You are very welcome. I live in a small town myself, and I know how frustrating it can be to find resources. I wish you well with your education.

You are welcome. I'm glad these videos are still helping people.

Why encrypt a message? That is mainly a history question rather than a math question, but any time you need to transmit information and make it difficult/impossible for anyone that intercepts the message to make use of that information. In modern times we think mainly of digital encryption of data such as credit card numbers, which often have to be transmitted through non-secure servers, but you absolutely don't want anyone other than a trusted recipient to have that number. This would be a poor way to encrypt such a thing, but this video is only the briefest glimpse into a huge field of mathematics.

The group operation is addition (mod 6), not multiplication. 3 + 3 = 6, which is equal to 0 when taken mod 6.

@@patrickjones1510 ok sir..thank you sir..

You're correct. In trying to go quickly, I didn't notice that I had already subtracted the x away. In the end, it doesn't change the conclusion, since any non-zero remainder shows it doesn't divide evenly.

In general, I was following "Contemporary Abstract Algebra," by Joseph A. Gallian. I was using the 9th edition, but as is often the case, there isn't much difference between editions. If I recall correctly, this first introductory video was not taken from the text, though.

@@patrickjones1510 Thanks! I really like your approach which seems to introduce each topic with an excellent concrete example.