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Applied Combinatorics, by Alan Tucker
PDF Ebook Applied Combinatorics, by Alan Tucker
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This book is designed for use by students with a wide range of ability and maturity. The stronger the students, the harder the exercises that can be assigned. The book can be used for one-quarter, two-quarter, or one-semester course depending on how much material is used.
Combinatorical reasoning underlies all analysis of computer systems. It plays a similar role in discrete operations research problems and in finite probability. This book teaches students in the mathematical sciences how to reason and model combinatorically. It seeks to develop proficiency in basic discrete math problem solving in the way that a calculus textbook develops proficiency in basic analysis problem solving.
The three principle aspects of combinatorical reasoning emphasized in this book are: the systematic analysis of different possibilities, the exploration of the logical structure of a problem (e.g. finding manageable subpieces or first solving the problem with three objects instead of n), and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games.
- Sales Rank: #1594945 in Books
- Published on: 2001-08-07
- Original language: English
- Number of items: 1
- Dimensions: 9.37" h x .88" w x 6.42" l, 1.65 pounds
- Binding: Hardcover
- 464 pages
Most helpful customer reviews
13 of 15 people found the following review helpful.
Excellent for applications
By Ragnarok Books
The book covers the fundamentals of graph theory and combinatorics (enumeration) and is designed for first courses for undergraduates.
The material is presented in a clear, friendly manner. The sections are short and specific and the emphasis is on problem-solving. Many examples are provided and constitute the majority of the book's volume. Each section ends with 20-30 exercises with answers (not full solutions) at the end of the book.
The book is excellent for computer science and applied math majors looking for a clear, application-based introduction to combinatorics and graph theory. It is also excellent for self-study.
The book's main flaw is that the proofs are not rigorous and are sometimes more intuitive than mathematical. For pure math students looking to explore graph theory and combinatorics in a more rigorous manner, other books (e.g. Diestel, "Graph Theory") will serve that purpose better.
5 of 11 people found the following review helpful.
An almost ideal introduction book to combinatorics
By Sen Peng Eu
There have been wonderfully written reviews of this book, but since this is really an excellent textbook, I am urged to praise again. Fully recommended.
This book is easily and clearly written; covers almost every important basic concept and technic in graph theory and enumerative combinatorics, with neatly selected and wonderfully organised exercises.
And I highly suggest the author give the references to those last exercises in every section, since each of them does lead into a theory.
3 of 5 people found the following review helpful.
not impressed
By Jason Broadway
I am a math grad student taking graph theory this semester. As a math major, I understand that one should have the ability to "fill in the holes". You can overdo anything, however. This book is ruined by its lack of examples. Also, it is like the author is in a hurry when he is talking about key ideas. Definitions are often stated in a rushed way that confuses me. Yet, he rambles on when discussing less relevant things. In short, this is a very hard text to read. Easy exercises seem hard because little foundation has been laid. I only paid $17 for this book on amazon. I could not imagine paying $100 for it.
I will admit that this book is a good source for exercises. Also, the proofs are fairly readable, provided you can grasp the "under-explained" key concepts that are less than readable.
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