What is Discrete Math?

Date: 02/12/2001 at 21:51:38
From: Bill Riddley
Subject: Discrete mathematics

In the Ontarion curriculum for grade 12, Discrete Mathematics will be 
offered. What is it, and, more importantly, where does the term 
"discrete" come from in its mathematical context?

Date: 02/13/2001 at 14:15:11
From: Doctor Twe
Subject: Re: Discrete mathematics

Hi Bill - thanks for writing to Dr. Math.

Discrete math is a catch-all category generally used to cover an 
array of topics needed to prepare students for computer science 
courses. The topics typically include algorithms, combinatorics 
(permutations and combinations), graph theory, and order/lattices. It 
may also include propositional calculus (don't let that name fool 
you - it's symbolic logic, not at all related to "the calculus"), 
elementary number theory, set theory, and discrete and recursive 
functions.

In math, objects are said to be either continuous (like the real 
numbers) or discrete (like the integers). These are the mathematical 
equivalent of analog and digital in electronics. The course name
"Discrete Math" comes from the fact that most of the objects studied 
in the course are discrete. For example, permutations and 
combinations involve counting sets with discrete elements. The number 
of permutations or combinations is an integer - also a discrete 
object. In symbolic logic, propositions are either true of false - 
nothing "in between."

The following article from the Eisenhower National Clearinghouse, 
which attempts to answer the question, What is discrete mathematics?, 
might be of interest to you:

Implementing the Discrete Mathematics Standards: Focusing on Recursion
Margaret J. Kenney and Stanley J. Bezuszka
http://www.enc.org/resources/records/full/0,1240,002403,00.shtm   

And see the 1989 NCTM Standards:
http://standards.nctm.org/Previous/CurrEvStds/9-12s12.htm

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/