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Discrete Mathematics by Laszlo Lovasz, Jozsef Pelikan , Katalin L. Vesztergombi ISBN-10: 0387955852

A First Course in Discrete Mathematics (Springer Undergraduate Mathematics Series) ISBN-10: 9781852332365

are these two books suitable as Discrete Maths introductory course for undergraduate Math major?

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Are you asking if it is good to use the two in opposition of just one of the two? Or are you asking if those a good books, independently of each other? More interestingly, what possible reasons would there be for it not to be ok? –  Mariano Suárez-Alvarez Apr 10 '11 at 23:06
I mean using both two books instead of Rosen's Discrete Mathematics and its applications. Because the Rosen's book seems to be nearly 1000 pages. But these two books are around 200-300 pages size. So, would it be missing some important points or something like that ? Because in Rosen's book, it is indeed complete, including logic, set, algorithms, induction and proof, probability, graphs. But I want to use some seperate books such as Mathematical Logic, Set Theory, Graph Theory, Probability Theory books to learn deeper after the two books above. But I'm not sure whether my idea is reasonable. –  Xingdong Apr 10 '11 at 23:15
I personally read linear algebra done right by sheldon axler as my 2nd year linear algebra textbook (it's a Springer book). I wouldn't recommend it. It's decent in terms of theory but seriously lacks motivation and examples. Hope that helps a little. –  fdart17 Apr 11 '11 at 0:45
@Cplayer: How does your comment relate to the question? Because it's also a Springer math book? –  joriki Apr 11 '11 at 10:31
@Cplayer: if you are judging the quality of all Springer books based on what you thought about your 2nd year linear algebra textbook... that's the funniest comment I have read on this site :) –  Mariano Suárez-Alvarez Apr 11 '11 at 14:51
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up vote 2 down vote accepted

There are a number of competing criteria: max number of books, min cost (which may involve owning some books already), max depth of coverage, max breadth of coverage, max quality of writing for your level of expertise (this one is complex),... all with varying degrees of dependence.

Rosen (the discrete math text) is growing by committee in the classic commercial math text book style (adding more and more sections and history and examples and subareas) in order to be -the- text book, so that you wouldn't need any others. I personally feel this is part of the textbook publisher thrashing scheme to pull money out of students. The book may be good and constantly getting 'better', but has that general 'bloating' feel to it.

I think you can decide for yourself on a first pass the coverage of the two cheaper books against Rosen (or between any two adversarial choices) by comparing their table of contents (Rosen's is not on Amazon but directly through the publisher mhhe.com). I have used Rosen and like it for readability/I have heard that students don't care for it; I have never used Anderson or Lovasz (Lovasz's advanced books are excellent). Rosen seems geared towards CS; both Anderson and Lovasz touch on finite fields/designs which Rosen ignores altogether (but Anderson spends 1/4 of his text on it).

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It doesn't really matter what you use, up to a certain extent. If you use 2 different discrete math books and also several other books on other subjects, you will learn a lot. In fact, if you use separate books for the various topics, you'll probably learn more than you would by reading Rosen's book because a textbook on a subject will have a lot more in it than a chapter of another textbook. But, it'll also take you longer because you'll have more to read that way.

I know nothing about Rosen's discrete math book, but I have read his number theory book, well 2/3rds of it. It also is very long and you don't need to know every detail in his book. And you'd still learn a lot of number theory if you picked up George Andrews' "Number Theory" which is only about 250 pages. The fact that George wrote a book on it shows that he thinks what is in his book is a good start for anyone wanting to know number theory, and that it contains all the most important things, in his opinion. Rosen's book has all the most important stuff and a lot more stuff as well.

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Why would you say that Andrews or Rosen is of the opinion that their book contains "all the most important things" in number theory? If it helps, I have on my webpage about 250 pages of notes from an undergraduate number theory class and I am under no illusions whatsoever that they contain all the most important things. There are many, many important things in (even very elementary) number theory, far too many to put into one textbook of any reasonable size. –  Pete L. Clark Apr 11 '11 at 14:23
@Pete The most important, in his opinion, basic ideas that can fit in one semester of an elementary number theory course. Something like that. I don't mean that you will have a complete knowledge of all important number theory ideas after reading a book. That's the point. It's short, it can't contain everything but that means the author picks out what he thinks of as most important and puts that in, with the restriction that the book isn't going to be that long. –  Graphth Apr 11 '11 at 15:34
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