Discrete Math: What's the Best Way to Get Started?

[bonfire09]

Would learning discrete math be more beneficial then diving into velleman's book right away? and what is a good book on discrete math?

 

[bonfire09]

well actually I was a little too vague. What I'm looking for is a book that has a good introduction to logical connectives, logical equivalences, operations on sets, etc. Basically what vellemen covers in the first two chapters in his book. I have a semi-good grasp of it but
when I have to solve problems like use the laws in the text to find a simpler and equivalent formula to this for example (P ^R) v [~R ^(P V Q)]. Thats where I am having trouble.

 

[Sankaku]

Here are a few thoughts:

1) While it is good to play around with the raw logical statements and get used to them, in real life you don't meet things that look that artificial. On the one hand it is really just a kind of algebra (high-school type algebra) where you follow the rules about moving things around. The abstract notation doesn't really give you any intuition about what is going on, though.

2) A discrete math book may or may not be what you are looking for; however, the benefit is finding something to apply your proof-learning toward. Velleman is a pretty good book, but I think learning proofs in the context of some basic discrete math is a great idea.

A book I would recommend:

https://www.amazon.com/dp/0131679953/?tag=pfamazon01-20

I know it is very difficult to ignore bad reviews on Amazon, but keep in mind that most of those people are really just annoyed comp-sci majors who are complaining about learning proof-based mathematics they were not expecting. I think it is actually a very good intro book with an emphasis on learning proofs and giving lots of worked examples/exercises. However, don't pay full price. Find a second hand copy somewhere.

The other option is to compare Velleman to some of the free proof textbooks and see if something else is better for your learning style.

http://www.people.vcu.edu/~rhammack/BookOfProof/index.html
http://www.math.vt.edu/people/day/ProofsBook/

I have not personally used either of those books, though, so I can't comment on them.

 

[Dembadon]

I've worked through many of the exercises in Hammack's book. They range from boring to difficult^*. His exposition can be a bit wordy at times, but some people find his style helpful. Since it's free, you should work through some of the sections and see if you like it. I didn't hate it, but I didn't really like it either.

^*if this is your first exposure to proofs in mathematics