Hey! Your method of teaching the material is really good, this series is the reason I'm confident for my final coming up. Thank you so much!! I wish I had found this before the midterm though lol
You know the video is good when you clarify one of your doubts just one minute into the video! Great work, this series has been helping me out a lot, specially because of all the examples you give but also the 'talked through' explanations
This play list "Abstract Algebra" is completely out of order. I can't help but feel that homomorphisms should be introduced *before* isomorphisms, as the latter is just a special case of the former.
I think it depends on the intended audience of the class/video/textbook. In a second course on abstract algebra, I would agree with you and define homomorphism first. However, in a first course in abstract algebra, I think I would go with isomorphism first. To me, the concept of "isomorphism" is much easier to motivate than the concept of "homomorphism". What does it mean for two groups to be "the same" algebraically? I think it's reasonable to come up with a definition for this. Now, you could say that homomorphisms show us how to groups can be related, and isomorphism is a strong form of this relation, but I find it harder to come up with the concept of a homomorphism from scratch than it is to come up with the concept of isomorphism from scratch. From there, you can ask how weakening the isomorphism condition still gives information about how two groups are related to each other, and have that lead into the definition of a homomorphism. One of the difficulties of learning abstract algebra is that it's hard to gain intuition for a lot of the concepts. So if the instructor/textbook can motivate the concepts, hopefully it can ease the difficulty of the lack of intuition.
Isomorphisms are invertible homomorphisms. Injective is dual to surjective synthesizes bijective or isomorphism. Isomorphism (absolute sameness) is dual to homomorphism (relative sameness, difference). Duality creates reality!
Hey! Your method of teaching the material is really good, this series is the reason I'm confident for my final coming up. Thank you so much!! I wish I had found this before the midterm though lol
You know the video is good when you clarify one of your doubts just one minute into the video! Great work, this series has been helping me out a lot, specially because of all the examples you give but also the 'talked through' explanations
Stoked on this new channel!
Great videos. I will use this to relearn Abstract Algebra.
This play list "Abstract Algebra" is completely out of order. I can't help but feel that homomorphisms should be introduced *before* isomorphisms, as the latter is just a special case of the former.
I think it depends on the intended audience of the class/video/textbook. In a second course on abstract algebra, I would agree with you and define homomorphism first. However, in a first course in abstract algebra, I think I would go with isomorphism first.
To me, the concept of "isomorphism" is much easier to motivate than the concept of "homomorphism". What does it mean for two groups to be "the same" algebraically? I think it's reasonable to come up with a definition for this. Now, you could say that homomorphisms show us how to groups can be related, and isomorphism is a strong form of this relation, but I find it harder to come up with the concept of a homomorphism from scratch than it is to come up with the concept of isomorphism from scratch. From there, you can ask how weakening the isomorphism condition still gives information about how two groups are related to each other, and have that lead into the definition of a homomorphism.
One of the difficulties of learning abstract algebra is that it's hard to gain intuition for a lot of the concepts. So if the instructor/textbook can motivate the concepts, hopefully it can ease the difficulty of the lack of intuition.
This make so much sense and meaning and can relate to it
Isomorphisms are invertible homomorphisms.
Injective is dual to surjective synthesizes bijective or isomorphism.
Isomorphism (absolute sameness) is dual to homomorphism (relative sameness, difference).
Duality creates reality!
Excellent. I love these videos!
I like how he cleans the board 😹🤭❤️
Pls i would be very happy if you could kindly take your time for others to also understand better. Thanks