Subject: Re: What is discrete mathematics?
Date: Tue, 23 Sep 1997 15:28:53 -0400
From: Alex Bogomolny
No one would be able to give you an exact definition. Two books on Discrete Mathematics (DM) would have a non empty intersection but also parts not included in other books - all depending on the tastes of the author.
Still I think there are a few chapters common to every DM book:
- Finite set theory. I have just mentioned the word "intersection". There are other things one may want to know about finite sets: how two sets are related, in how many ways one may split it into two, three, etc. subsets, how many functions are defined on a set, and more.
- Graphs. Many real life problems are naturally represented by graphs: itineraries, goods flow, maps, problem solutions, etc.
- Combinatorics. In how many ways one may exctract two socks of the same color from a drawer that contains 5 blue and 7 red socks?
- Boolean Algebra. See my Magic Squares game
- Languages and grammars. To communicate with computers one needs a language specified according to some rules. What are they?