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:

  1. 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.
  2. Graphs. Many real life problems are naturally represented by graphs: itineraries, goods flow, maps, problem solutions, etc.
  3. 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?
  4. Boolean Algebra. See my Magic Squares game
  5. Languages and grammars. To communicate with computers one needs a language specified according to some rules. What are they?


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