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)."

Comments

Good Books

[Crutcher]

the following are very good books on proof and discrete math. Some of the titles are whimsical, but they are not toy books, they are very valuable.

"How To Prove It", "How To Solve It", "Induction and Analogy in Mathematics", and "Patterns of Plausible Inference".

However, it seems you are looking for a book to cram for a test in discrete math. Good luck, not going to find one. More so than any of the lower mathematics, discrete is the beginnings of higher logical analyisys, and you can not really 'cram' it. You have to really read the work, and really work the problems. It has to become part of you.

There seems to be this trend to blame difficulty in learning a subject on the books or the teachers. There are many, many things in the world that you are not smart enough to do; you need to accept this, and figure out what problems you can deal with.

I am not batman, I am not Johan Sebastian Bach, and I am not Richard Feynman, I have accepted this; perhaps you are not capable of Discrete Mathematics. If not, you need to leave CS, and go get in MIS or something, you will be happier.

Re:Good Books

[Anonymous Coward]

i agree that discrete math is not necessarily intuitive to everyone and doing well in this subject requires lots of work, however, stating that not understanding it means you should leave CS is an incredibly arrogant statement.

i believe that learning is different for everyone, perhaps you understand a subject a way that a professor or a certain text presents the topic. others do not, there is bound to be a text or a tutor who'd be able to break down the topic and present it in a way you would understand

this may not apply to all areas, but i certainly believe that it applies with discrete math.

also, to imply that a CS major is somehow superior in intellect to an individual in MIS is proposterous! it's a matter of preference, and different mindset

btw, i was a CS major when i was in school, i preferred doing the programming and the math over the business oriented MIS track. so assuming i took it personally because i did MIS is invalid.

Re:Good Books

[HalfFlat]

From my experience tutoring early-level University maths, it really seems that the overwhelming majority of people are capable of learning and understanding this level of mathematics, and it's not at all clear that the few remaining lacked capability rather than simply lacked sufficient motivation. (This is not to brush them off - maths can be really hard!)

Almost every time it comes up in conversation that I'm working as a mathematician, I hear phrases such as: "oh, I was never any good at maths", or "I hated maths in highschool", or similar. But when I take the time to explain conceptually the sorts of things I'm dealing with, they typically can get some sort of feel for what's going on, inasmuch as I can communicate what I understand myself.

When I was in highschool and primary school, mathematics was in fact almost uniformly taught really badly. Rote memorisation, ill-explained rules, and arbitrary problems were the rule. The concept of proof, fundamental to mathematics and certainly crucial to passing a University maths course, is never introduced let alone explained properly. It seems only the self-motivated students really get anything out of these maths courses.

Further, there seems to be a huge gap between highschool level maths texts, which when not outright wrong, generally do a poor job of explaining anything conceptually, and university level texts, which usually preusme that the reader has already mastered the basics and has a fairly firm notion of what constitutes a proof and logical reasoning.

So it's not surprising that many people have problems with maths, as one can blame the teaching approaches and books to a large degree. The proof comes when tutoring students who want to learn (or at least pass their course) but haven't got the basics down -- these students, almost without exception, have been able to pass their course and even gain an interest in mathematics given approriate guidence and help.

In all likelihood, the original poster is capable of discrete mathematics.

Re:meta-"Ask Slashdot"

[zhiwenchong]

No, the beauty of being in a university environment is the existence of a place called the library. You can browse and borrow books for weeks, even a whole semester. Then if you decide you want to keep a certain book, you can go to a second-hand bookstore and pick up a copy, cheap. That's what I did.

(In Montreal, there is a bookstore on rue Milton and rue Durocher called "The Word" that sells cheap 2nd hand texts in very good condition. I picked up my copy of Rosen and the solution manual for C$2)

Another endorsement for Rosen, and some advice...

[Farley Mullet]

First, my background. I did an undergraduate degree in math and philosophy, and I'm doing graduate work in Mathematics right now, and I've t/a'ed a few introductory math courses. It was suggested to me by a prof. that before I graduate I should take a basic course in discrete math, and so in my final year of my undergrad, I took the introductory course in discrete math. We used Rosen's book, which I borrowed from a friend, and, as I recall, it was a clearly written book with good examples and almost all of the formulas and information where you think it should be. Plus, it's reassuringly huge.

And now for the unsolicited advice. . .

You absolutely can't learn math from a book; math is a learn-by-doing subject. Books and teachers can help by suggesting techniques, or walking you through things, but you get to know how to do things by doing them again and again and again. It's a bit like sports in this respect: you can watch all the basketball you want on T.V., read all the books you want, and go to as many "shot doctors" as you like, but the only way you're going to make your shot better is by putting the hours in shooting again and again. So it is with math: books and examples and teaching can make it easier for you to practice and revise, but actually working problems out, and proving things for yourself are the only ways that you'll get better.

So how do you put this into practice?

Well, I have two concrete suggestions: first, if it's at all possible (and in my experience, it usually is) get ahold of all the past exams you can, and start working on the problems on the tests. The first few tests you do, have your notes, and whatever books you find useful with you, so you can look at how your prof., or Rosen, or Grimaldi, or whoever does similar problems or proofs, and so you can check facts and formulas that you use. Make sure that you save a few old tests to do without aides once you're confident and comfortable. My other big piece of advice is to work in a group when you do homework or problem sets or studying. The more backgrounds and perspectives and ways of understanding that you have to bring to bear on a problem, the better off you are, and with any luck you'll learn something from the folks you're working with. Plus, it's good practice having to explain and defend your proofs and solutions to classmates, and it's worthwhile to see how other people do the same.

This is what I've learned from taking, tutoring, T/A'ing and marking math courses for the half decade, I hope you find it helpful.