Another wonderful lecture. Second time I stumbled upon your content through my recommended feed. Pretty sure I already commented on your other video but you are a real standout among teachers in how coherent and neat your lectures tend to be. Solid script, good pacing, clear articulation. Keep up the excellent work!
Fantastic explanation of cyclic groups and their isomorphisms! You really made the concept of generators and cyclic subgroups so clear and accessible. I especially appreciated how you demonstrated the isomorphisms with both finite and infinite cyclic groups, and the way you showed that the powers of an element always form a cyclic subgroup was super insightful. This video is a great resource for anyone diving into group theory. Thank you for making such complex topics understandable and engaging!
Abstract algebra is really easy if you are willing to “ not tie your mind to past concepts and their definitions “. The math is extremely easy, but you have to let your mind adjust to new and different ideas and ways of doing things. Mixing visual, hands on problems and theory together in the lessons helps that hurdle .
Thank you for your videos, they really help me grasp these topics!! I wondered if you could please do a video on cyclic subgroups, the greatest common divisor, prime numbers, and all that mess? It's very confusing to me!
1:22 - what is the definition for a generator under addition? this is so confusing to have the definition for G, and then immediately a new concept that's not defined is presented
1:47 like saying Z= makes no sense given the definition that G={a^n : n in Z} (every element in G={1^n : n in Z } is 1). Where is the generator for addition defined
For a generator under addition it would look more like adding ‘a’ n times. So contains all possible sums of 1 and it’s additive inverse (-1) which clearly generates all integers.
Glad to hear it! Thanks for watching and check out my Abstract Algebra playlist if you haven't! th-cam.com/play/PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN.html Let me know if you have any video requests!
Nope, that is not necessary. For example the additive group of integers is itself the cyclic subgroup generated by 1, which certainly has infinite order.
Thank you, I work very hard on these 🙌 It’s summer now, I hope to make significant progress on producing more videos for my core playlists, and hopefully Wrath of Math will grow very healthfully this Fall!
@@WrathofMath It might be neat to have a video explaining why if A generates a cyclic group G, then a function that multiplies every element in G with A is an automorphism of G. I bet you could work examples like Z10 and Z15 into such an explanation, and you would be laying the ground work for talking about primitive roots. Just a thought.
Another wonderful lecture. Second time I stumbled upon your content through my recommended feed. Pretty sure I already commented on your other video but you are a real standout among teachers in how coherent and neat your lectures tend to be. Solid script, good pacing, clear articulation. Keep up the excellent work!
Thanks so much! Let me know if you ever have any questions!
Fantastic explanation of cyclic groups and their isomorphisms! You really made the concept of generators and cyclic subgroups so clear and accessible. I especially appreciated how you demonstrated the isomorphisms with both finite and infinite cyclic groups, and the way you showed that the powers of an element always form a cyclic subgroup was super insightful. This video is a great resource for anyone diving into group theory. Thank you for making such complex topics understandable and engaging!
Abstract algebra is really easy if you are willing to “ not tie your mind to past concepts and their definitions “. The math is extremely easy, but you have to let your mind adjust to new and different ideas and ways of doing things. Mixing visual, hands on problems and theory together in the lessons helps that hurdle .
Ok...where did the hoodie come from?
broo i burst out laughing when i see this comment🤣🤣🤣good one
Ahahahhahauaha😂😂😂
He said Amazon in another comment
Perfect explained! Thank you soo much!!
Thank you for your videos, they really help me grasp these topics!! I wondered if you could please do a video on cyclic subgroups, the greatest common divisor, prime numbers, and all that mess? It's very confusing to me!
1:22 - what is the definition for a generator under addition? this is so confusing to have the definition for G, and then immediately a new concept that's not defined is presented
1:47 like saying Z= makes no sense given the definition that G={a^n : n in Z} (every element in G={1^n : n in Z } is 1). Where is the generator for addition defined
For a generator under addition it would look more like adding ‘a’ n times. So contains all possible sums of 1 and it’s additive inverse (-1) which clearly generates all integers.
i just love your videos, thank you for this
Thanks for watching!
Challenge at 2:36 is 5, 5 generates 5,2,7,4,1,6,3,0 then repeats
Thank you for this video :) it helped a lot
Glad to hear it! Thanks for watching and check out my Abstract Algebra playlist if you haven't! th-cam.com/play/PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN.html
Let me know if you have any video requests!
Where did you get that trigonometry hoodie
Amazon!
what specific song plays at the end of this?
9:35 should element 'a' be of only finite order to form a cyclic sub group?
Nope, that is not necessary. For example the additive group of integers is itself the cyclic subgroup generated by 1, which certainly has infinite order.
How will you generate negative integers using the generator ?? Please help
I believe that should be a^-1. For example 1^-1 = -1, 1^-3=-1 (-1×-1×-1=-1). That should be an alternating group. I'm open to corrections tho
@@respectfullysammy i referred a book in which, it was written, 1^-3 = (-1-1-1) =-3
Thank you for responding..
Thank you
Welcome!
Where are you getting 10, 5, and 8? 2:26
I am adding 3 (mod 8) repeatedly. So 7+3 = 10. But 10 mod 8 is 2. Then 2+3=5 and 5+3=8, but 8 mod 8 is 0.
I've always said this, you are the best
Thank you, I work very hard on these 🙌 It’s summer now, I hope to make significant progress on producing more videos for my core playlists, and hopefully Wrath of Math will grow very healthfully this Fall!
Sir please share some examples of Cyclic groups like Z10 Z15 like
Thanks for watching, and will do, just give me some time! Looking do make a permutation group lesson next.
@@WrathofMath It might be neat to have a video explaining why if A generates a cyclic group G, then a function that multiplies every element in G with A is an automorphism of G. I bet you could work examples like Z10 and Z15 into such an explanation, and you would be laying the ground work for talking about primitive roots. Just a thought.
Sir I'm your Subscriber
Thanks for watching!
@@WrathofMath
Thanks a lot Sir
@@WrathofMath sir can I get yours whatsapp Number please
(2^0) = SU(1)
(2^1) = U(1)
(2^2) = U(2)
(2^3) = SU(3)
You pronounce Cyclic as "Siclic".
I just login to say thank you very much, your classes are the best!!! Hero of nice explaining 🤍 thank u & wish u the best