Dihedral Group (Abstract Algebra) 

Friends? What are those?

time to get new friends fool. lol

those "friends" will soon not be able to be employed anymore when robots take over. Only creative jobs will survive. So you will surpass them later if they don´t respect your interests now!

You made the wrong friends

I don't know why but I read your comment in Electroboom Mehdi Sadaghdar's voice 😂

She doesn't write these, but her delivery is nice :)

@@markdstump I am so upset I think she is AI...

@@judithbenami3964 Don't worry, Liliana​ ​de​ ​Castro is real.

LOL THIS

You are so kind! Thank you for watching. :)

We're so glad you found our video helpful! This was wonderful to hear. We're so glad you are learning Abstract Algebra with us. Happy New Year! :)

I am studying math and taking a course about groups this semester and rings next semester. I am happy that I found your channel it's very easy to understand. Happy New Year to you as well! :)

dear how can i get relative theorems on each topic???????

Love this idea! 💜🦉

Thank you so much, Jacob! We're so glad you've subscribed to our channel! We're a small team here at Socratica. We do most of our work in the Adobe Suite (Premiere, After Effects). Thank you for your kind comment! :)

yes, they are a didactical masterpiece!

Let me know when someone figures this out

Even the most abstract concepts in advanced math come from something more intuitive, whether it's examples, geometric intuition, or something else more concrete. It is always a good idea to be able to think of these examples when thinking of the definitions or theorems. When writing a proof, you do not use these ideas in your proof and instead keep it formal, which I think what was being emphasized during your Real Analysis class. Unfortuantely, many professors ignore the intuition and just give formal definitions and proofs without motivating them or giving a clear picture of the concept first. In this channel, the videos are meant for understanding, and not formalism, which is why they are clear and inutitive.

We're so glad we could help. Try to find a good study group so you can help each other - hang in there!! 💜🦉

yes. It´s very sad she gets so little money.

Thank you so much, Shubhra! We're so glad you are watching! :)

MrVictius Polynomial equations are *closed* on the set of complex numbers, which means that any arithmetic operation used in a polynomial equation works inside the set and cannot escape it, therefore all solutions to such equation (its roots) are in this set. Now take a look at some of such equations and their solutions, and you should notice that there's a finite number of them (equal to the degree of the equation; e.g. a second-degree polynomial has two complex roots, third-degree polynomial has three etc.). And these roots are related to each other: if you take first of them and multiply by itself, you'll get the second root. Do it again, and you will get the third one. Repeating it will always give you the next root in a row. Until you make a full circle and end up where you started. Therefore they make a cyclic group. In the complex plane, they're usually located at the vertices of a regular polygon. You can do the same with any other of the roots of a polynomial. The bigger angle they make with the real axis, the more they "jump" in a rotation. E.g. if you multiply by the second root, you make twice the rotation of the first root in each step, jumping every other root. Multiplication by the third root jumps over three roots at a time. But no matter which one you choose, you always end up in one of the roots of your polynomial. No other number can be reached this way.