A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.
Principles and Techniques in Combinatorics
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"This book should be a must for all mathematicians who are involved in the training of Mathematical Olympiad teams, but it will also be a valuable source of problems for university courses." Mathematical Reviews
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Most Helpful Customer Reviews
19 of 19 people found the following review helpful
Format:Paperback
I wish I had this book on hand during my course in combinatorics. It is a must-have introduction for math undergrads and the general public alike. (Never let the price of a mathematics book fool you. Like a classical music CD, the value of the a math book is entirely determined by its content.) It is lucidly written, which is critical for this ostensibly simple field. Fuzzy explanations can lead readers far astray; poor examples can obscure key concepts. Michael Tucker's "Applied Combinatorics" suffers from this very problem. However, this is not so with Chen and Koh's volume. They are kind enough to provide multiple combinatorial proofs for a considerable number of problems, and they do so in the familar AMS format. There are an abundance of problems at the end of each chapter. Their chapters on Inclusion-Exclusion and recurrence relations shine brightly. Pick it up now!
11 of 12 people found the following review helpful
Format:Paperback|Amazon Verified Purchase
Oh how I wish I had found this book at the beginning of my semester of combinatorics instead of at its end...
When I found this tome here on Amazon it was at the behest of a reviewer that stated the strength of this book in the explanation of Recurrence Relations. I can't agree further. The text assigned for my class was Tucker's Applied Combinatorics book, and to be frank, it's a fairly decent text that does have an incredibly strong introduction to Generating Functions that goes down as one of the finest I have encountered. However, this book also discusses sequence creation using generating functions, something that Tucker leaves out. This book is a *true* introduction to combinatorics, explicitly detailing every step of every proof--something direly missing in most other texts of this type. Most people taking this class have only had a rudimentary sampling of proof techniques (comp-sci majors usually take combinatorics) and this book helps fill in the missing gaps left in slightly higher-flyers such as Tucker's.
But the reason this one is such a gem in recurrence relations is that it goes in depth in teaching you HOW TO MODEL with this tool. Tucker assumes you can do that already. His chapter on modeling is light on problems and doesn't explain the examples as clearly as this one does. This book also shows some incredibly creative problem solutions that crafty high-schoolers have devised (being olympiad trainers) that help you think about other implications in things such as Pascal's triangle. It does a great job of improving mathematical thinking and if I didn't enjoy Tucker's chapter on generating functions so much I would sell that thing in a heartbeat.
In studying for my combinatorics final I have also found that its plain explanations of other material from earlier chapters would have saved me (a whole lot) of 'head against the wall bashing.'
This book underlines the difference in how people who trained in education write books vs. people who typically write college textbooks. I know its typical as a native english speaker to think twice when buying a book written by a foreign sounding name, but trust me, you get the thing you always hope for in a math textbook. (Clarity, blessed, beautiful, sweet sweet clarity!)
If you're a student who enjoys--but struggles with--higher math, this is the book to get, hands down.
When I found this tome here on Amazon it was at the behest of a reviewer that stated the strength of this book in the explanation of Recurrence Relations. I can't agree further. The text assigned for my class was Tucker's Applied Combinatorics book, and to be frank, it's a fairly decent text that does have an incredibly strong introduction to Generating Functions that goes down as one of the finest I have encountered. However, this book also discusses sequence creation using generating functions, something that Tucker leaves out. This book is a *true* introduction to combinatorics, explicitly detailing every step of every proof--something direly missing in most other texts of this type. Most people taking this class have only had a rudimentary sampling of proof techniques (comp-sci majors usually take combinatorics) and this book helps fill in the missing gaps left in slightly higher-flyers such as Tucker's.
But the reason this one is such a gem in recurrence relations is that it goes in depth in teaching you HOW TO MODEL with this tool. Tucker assumes you can do that already. His chapter on modeling is light on problems and doesn't explain the examples as clearly as this one does. This book also shows some incredibly creative problem solutions that crafty high-schoolers have devised (being olympiad trainers) that help you think about other implications in things such as Pascal's triangle. It does a great job of improving mathematical thinking and if I didn't enjoy Tucker's chapter on generating functions so much I would sell that thing in a heartbeat.
In studying for my combinatorics final I have also found that its plain explanations of other material from earlier chapters would have saved me (a whole lot) of 'head against the wall bashing.'
This book underlines the difference in how people who trained in education write books vs. people who typically write college textbooks. I know its typical as a native english speaker to think twice when buying a book written by a foreign sounding name, but trust me, you get the thing you always hope for in a math textbook. (Clarity, blessed, beautiful, sweet sweet clarity!)
If you're a student who enjoys--but struggles with--higher math, this is the book to get, hands down.
6 of 8 people found the following review helpful
Format:Paperback
A very clearly written classic of an important topic, with lots of problems meant for mathematical competition training. Highly recommended.
Most Recent Customer Reviews
Excellent book
We used this book in my high school Combinatorics class. I took another combinatorics class at my university, and this book is still a great companion to the class material. Read more
Published 4 months ago by anonCustomer
A useful book on combinatorics
This is a useful book on combinatorics. Concepts are explained clearly and simply without excessive elaboration. Read more
Published on July 20, 2008 by Chee Lim Cheung
Inside This Book
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First Sentence:
In our everyday lives, we often need to enumerate "events" such as, the arrangement of objects in a certain way, the partition of things under a certain condition, the distribution of items according to a certain specification, and so on. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nth subdivision, distinct boxes, exponential generating function, generating function for the sequence, ramsey numbers, nonnegative integer solutions, increasing mappings, linear recurrence relations, quaternary sequences, identical boxes, multinomial coefficients, positive divisors, distinct objects, binomial coefficients, identical objects, counting problems Key Phrases - Capitalized Phrases (CAPs): (learn more)
Crux Mathematicorum, Mathematical Gems New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In our everyday lives, we often need to enumerate "events" such as, the arrangement of objects in a certain way, the partition of things under a certain condition, the distribution of items according to a certain specification, and so on. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nth subdivision, distinct boxes, exponential generating function, generating function for the sequence, ramsey numbers, nonnegative integer solutions, increasing mappings, linear recurrence relations, quaternary sequences, identical boxes, multinomial coefficients, positive divisors, distinct objects, binomial coefficients, identical objects, counting problems Key Phrases - Capitalized Phrases (CAPs): (learn more)
Crux Mathematicorum, Mathematical Gems New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 18
books:
See all 18 books this book cites
- Introduction to Combinatorial Mathematics (Computer Science Series) by Chung L. Liu in Back Matter
- Principles of combinatorics, Volume 72 (Mathematics in Science and Engineering) by Berge in Back Matter
- College Mathematics by Robert Carman on page 223
- Applied Combinatorics by Alan Tucker in Back Matter
- Computer Programming (Looking at Series) by Penny Holland in Back Matter
See all 18 books this book cites
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