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Discrete Mathematics: Elementary and Beyond
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. Laszlo Lovasz is a Senior Researcher in the Theory Group at Microsoft Corporation. He is a recipient of the 1999 Wolf Prize and the Godel Prize for the top paper in Computer Science. Jozsef Pelikan is Professor of Mathematics in the Department of Algebra and Number Theory at Eotvos Lorand 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.
- GenresMathematics
290 pages, ebook
First published January 1, 2003
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Displaying 1 - 4 of 4 reviews
June 29, 2021
2.0 out of 5 stars
If You're Brilliant and Don't Mind a Lack of Rigor, Try It.
December 21, 2004
Ouch. I definitely made a mistake trying this book. From what I can see, the only set of people who might find this book useful would be genius non-Math-types. My handy-dandy way of explaining this is by mapping the universe of all possible readers onto a set of x-y axes. Let the x axis run from "non-Math-types" up through "Math-types." Let they y axis go from "non-geniuses" up through "geniuses:"
- Quadrant I: if you're a genius Math-type, you'll be aghast at the lack of rigor in the proofs and at all the steps missing from the few proofs given. But, you might be able to work through the material on your own. My guess, though, is that you'll throw the book across the room in disgust, instead.
- Quadrant II: if you're a genius non-Math-type, you might find the lack of rigor in the proofs tolerable. Plus, you, like the Quadrant Is, might be able to work through the material enough so that you can follow the author's explanations. If you're smart enough and have enough familiarity with the material before reading this book, you might find its terseness acceptable.
- Quadrant III: if you're a non-genius non-Math-type (i.e., "normal"), you'll be lost. You (we) won't understand what the point of this is, won't be able to work thru all the missing steps in the few proofs given, and will rant and rave when the authors "prove" one thing, give one example, and then ask the reader to prove the several follow-up theorems as an exercise. With, essentially, one example to work from in a subset of each topic, you'll never be able to work through the few questions with answers (which answers are short to the point of worthlessness) and will throw up your hands in dismay when attempting to solve the non-answered end-of-chapter questions.
- Quadrant IV: if you're a non-genius Math-type, you will join the Quadrant Is in horror at the lack of rigor, but, like the Quadrant IIIs, will be horribly frustrated since you won't be able to force your way through the material on your own. A definite lose-lose situation, here.
The really odd thing with this book is that, in the universities, Discrete Math (the subject) is usually a required course for Computer Science majors and is a PRE-CALCULUS course. There's absolutely no way that any such student at that point in his degree could get through this book. I received my B.S. in Mathematics from the University of Michigan well over 20 years ago (so I've forgotten most everything, plus I was a Quadrant IV type but figured it out much later and migrated to Quadrant III), but there are entire chapters in this book where I only understand words like "the" and "and." The authors assume an extremely in-depth degree of mathematical knowledge on the part of the reader. Also, there's nothing to tie the subject matter back to anything a CS person (or any non-math-type) could use in his degree, profession, or life. So, once again, this book is very poorly matched against any intended audience.
I'd also like to point out that I doubt this book would ever be chosen by any academic institution for teaching. It just doesn't follow the established norms on how to teach. Specifically, it should: 1) tell the readers what it's going to say, 2) tell them, and 3) tell them what it just told them. Each chapter and section in this book just starts out talking about something. You really have no idea where the authors are going until they actually get there. What the book really, REALLY needs is for the authors to state exactly what they're going to do in a section and chapter, do it, and then summarize it. Ditto for the book as a whole. The preface needs some kind of overall game plan so the people reading the book know where they're going.
If You're Brilliant and Don't Mind a Lack of Rigor, Try It.
December 21, 2004
Ouch. I definitely made a mistake trying this book. From what I can see, the only set of people who might find this book useful would be genius non-Math-types. My handy-dandy way of explaining this is by mapping the universe of all possible readers onto a set of x-y axes. Let the x axis run from "non-Math-types" up through "Math-types." Let they y axis go from "non-geniuses" up through "geniuses:"
- Quadrant I: if you're a genius Math-type, you'll be aghast at the lack of rigor in the proofs and at all the steps missing from the few proofs given. But, you might be able to work through the material on your own. My guess, though, is that you'll throw the book across the room in disgust, instead.
- Quadrant II: if you're a genius non-Math-type, you might find the lack of rigor in the proofs tolerable. Plus, you, like the Quadrant Is, might be able to work through the material enough so that you can follow the author's explanations. If you're smart enough and have enough familiarity with the material before reading this book, you might find its terseness acceptable.
- Quadrant III: if you're a non-genius non-Math-type (i.e., "normal"), you'll be lost. You (we) won't understand what the point of this is, won't be able to work thru all the missing steps in the few proofs given, and will rant and rave when the authors "prove" one thing, give one example, and then ask the reader to prove the several follow-up theorems as an exercise. With, essentially, one example to work from in a subset of each topic, you'll never be able to work through the few questions with answers (which answers are short to the point of worthlessness) and will throw up your hands in dismay when attempting to solve the non-answered end-of-chapter questions.
- Quadrant IV: if you're a non-genius Math-type, you will join the Quadrant Is in horror at the lack of rigor, but, like the Quadrant IIIs, will be horribly frustrated since you won't be able to force your way through the material on your own. A definite lose-lose situation, here.
The really odd thing with this book is that, in the universities, Discrete Math (the subject) is usually a required course for Computer Science majors and is a PRE-CALCULUS course. There's absolutely no way that any such student at that point in his degree could get through this book. I received my B.S. in Mathematics from the University of Michigan well over 20 years ago (so I've forgotten most everything, plus I was a Quadrant IV type but figured it out much later and migrated to Quadrant III), but there are entire chapters in this book where I only understand words like "the" and "and." The authors assume an extremely in-depth degree of mathematical knowledge on the part of the reader. Also, there's nothing to tie the subject matter back to anything a CS person (or any non-math-type) could use in his degree, profession, or life. So, once again, this book is very poorly matched against any intended audience.
I'd also like to point out that I doubt this book would ever be chosen by any academic institution for teaching. It just doesn't follow the established norms on how to teach. Specifically, it should: 1) tell the readers what it's going to say, 2) tell them, and 3) tell them what it just told them. Each chapter and section in this book just starts out talking about something. You really have no idea where the authors are going until they actually get there. What the book really, REALLY needs is for the authors to state exactly what they're going to do in a section and chapter, do it, and then summarize it. Ditto for the book as a whole. The preface needs some kind of overall game plan so the people reading the book know where they're going.
October 19, 2018
This book is not helpful to students who have no experience with discrete mathematics.
November 2, 2023
They use the term "Review Questions" as a way to not leave a solution. I'm confused, it seems after chapter 4 they didn't feel like offering solutions to problems so they made a category dedicated to questions they weren't gonna offer one for, and the ratio to questions they offer solutions grow scarce the more I read the book, if you didn't feel like finishing a book don't publish and charge for one!
November 18, 2009
I'm going to use this next term. I've never used it, but it looks pretty great. Plus it's supercheap ($30) and available online for free through the library. And the coauthor is Pelikan, which is just a superior name.
If anyone out there has used this before, I'd love feedback on how it went and what you thought.
If anyone out there has used this before, I'd love feedback on how it went and what you thought.
Displaying 1 - 4 of 4 reviews