Hundreds of Combinatorics Video Lectures

If you are taking mathematics courses related to combinatorics or probability, I found a page from UCLA containing hundreds of video lectures on the said subjects. It is a collection of lectures from 1993 up to the present and includes lectures from famous mathematicians such as Terence Tao.

For more free video lectures, visit the All for Free page of Math and Multimedia. It also contains posts which links to hundreds of free ebooks and software.

Understanding the Basics of the De Morgan’s Laws

In the previous two posts, we have discussed about the logical operators and, or, and not.  Those two articles are preparation for this post.

Consider the following inequalities.

1.) $x \leq 8$

2.) $-2 < x < 3$

The first inequality can also be represented as $x < 8$ or $x = 8$

Now, how do we find

not ($x < 8$ or $x = 8$).

To easily understand the question, we graph $x \leq 8$ first and then see what’s not on that graph.  » Read more

What exactly is the vertical line test?

A function as we have discussed is a relationship between two sets, where each element in the first set has exactly one corresponding element in the second set. If we think of candies which cost 10 cents each, then we can say that 1 candy costs 10 cents, 2 candies cost 20 cents, 3 candies cost 30 cents, and so on. We can think of this relationship as a function since for each number of candies, there is only one possible price.

If we consider the relation y = 2x, then we can say that it is a function since for every value we substitute to x, there is one and only one corresponding value for y. For instance, if x = -3, then y = -6 and and if x = 9, then y = 18 (one y for each x).  » Read more