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Schaum's Outline of Theory and Problems of Combinatorics including concepts of Graph Theory 1st Edition

by V. K. Balakrishnan (Author)
4.4 4.4 out of 5 stars 38 ratings
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Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you

  • Practice problems with full explanations that reinforce knowledge
  • Coverage of the most up-to-date developments in your course field
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    Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!

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  1. ISBN-10
    007003575X
  2. ISBN-13
    978-0070035751
  3. Edition
    1st
  4. Publisher
    McGraw Hill
  5. Publication date
    November 22, 1994
  6. Part of series
    Schaum's Outlines
  7. Language
    English
  8. Dimensions
    7.9 x 0.44 x 10.7 inches
  9. Print length
    200 pages
  10. See all details
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Product details

  • Publisher ‏ : ‎ McGraw Hill; 1st edition (November 22, 1994)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 200 pages
  • ISBN-10 ‏ : ‎ 007003575X
  • ISBN-13 ‏ : ‎ 978-0070035751
  • Item Weight ‏ : ‎ 11.6 ounces
  • Dimensions ‏ : ‎ 7.9 x 0.44 x 10.7 inches
  • Customer Reviews:
    4.4 4.4 out of 5 stars 38 ratings

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V. K. Balakrishnan

V. K. Balakrishnan

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4.4 out of 5 stars
4.4 out of 5
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38 global ratings

Top reviews from the United States

Steve
5.0 out of 5 stars Excellent Text Book
Reviewed in the United States on October 3, 2010
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This is great textbook. Like all the Schaum Outlines, the focus is on problem solving. The author (Prof. V.K. Balakrishnan) does an absolutely marvelous job in leading the reader to an understanding of basic combinatorics via a seemingly endless series of problems. The problems are clearly stated and the solutions are well done. The general quality of the book is very high.
If you need more exposition, I would suggest something like Notes on Introductory Combinatorics by Polya, Tarjan and Woods, but as I say, I think the book by Balakrishnan is just fine as it is.
3 people found this helpful
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Robert J. Newell
4.0 out of 5 stars An excellent supplement, but not a primary source
Reviewed in the United States on July 21, 2015
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I bought this book to provide myself with a review and extension of what I already knew about the topic. For that purpose, the book is excellent, and I've always liked the Schaum approach of providing a lot of detailed examples to illustrate and then build upon th relatively short explanations of theory in the book.

And that's the issue if you've not studied this topic before or are not using the book in conjunction with a regular textbook. The explanations are too brief to really teach the material. This is a big variable in Schaum publications. Some books in the line do better, many don't.

Know what to expect when you buy this book, and you won't be disappointed. If you try to use it as a primary text to introduce yourself to combinatorics, you're on the wrong path.

That said, the book is comprehensive enough to be useful, and the wide range of example problems will solidify your knowledge.

