Combinatorics and Graph Theory (Undergraduate Texts in Mathematics) |  | Authors: John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff
Publisher: Springer
List Price: $59.95
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Rating:  6 reviews
Sales Rank: 842022
Media: Hardcover
Edition: 1
Pages: 304
Number Of Items: 1
Shipping Weight (lbs): 1.1
Dimensions (in): 9.2 x 6.4 x 0.9
ISBN: 0387987363
Dewey Decimal Number: 511.6
EAN: 9780387987361
ASIN: 0387987363
Publication Date: July 19, 2000
Availability: Usually ships in 1-2 business days
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Product Description
This book evolved from several courses in combinatorics and graph theory given at Appalachian State University and UCLA. Chapter 1 focuses on finite graph theory, including trees, planarity, coloring, matchings, and Ramsey Theory. Chapter 2 studies combinatorics, including the principle of inclusion and exclusion, generating functions, recurrence relations, Pólya Theory, the stable marriage problem, and several important classes of numbers. Chapter 3 presents infinite pigeonhole principles, König's lemma, and Ramsey's theorem, and discusses their connections to axiomatic set theory. The text is written in an enthusiastic and lively style. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline. The text is primarily directed toward upper-division undergraduate students, but lower-division undergraduates with a penchant for proof and graduate students seeking an introduction to these subjects will also find much of interest. John Harris did his undergraduate work at Furman University, and he received his Ph.D. from Emory University. He has taught at Appalachian State University and at Furman. His primary mathematical interest is finite graph theory, focusing mainly on subgraphs, paths, and cycles. Jeff Hirst is a mathematical logician and has published a number of papers analyzing the logical strength of theorems of infinite graph theory and combinatorics. He received his B.A. and M.A. from the University of Kansas, and his Ph.D. from the Pennsylvania State University. He has taught at the Ohio State University and Appalachian State University. Michael Mossinghoff received his undergraduate degree from Texas A & M University, his M.S. in computer science from Stanford University, and his Ph.D. in mathematics from the University of Texas at Austin. He has taught at Appalachian State University and UCLA. His research concerns analytic and algorithmic problems in number theory and combinatorics.
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Showing reviews 1-5 of 6
Doesn't Give Away the Store... June 19, 2009
avgvstvs (Omaha NE)
1 out of 1 found this review helpful
My background: I am an MIS major that discovered too late that he had an intense love for the mathematics behind the magic of computer science. I had previously only taken business calc(!) and Discrete Math (for CS majors). The book assigned was Tucker's book which does a great job on generating functions, but loses brevity completely when entering the field of recursive relations.
This book's explanations dealing with poker hands did what Tucker's and Grimaldi's books left me hanging on. Treatment on the binomial theorem and its related applications was also very thorough and at an acceptable level. The beauty of this book however is that the exercises rapidly increase in punch, and I still return to it from time to time to tease out new relationships.
It's introduction to graph theory is also very stellar... and it decides to introduce it before the combinatorial arguments, which if I'd had a little stronger comp sci background before taking the class, I would have found a much more gradual introduction to the general theories.
I'm still raising in mathematical ability, and I plan on tackling this book when I've gotten a little more maturity under my belt.
Excellent book. Hands down.
An excellent book January 10, 2009
Shahab (India)
I haven't gone through the whole book yet but the portion on graph theory that I have read is brilliantly written. The authors inject humor and beauty in the subject. If you are a self learner then this book is ideal for you. The only negative point is the total lack of answers/hints to the problems in the exercises.
Glorious November 19, 2007
J. Wilkes
1 out of 1 found this review helpful
The authors of this book have managed to teach, in a complete and thorough manner, enough material to fill a book more than twice the size of this one. Do not mistake its brevity for a Rudin-esque lack of explanation, or for a lack of substance. Explanations are provided, a good deal of material is covered, and the book remains so concise and to the point that I have no complaints whatsoever.
Very few math books lend themselves well to being read cover-to-cover, but the unassuming nature of this book makes it perfect for a leisurely and fun read, or for a classroom.
Fans of the writing style of Joseph Gallian's "Contemporary Abstract Algebra" will enjoy this book's ability to present material in a friendly way without oversimplifying.
Buy this book.
A truly elegant introduction to combinatorics May 23, 2007
Peter M. Magyar (East Lansing, MI United States)
5 out of 5 found this review helpful
Unlike its competitors, this book states simple concepts simply. It gives an excellent selection of the most important techniques and examples, without endlessly repeated "real-world" applications. In 80 pages, it covers the most interesting topics in graph theory, including: Cayley's tree-counting theorem, vertex coloring (with proof of the 5-Color Theorem), Hall matching theorem, Ramsey numbers, and stable marriage. Another 80 pages contains the main concepts of enumeration: elementary combinations (poker hands), inclusion-exclusion, generating functions for Fibonacci and Catalan numbers, Polya counting of symmetry classes, Stirling numbers. There is final section on infinite sets and graphs.
The book covers quite as much as similar ones of twice the length. Finally, a textbook which is not afraid to be brief!
Perfect book for self teaching March 4, 2007
Richard A. Robertson (Jacksonville, FL United States)
12 out of 13 found this review helpful
I am a math student with Indiana University working out of this book for independent study credit. When my adviser and I sat down to discuss books, we sifted through 10 to 12 books, and it was clear from the start that this book was the best. And I haven't changed my mind since. The book is clear, concise, and easy to read. Excellent for anyone who is teaching themselves, which of course means it's great for a full course with actual instructors.
Showing reviews 1-5 of 6
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