Thanks mate for this vid, really saved my ass here on the night before my Maths C exam. Reading the textbook gets real technical and I end up ongoing much more than is needed for the test. This explained everything perfectly. Cheers, keep up the vids. P.s I'm subscribed now ;)
Prof. Learnifyable: Many thanks for the new video on the Definition of a Cyclic Group. As usual, I love your examples cited and your explanations. You are indeed a born teacher with the gift of communicating higher math really well! You do have a fairly large number of followers: Within 24 hours there are over 15 views of this video! Please find below a natural extension of your examples mentioned in your video. Any cyclic group of order n is isomorphic to Zn: For the dihedral group of an equilateral triangle (D3), = = {r1, r2, r0} is isomorphic to Z3 = {mu1, r0} is isom to Z2 [ mu represents a flip] = {mu2, r0} is isom to Z2 = {mu3, r0} is isom to Z2 Look forward to seeing more abstract-algebra videos from you soon. I understand that you have a tight schedule. When do you think is a good time to introduce isomorphic groups (long-awaited for)? Respectfully yours, Benny, Calif. 2-13-2015
Hi Benny, I'm glad to see that you are still enjoying the videos. I have quite a bit more to say about cyclic groups, but I suppose I could make a video exploring isomorphisms. I had planned on using the group of units mod n to show the relationship between cyclic groups and abelian groups. But, in order to do that, I need to make a video introducing the units mod n. But, in order to do that, I need to explain congruence mod n. There is just so much to discuss and so little time! More videos are on the way!
How do you find the generators for something multiplicative? The examples you gave were excellent and helped a lot, but you didn't do an example like U(10)..
This is confusing. You should teach it without the table. So we can apply it to different problems. “1+1is 2 .. 3+1 is 4” why are we just adding 1!?????