Basic abstract algebra, pt.10

This is a video series about basic abstract algebra and group theory. We will keep it basic so that anyone can follow the videos.

This is the tenth video in the series. We start looking at elementary number theory, and only make a few definitions to get familiar with the concepts.



(Music: Nine Inch Nails - The Downward Spiral)

Category:

Education

Tags:

• basic
• abstract
• algebra
• cyclic
• group
• number
• theory
• mathematics
• math
• theorem
• prove
• proof
• science
• axioms
• subgroup
• abel
• abelian
• division
• algorithm
• modulo
• divisible

[bosseyedbill]

nice.rubbish music.can you do something on exponential multiplicative and RSA's.and while your about it can you explain isomphism 'so i can understand it easily' ? thanks

[VeritySeeker]

I've tried to explain isomorphism in the video series, and I received a lot of questions on them. I do not see how I can explain isomorphism any better than I tried in my videos. Feel free to ask questions, though.

[VeritySeeker]

Oh and about the music. I can't please all the different tastes around ;).

[flyfish89]

You have the gift my friend. When I watch your videos, everything I didn't understand before is suddenly clear as day. I have told everyone in my abstract algebra course about your videos. Once again thanks! Todd

[VeritySeeker]

Thanks a lot. I hope they can be of some kind of help or motivation. I noticed your name. Are you a fly fisher? It is a big, big hobby of mine :).

[mwdavis]

Excellent! Can't wait for the next one :)

[intemperate7]

@VeritySeeker I love your videos. thank you so much for doing this. I will definitely subscribe

[andrewg86]

@VeritySeeker

You have explained it quite clearly! many thanks

[Yaldatchayil]

Nice video! We also use modular space (specifically, Z12) in twelve-tone music theory. We think of it this way: if a = b mod 12, a and b are the same pitch-class (the same note in different octave registers).

[TraleeFair]

This was the easiest of the set so far.

I was ahead of you in each step.

However, did you mean n factorial when you said n!

I don't think you did but shouldn't you be attentive to sources of confusion?

[lwqeva]

1:28  Should be " r is a non-negative integer smaller than |m|. ", because r could be zero..

[shweddedglowy]

In one of my first math lectures at uni, isomorphism was explained by using drawings of structures. That is, the names of the elements were different, but the basic drawing was the same. This mental image helped me a lot.

[interted]

And about the music. It's excellent mate, don't listen to some people!

[interted]

excellent lectures so far! i have read a book about number theory and abstact algebra and I was confused. But not that i see your videos, i conclude that the book was very bad written!

only one thing about your video. wouldn't it be better to symbolize modulo with m, and not with n as you do? because it confused me a bit.

[danielkim116]

love the background music :)

[johnny88374]

My head was a jumbled mass of confusion! Too much information and no idea how to organize them.. And then I came across your vids... Thanks a million! You set my mind straight again.. I mean, of course, there is still the absolute necessity to study by oneself, but your vids are a great guide!... You really understand Abstract Algebra, don't you? You wouldn't be able to explain it so comprehensively and so well if you didn't. Keep up the good work!! P.S. That is so cool about the CD. =)