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Discrete Mathematics: Elementary and Beyond (Undergraduate Texts in Mathematics) 2003rd Edition

4.1 out of 5 stars 16 customer reviews
ISBN-13: 978-0387955858
ISBN-10: 0387955852
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Editorial Reviews

Review

From the reviews:

"The goal of this book is to use the introduction to discrete mathematics … . Consequently, the authors … take a lot of time to explain proof techniques and to motivate definitions and style. The language is very informal and easy to read. The level is always introductory which makes it possible to give a taste of a wide range of topics … . There are a lot of exercises … which makes it perfectly suitable for self-study." (T. Eisenkölbl, Monatshefte für Mathematik, Vol. 144 (2), 2005)

"The book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics … . Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures, and exercises spread throughout the book." (Zentralblatt für Didaktik der Mathematik, January, 2004)

"The title of this book is quite apposite … . The text is, in fact, based on introductory courses in discrete mathematics … . the emphasis throughout the book is on finding efficient and imaginative ways to tackle problems and to develop general results. … I would see it as a valuable resource of enrichment activities for students … . is eminently suited for self-study (there are plenty of exercises and solutions) and can be warmly recommended for the school library." (Gerry Leversha, The Mathematical Gazette, Vol. 88 (512), 2004)

"This book is an excellent introduction to a lot of problems of discrete mathematics. … The authors discuss a number of selected results and methods, mostly from the areas of combinatorics and graph theory … . This book is appealed to a broad range of readers, including students and post-graduate students, teachers of mathematics, mathematical amateurs. The authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures and exercises spread throughout the book." (M.I Yadrenko, Zentralblatt MATH, Issue 1017, 2003)

"This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics … . Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures, and exercises spread throughout the book." (L’ Enseignement Mathematique, Vol. 49 (1-2), 2003)

"The aim of this book is NOT to cover discrete mathematics in depth. Rather, it discusses a number of selected results and methods … . The authors develop most topics to the extent that they can describe the discrete mathematics behind an important application of mathematics … . Another feature that is not covered in other discrete mathematics books is the use of ESTIMATES … . There are questions posed in the text and problems at the end of each chapter with solutions … ." (The Bulletin of Mathematics Books, Issue 43, February, 2003)

From the Back Cover

 Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear programming, coding theory and the theory of computing. This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number theory, probability, and combinatorial geometry. Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures and exercises spread throughout the book.

László Lovász is a Senior Researcher in the Theory Group at Microsoft Corporation. He is a recipient of the 1999 Wolf Prize and the Gödel Prize for the top paper in Computer Science. József Pelikán is Professor of Mathematics in the Department of Algebra and Number Theory at Eötvös Loránd University, Hungary. In 2002, he was elected Chairman of the Advisory Board of the International Mathematical Olympiad. Katalin Vesztergombi is Senior Lecturer in the Department of Mathematics at the University of Washington.

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Product Details

  • Series: Undergraduate Texts in Mathematics
  • Paperback: 284 pages
  • Publisher: Springer; 2003 edition (October 10, 2008)
  • Language: English
  • ISBN-10: 0387955852
  • ISBN-13: 978-0387955858
  • Product Dimensions: 6.1 x 0.7 x 9.2 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (16 customer reviews)
  • Amazon Best Sellers Rank: #169,919 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Hernadvolgyi Istvan on December 4, 2006
Format: Paperback
I am really surprised at my fellow reviewer's statements indicating that you need to be a genius to understand this book. In fact, it is really the opposite; the authors took an effort to make the material approachable to the mathematically minded and provide motivating context for each example. While at the authors, you should note that these people are some of the most well known researchers in this area and Dr. Lovasz is also an exceptional lecturer. I believe all possess Erdos number 1 :) It is surely not a textbook, in the sense of Rosen's "Discrete Mathematics and its Applications" nor it strives for completeness like Reinhard Diestel's "Graph Theory". Instead it is a selection of topics that give a good introduction into discrete mathematics with carefully selected insightful problems with solution hints! So, yes, I think it is great for self study and especially for those (as the introduction suggests) who have had a more analysis-biased introduction into Mathematics. Instead of being a collection of theorems and proofs, the problems in this book build on the absolute necessary basics (often just high-school math) and, yes, skip unnecessary notation and pseudo-rigor. I should also note that I am basing this review on the Hungarian edition, which also reads well but I have not actually seen the original English text.
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Format: Paperback
For my purposes, this textbook has no competitors. But first, let me explain my situation: I teach a 100-level college discrete math course. By "100-level," I mean something about as advanced as high school trigonometry/pre-calculus, with high-school-level algebra as the only prerequisite. Unlike many discrete math courses, mine is not primarily aimed at computer science majors -- they generally make up only about a third of the enrollment. As a whole, what my students need is to get a sense of what mathematics is like outside of the calculus sequence, and also a good introduction to reading and writing proofs. With all of that in mind, this is by far the best individual textbook I could use, to my knowledge (and I have looked over an absurd number of other discrete math texts). To be honest, sometimes I suspect I could write a better introductory discrete math textbook than this one, but I must be wrong, since apparently no one else can.

The best qualities of this textbook are its very broadly accessible style and, at the same time, the fact that it doesn't treat mathematics like a mere sequence of rules to be memorized and procedures to be "mastered." Unfortunately, that cookbook kind of presentation, followed by a mechanical regurgitation of pointless "skills," is what most of today's students seem to crave in math (witness the popularity of Khan Academy, for example). This textbook is one of those rare gems that puts mathematics in its proper light, as a field of real human curiosity, in some ways resembling an expressive art as much as a science.

One major problem with textbooks in this subject is that there are about a half dozen different versions of a "discrete math" course, some bearing almost no resemblance to others.
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Format: Paperback Verified Purchase
It's difficult to give this book an accurate rating. Certain portions of the book are excellent and well written while other sections will skim over a lot of information that I find important to the topic area. The review questions are answered in the back of the book but they are not explained well. At first glance, this book seems good, however if you take a glance at how other authors approach similar subject areas (Book of Proof by Richard Hammack) you will become more aware of the shortcomings of this book.
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Format: Hardcover Verified Purchase
Before the reader grumbles at my 1 star rating, let me please explain exactly what it is I am in fact rating.
I bought this book with high hopes. Initially there were two front running candidates I had to choose from, this
book and the very well known book of Norman Biggs published by Oxford University Press. The latter was more expensive so
I took book of Lovasz. I chose poorly, very poorly.
When this book arrived and I quickly noted that it was like many so-called "hard cover" Springer books, that is, it's not a hard cover book at all.
It's a paperback book with a shabby cardboard "hard cover" glued onto it, which for some strange reason incurs a greater fee.
However this is not the worst of it. The print quality was appalling. It's like a photocopied book (and most likely is a photocopy)
where the photocopier's toner ran out three weeks ago. The physical quality of the book is just rubbish.
This is not an isolated event, certainly not in my experience or my colleagues. A few months back I bought a copy of Bondy and Murthy's
classic Springer GTM on Graph Theory. This is a large book, 600+ pages and a "hard cover", according to Springer.
The spine of the book cracked as soon as I opened it and for the same reason. It was not properly bound and is effectively a
paperback book with a cardboard cover glued on it. I took this book to a German book binder who pulled it apart and bound it
properly. Now it "functions" as a book should. That was $50AUD extra cost.
My advice to anyone buying a Springer "hard cover" book is to factor in $50 for a rebind, assuming of course that there
was toner in the printer. If not even a rebind is a waste of time.
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