Watch a video on you-tube "Symmetry, Eames Office". I saw that video around 50 years ago at the Calif. Museum of Science and Industry in L.A. The narrator mentions group theory at the end. So now I'm finally learning what is group theory (!).
I really appreciate your lectures and its been helping me a lot. Do you happen to have Abstract Algebra II which covers ring and field etc? If so, could you please upload them? Thank you so much.
Thanks. I actually do not have anything much beyond what is posted here at the moment. If all goes as planned, we get to rings and things at the end of October and I'll talk about the basics of ring theory for about 3 weeks at the end of this course. In the spring we'll go deeper into ring theory and further topics...
James Cook thanks sir :) and as for "rfr^(-1)f" at the end of the video. Is it correct that rfr^(-1)f=rfr^2f=rfrffrf=rr^(-1)r^(-1)=r^2 ? It's written "rfrfrf=rf" in the video, I feel like maybe an "f" is missing.
If I am not wrong, isn't the centre of a group the maximal Abelian subgroup of the group ? I mean it just extracts out the Abelian component of the Group. If the group G is Abelian itself then then the whole portion is the maximal Abelian subgroup, so G is the centre of itself.
That sounds correct, but that is not the way we have defined it in this course, I think that would be a theorem for us here. But, yeah, the center of an abelian group is the whole group since all the elements commute with one another.
it helps me a lot :D
Watch a video on you-tube "Symmetry, Eames Office". I saw that video around 50 years ago at the Calif. Museum of Science and Industry in L.A. The narrator mentions group theory at the end. So now I'm finally learning what is group theory (!).
I really appreciate your lectures and its been helping me a lot. Do you happen to have Abstract Algebra II which covers ring and field etc? If so, could you please upload them? Thank you so much.
Thanks. I actually do not have anything much beyond what is posted here at the moment. If all goes as planned, we get to rings and things at the end of October and I'll talk about the basics of ring theory for about 3 weeks at the end of this course. In the spring we'll go deeper into ring theory and further topics...
James Cook thanks sir :) and as for "rfr^(-1)f" at the end of the video. Is it correct that rfr^(-1)f=rfr^2f=rfrffrf=rr^(-1)r^(-1)=r^2 ? It's written "rfrfrf=rf" in the video, I feel like maybe an "f" is missing.
I know there is an error in there, let me calculate again rfr^(-1)f = rffr = rr = r^2. Yes I also calculate r^2 when I do it over.
If I am not wrong, isn't the centre of a group the maximal Abelian subgroup of the group ? I mean it just extracts out the Abelian component of the Group. If the group G is Abelian itself then then the whole portion is the maximal Abelian subgroup, so G is the centre of itself.
That sounds correct, but that is not the way we have defined it in this course, I think that would be a theorem for us here. But, yeah, the center of an abelian group is the whole group since all the elements commute with one another.