of Inclusion and Exclusion
Introduction to PIE
27(3)
Proof of PIE
30(2)
Derangements
32(2)
Partitions
34(1)
Balls into Boxes
35(3)
A Plethora of Problems
38(1)
Eating Out
39(4)
Generating Functions
What Is x?
43(1)
An Algebraic Excursion to R[ [ x]]
44(2)
Introducing Generating Functions
46(1)
Clotheslines
47(5)
Examples and Homework
52(5)
Computations
57(2)
Exponential Generating Functions
59(5)
Comprehensive Exams
64(3)
Groups
Symmetry Groups
67(4)
Legendre's Theorem
71(3)
Permutation Groups
74(3)
Generators
77(3)
Cyclic Groups
80(2)
Equivalence and Isomorphism
82(3)
Actions
The Definition
85(3)
Burnside's Lemma
88(6)
Applications of Burnside's Lemma
94(6)
Polya's Pattern Inventory
100(8)
Necklaces
108(5)
Recurrence Relations
Examples of Recurrence Relations
113(4)
The Fibonacci Numbers
117(4)
A Dozen Recurrence Problems
121(1)
Solving Recurrence Relations
122(3)
The Catalan Numbers
125(8)
Nonhomogeneous Recurrence Relations
133(4)
Mathematical Induction
The Principle of Mathematical Induction
137(5)
The Strong Form of Mathematical Induction
142(4)
Hall's Marriage Theorem
146(7)
Graphs
The Vocabulary of Graph Theory
153(7)
Walks, Trails, Circuits, Paths, and Cycles
160(8)
Trees
168(7)
Degree Sequences
175(2)
Euler's Formula
177(6)
The Back of the Book 183(64)
Index 247


From the reviews:



"Much of Martins charming and accessible text could be used with bright school students. The book is rounded off by a section called The back of the book which includes solutions and discussion of many exercises. George E. Martin is a remarkable writer who brings combinatorics alive. He has written a splendid introduction that requires very few prerequisites, yet soon delivers the reader into some highly effective methods of counting. The book is highly recommended." (S. C. Russen, The Mathematical Gazette, Vol. 88 (551), 2004)



"This truly is an undergraduate mathematics text; parts of it could be the text for a high school combinatorics course. The author has made a successful effort to illuminate and teach the elementary parts of combinatorics. He uses examples and problems to teach; there are 245 problems in Chapter 1! If I were not retired and had been asked to teach an undergraduate course in combinatorics, I would have liked to use this book." (W. Moser, Mathematical Reviews, Issue 2002 g)



"This book is a nice textbook on enumerative combinatorics to undergraduates. It introduces the most important ideas . A lot of easy applications are given and homework is listed (with hints). The book also touches some elementary graph enumeration problems. The text is clear and easy to follow. It is even suitable to learn it alone, which is also aided by nice exam problems." (Péter L. Erdös, Zentralblatt MATH, Vol. 968, 2001)



"The teaching of topics in discrete mathematics is becoming increasingly popular and this text contains chapters on a number of pertinent areas for exposure at an elementary level. The author uses non-worked discovery-type examples to lead into observations about the material. There are many interesting exercises for the student to attempt. These are spread throughout the various chapters and are effective in developing interest in the topics. The book contains aBack of the Book section rather than an Answers section." (M. J. Williams, The Australian Mathematical Society Gazette, Vol. 29 (1), 2002)