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Discrete Math Textbook Recommendations?
JonnyRo88 asks: "I am an undergraduate CS major at the University of Central Florida. I took a Discrete Math course this past semester and had a VERY difficult time with the text book the class used: 'Discrete and Combinatorial Mathematics' by R. Grimaldi. I do not attribute my difficulties to the book itself, rather I just feel that my learning style is incompatible with the way this book is laid out. I'm sure that others have had similar experiences where they could just not -click- with a book. Like many people I know I tend to learn almost all of the class material from the book. I learn really well from books that focus heavily on examples and explanations on how those examples work. I would love to hear what Slashdot readers consider their most useful Discrete Math textbook. Most interesting are books that have very good discussions on the basic strategies of proofs. I am currently preparing to take an exam that the department requires all CS majors take before they can move to higher level classes, it will test me on my knowledge of discrete math, specifically proofs (by induction, disproof by contradiction, direct proof, recursive definitions, etc)."
I did a lot of math tutoring in college, and I noticed that all of the discrete books were absolutely god-awful basically just TeX documents with covers, with the exception of one: Kenneth Rosen's "Discrete Mathematics and its Applications". Best. Discrete Book. Ever.
As far as I know, this is the standard text at many colleges. Rosen's approach is mathematically rigorous yet practical at the same time. .
This was also the book from which I first discovered Fermat's Last Theorem, so it is not the typical dry textbook that we all know about.
Walmart sells it for less than Amazon
I have to second the recommendation of "How to Solve It".
The professor of my first discrete math class recommended it to me, and it was very helpful.
As I'll be graduating from UCF this fall with a CS degree, I suppose I'm qualified to answer... On with it then... First of all, if you're really having trouble with the class, it's probably best to seek help that's actually breathing, as a book often fails to give that last bit of insight that's keeping you from understanding the methods. Second, don't worry about the foundation exam, if you know the basics, and can do common proofs from discrete, it's actually quite easy. As for the book, I took Intro to Discrete in 1999, and the book we used then was excellent, James Hein's "Discrete Structures, Logic, and Computability". If automata and languages are the ones giving you trouble after reading that book, check out the upper level (COT4210) book, Sudkamp's "Languages & Machines". The first book should give you plenty for that class, though... Oh, and one more free tip: when you take 4210, don't take Torosolu's class, try for (Drs.) Llewellyn, Dutton, Workman, or Guha (Arup)'s class. Actually, in all cases, try to get those professors...
--That's the point of being root, you can do anything you want, even if it's stupid.
I go to UCF and I got a B in Dr. Lang's discrete class and passed the foundation. I got through just studying Lang's and Guha's notes. I didn't even touch that terrible book. For the foundations exam, the best thing is to practice using old exams.
So, at Carnegie Mellon, for undergrad Discrete math we have two main courses. The first one is sort of wimpy, but the second one is AMAZING! The professor keeps the text book online as a bunch of lectures and assignments. See http://www.discretemath.com and click calendar.
Enjoy
--Alex
You know, if the questioner hadn't specifically said Grimaldi was no help, it would have been my recommendation. But it could be that it was more accessible to me after having digested Godel, Escher, Bach by Hofstaeder in high school. That covers much of the same subject area in a more conversational, but yet rigorous, way. I'm only the 94,161th person to recommend GEB, but I would suggest trying some of the included exercises as you read through it; they really help build an understanding for discrete mathematics, which helps in understanding everything from regular expressions on up. And it won the Pulitzer.
--
I don't want to rule the world... I just want to be in charge of mayonnaise.
Knuth, Graham and Patashnik, Concrete Mathematics.
Mind you, with Don Knuth and Ron Graham's names in the author list is going to be good. :-)
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They are the following.
Maurer, Stephen B. and Ralston, Anthony. Discrete Algorithmic Mathematics Reading, MA: Addison-Wesley, 1991.
Ross, Kenneth A. and Wright, Charles R.B. Discrete Mathematics, Englewood Cliffs, NJ: Prentice Hall, 1985, 1988, 1999. Third Edition.
In particular, the second textbook has plenty of examples. Answers to many of the odd-numbered problems are also included in the back of the book.
The book by Ross and Wright is essentially the best book on discrete mathematics if you are pursuing a course of self study. The best book also costs plenty of money but is worth it. You will find it to be a useful reference long after you have graduated with your degree in computer science. Discrete mathematics is, after all, the foundation of modern computer science.