In the computer era, combinatorics has moved from the back room to front and center. It's an important, wide-ranging topic. This book does it justice if used as intended --- as a supplement and extension to a primary source.
4 people found this helpful
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Chalam P.
5.0 out of 5 stars Five Stars
Reviewed in the United States on September 19, 2016
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good copy
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MPC
5.0 out of 5 stars Five Stars
Reviewed in the United States on June 29, 2015
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Great, came as described and on time.
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Laiguang Zeng
5.0 out of 5 stars Five Stars
Reviewed in the United States on November 3, 2016
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Good !
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Bafs
3.0 out of 5 stars Not terrible, but not what I hoped for.
Reviewed in the United States on August 30, 2020
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Not terrible, but not very good either. The downsides are no real explanations in narrative form, and sometimes no explanation at all. It just puts the problems on paper, and mentions briefly the methods for solving. The upside is that it covers more topics than shorter books. However, it is far from covering all of combinatorics. I'm still looking for the ultimate authority on the entire scope of this subject.
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Dr. Lee D. Carlson
4.0 out of 5 stars Nice job
Reviewed in the United States on February 5, 2002
Combinatorics is an area of mathematics that is frequently looked on as one that is reserved for a small minority of mathematicians: die-hard individualists who shun the limelight and take on problems that most would find boring. In addition, it has been viewed as a part of mathematics that has not followed the trend toward axiomatization that has dominated mathematics in the last 150 years. It is however also a field that has taken on enormous importance in recent years do its applicability in network engineering, combinatorial optimization, coding theory, cryptography, integer programming, constraint satisfaction, and computational biology. In the study of toric varieties in algebraic geometry, combinatorics has had a tremendous influence. Indeed combinatorial constructions have helped give a wide variety of concrete examples of algebraic varieties in algebraic geometry, giving beginning students in this area much needed intuition and understanding. It is the the advent of the computer though that has had the greatest influence on combinatorics, and vice versa.The consideration of NP complete problems typically involves enumerative problems in graph theory, one example being the existance of a Hamiltonian cycle in a graph. The use of the computer as a tool for proof in combinatorics, such as the 4-color problem, is now legendary. In addition, several good software packages, such as GAP and Combinatorica, have recently appeared that are explicitly designed to do combinatorics. One fact that is most interesting to me about combinatorics is that it gave the first explicit example of a mathematical statement that is unprovable in Peano arithmetic. Before coming across this, I used to think the unprovable statements of Godel had no direct relevance for mathematics, but were only interesting from the standpoint of its foundations.
This book is an introduction to combinatorics for the undergraduate mathematics student and for those working in applications of combinatorics. As with all the other guides in the Schaums series on mathematics, this one has a plethora of many interesting examples and serves its purpose well. Readers who need a more in-depth view can move on to more advanced works after reading this one. The author dedicates this book to the famous mathematician Paul Erdos, who is considered the father of modern combinatorics, and is considered one of most prolific of modern mathematicians, with over 1500 papers to his credit.
The author defines combinatorics as the branch of mathematics that attempts to answer enumeration questions without considering all possible cases. The latter is possible by the use of two fundamental rules, namely the sum rule and the product rule. The practical implementation of these rules involves the determination of permutations and combinations, which are discussed in the first chapter, along with the famous pigeonhole principle. Most of this chapter can be read by someone with a background in a typical college algebra course. The author considers some interesting problems in the "Solved Problems" section, for example one- and two-dimensional binomial random walks, and problems dealing with Ramsey, Catalan, and Stirling numbers. The consideration of Ramsey numbers will lead the reader to several very difficult open problems in combinatorics involving their explicit values.
Generalized permutations and combinations are considered in chapter two, along with selections and the inclusion-exclusion principle. The author proves the Sieve formula and the Phillip Hall Marriage Theorem. In the "Solved Problems" section, the duality principle of distribution, familiar from integer programming is proved, and the author works several problems in combinatorial number theory. A reader working in the field of dynamical systems will appreciate the discussion of the Moebius function in this section. Particularly interesting in this section is the discussion on rook and hit polynomials.
The consideration of generating functions and recurrence relations dominates chapter 3, wherein the author considers the partition problem for positive integers. The first and second identities of Euler are proved in the "Solved Problems" section, and Bernoulli numbers, so important in physics, are discussed in terms of their exponential generating functions. The physicist reader working in statistical physics will appreciate the discussion on Vandermonde determinants. Applications to group theory appear in the discussion on the Young tableaux, preparing the reader for the next chapter.
A more detailed discussion of group theory in combinatorics is given in chapter 4, the last chapter of the book. The author proves the Burnside-Frobenius, the Polya enumeration theorems, and Cayley's theorem in the "Solved Problems" section. Readers without a background in group theory can still read this chapter since the author reviews in detail the basic constructions in group theory, both in the main text and in the "Solved Problems" section. Combinatorial techniques had a large role to play in the problem of the classification of finite simple groups, the eventual classification proof taking over 15,000 journal pages and involving a large collaboration of mathematicians. Combinatorics also made its presence known in the work of Richard Borchers on the "monstrous moonshine" that brought together ideas from mathematical physics and the largest simple group, called the monster simple group.
The author devotes an appendix to graph theory, which is good considering the enormous power of combinatorics to problems in graph theory and computational geometry. Even though the discussion is brief, he does a good job of summarizing the main results, including a graph-theoretic version of Dilworth's theorem. Combinatorial/graph-theoretic considerations are extremely important in network routing design and many of the techniques discussed in this appendix find their way into these kinds of applications. The author asks the reader to prove that Dilworths' theorem, the Ford-Fulkerson theorem, Hall's marriage theorem, Konig's theorem, and Menger's theorem are equivalent. A very useful glossary of the important definitions and concepts used in the book is inserted at the end of the book.
61 people found this helpful
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Quikwitt
2.0 out of 5 stars All formulas and proofs, no actually applications ro examples
Reviewed in the United States on June 20, 2021
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This book is probably best for math majors going for masters or Ph'd's or masters. It contains no actually rel-world problems or applications for practical examples. It is just a book for formulas and proofs and problems asking you about formulas and proofs.
2 people found this helpful
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Omar
5.0 out of 5 stars Excellent book
Reviewed in Mexico on February 26, 2024
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I am interesting in combinatorics that is the only reason that I bought the book.
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cpp_man
3.0 out of 5 stars Printing sucks
Reviewed in Canada on April 7, 2024
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The book is great, but the printing quality is awful: it looks like a photocopy made from another photocopy...
Do not buy the "new" one, try to find the original printing by McGraw Hill.
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Amazon Customer
5.0 out of 5 stars Five Stars
Reviewed in India on March 25, 2018
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Excellent Book
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Hebert Perez-Roses
5.0 out of 5 stars Excellent book
Reviewed in Spain on September 8, 2017
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Like most Schaum books, this is an excellent collection of solved and unsolved problems, that are very useful for both students and teachers alike.
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A. Daniela
4.0 out of 5 stars A modest advice
Reviewed in the United Kingdom on March 19, 2013
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The book is deficient from the pedagogical point of view. The text can be used at most as workbook accompanied by one of the good books on the market.
I advise you to consult the various options available in a library before buying any book, to find the text more suitable to your level of maturity and way of thinking.
One person found this helpful
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