Revisiting Khan Academy After Four Years

It was four years ago when I discovered Khan Academy, which as far as I can remember a Youtube channel with more than a thousand videos. If I am not mistaken, it was only then managed by Salman Khan, it’s founder.

A year ago or two, when I searched the internet, I learned that Khan Academy has already its own website and it is run already by a group of educators. Three weeks ago, I started using the website. As of this writing, I have already watched 29 videos (oh yes, I watched them from start to end) and earned 56,340 points. 🙂  » Read more

Understanding the Concept of Inverse Functions

Let us consider the functions

f(x) = x^3  and g(x) = \sqrt[3]{x}.

The table on the left shows the ordered pairs (x,f(x)). We used f(x) and substitute them to x in the second table.

inverse functions

As we can see, all the values of g(x) are the same as those of x in the first table. For example,  if we have x = 3 in the first table, applying f, we get  27 as output. On the other hand, if we apply g to 27, the value returns to 3» Read more

How to Use the Factorial Notation

We have had several discussions about the factorial notation, so I think this introduction is a bit late. However, it is important that you know these basic facts in order to perform calculations and understand better in later discussions.

The factorial of a non-negative integer n is the product of all the positive numbers less than n. For example, the

4! = 4 \times 3 \times 2 \times 1 = 24.

and

5! = 5 \times 4 \times 3 \times 2 \times 1 = 120.

In Introduction to Permutations, we have discussed that there are n! ways to arrange n distinct objects into a sequence. For instance, if we have 3 objects namely A, B, and C, then they can be arranged in 3! = 3 \times 2 \times 1 = 6 ways. The arrangement are as follows:

ABC, ACB, BAC, BCA, CAB, CBA.

 We have also learned some reasons why mathematicians chose the definition 0! = 1. » Read more

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