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Discrete Math

 

What is "Discrete Math" ?

It is easy to ask, but hard to answer.

 

Let's first think of what it mean by "Discrete". I just googled out several different definition for "Discrete" as follows :

  • individually separate and distinct
  • defined only for an isolated set of points
  • a set only taking certain values

Is it clear enough ?

Don't worry if it is not very clear to you... (to be honest, it would not be clear even to me if I heard of it for the first time).

 

If you are familiar with the concept of "Continuous", you may define "Discrete" as "Not Continuous".

 

As you may guess, "Discrete Math" is a branch of mathematics that deals with "Discrete Values (or Discrete set)".

 

I know it may not be so clear to you.. to make it things even worse, Discrete Math is not something that we learned in high school math.

 

Very simply put (with a little risk of misleading), any bunch of objects you can count with your fingers can be called 'Discrete Object'. A branch of mathematics deals with discrete objects is called Discrete Mathematics.

 

I think the best way to understand the concept is to go through a lot of examples and just get familiar with them and then you would get your own intuitive understanding of the concept even though you may not be able to explain it clearly.

 

Example 1 >

 

A young pair of rabbits (one of each sex) is placed on an island. A pair of rabbits does not breed until they are 2 months old. After they are 2 months old, each pair of rabbits produces another pair each month. How many Rabits will be there after 10 month ?

==> You don't have to solve this problem now. Just think about the objects used in this problem. They are rabbits which are clearly countable (even with your fingers). These are discrete objects. The problem ask you to derive a certain 'rule' about the discrete object. so this can be a category of discrete math.

 

 

Example 2 >

 

In how many different ways can eight identical cookies be distributed among three distinct children if each child receives at least two cookies and no more than four cookies?

==> Now you may sense immediately that Cookies and children in this problem are all discrete objects.

 

 

Example 3 >

If k is a positive integer and k + 1 or more objects are placed into k boxes, then there is at least one box containing two or more of the objects.

==> This may sounds abstract and may not be very clear. This is about a positive integer which has discrete characteristics. More clearly, if  you think about 'boxes', you can intuitively know it is discrete object. So this statement can fall into Discrete Math. Actually this is a very famous principle called 'The Pigeon Hole Principle'.