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Discrete Mathematics: Elementary and Beyond (Undergraduate Texts in Mathematics) [Paperback]

by L. Lovász, J. Pelikán, K. Vesztergombi
4.1 out of 5 stars  See all reviews (10 customer reviews)

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Book Description

February 17, 2003 0387955852 978-0387955858 2003

Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.


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Discrete Mathematics: Elementary and Beyond (Undergraduate Texts in Mathematics) + Schaum's Outline of Discrete Mathematics, Revised Third Edition (Schaum's Outline Series)
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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.


Product Details

  • Series: Undergraduate Texts in Mathematics
  • Paperback: 284 pages
  • Publisher: Springer; 2003 edition (February 17, 2003)
  • Language: English
  • ISBN-10: 0387955852
  • ISBN-13: 978-0387955858
  • Product Dimensions: 3.6 x 2.4 x 0.2 inches
  • Shipping Weight: 15.2 ounces (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #228,457 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
21 of 23 people found the following review helpful
5.0 out of 5 stars unique in approach 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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8 of 8 people found the following review helpful
4.0 out of 5 stars Best low-level text on discrete math July 6, 2012
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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4 of 5 people found the following review helpful
4.0 out of 5 stars A Skim Along the Surface of Discrete Math December 22, 2010
Format:Paperback
This books is a decent introduction to discrete mathematics. Lovasz does a good job of making material easier by putting it into words. This unfortunately comes at a cost though. For example, in the first few chapters about combinatorics Lovasz does a good job of distinguishing permutations from combinations. However, when he tries to present proofs in every day language the lack of mathematical preciseness can get really confusing. This unfortunately only gets worse as more topics get introduced. The section about fast modular exponentiation is very dense and requires careful reading to follow the math. I feel like these topics could've been presented better if Lovasz simply wrote out the equations and the manipulations. The sections on graph theory and convex geometry go a bit too fast. They start off quite easy and then ramp up rapidly at the end of the chapter which leaves the reader with more questions than answers. The section on RSA was surprisingly good and really brought Fermat's theorem to life, but I do wish that this was done nine chapters earlier.

So, I've complained a lot, and you may wonder why I've given the book four stars. The reason is that the book fulfilled it's purpose very well; it gave me a brief introduction to the many fields of discrete math without totally burying me. The tone and style was easy enough for me to read in my leisure time while still introducing to me some solid mathematical concepts. Most of the basic theorems were very clear (though the more advanced ones were typically presented poorly like I said). Exercises were generally easy and reinforced the topics in the chapter. One of my favorite things about the book was the number of open problems Lovasz explained. More authors should present these in order to stimulate the reader.
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4.0 out of 5 stars Good intro with some great examples. February 3, 2012
Format:Paperback|Verified Purchase
In my mind this book is great for either teachers who want some neat examples for instruction, or for students who want a basic understanding.

It would not be my choice as an instructional text. However, I can see where it could help a student who wanted a resource beyond a textbook. ( though that might be a stretch).

There are exercises and answers. But do not look for any rigor or depth. ( don't even bother reading the chapter on probability, it will just confuse learning it for real ).
I believe the authors wanted broad coverage of topics, and to cover some things that are not part of some textbooks. Like it does give a pretty good view of Number theory. Yet probability is barely provided any depth worth reading.

The title is elementary and beyond.. well it is more elementary than beyond.

I take the book for what it is, and that is an intro, nothing more. There is alot to complain about with this book, it has value.
From what I have seen of some textbooks of discrete math, this book actually has alot of value.

Though I think it is a bit overpriced.
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