/sci/ - Science & Math

/gmmg/

>>11743148
Hmm, that is a valid point. But what if I am keeping your heart as a hostage so that you will grow big and strong on your quest to reclaim it? Then I can say "I raised that boy" when you have trained yourself to the psycho-physical peak.

>>11743796
Approach from some nice examples. If you want a general equivalence relation, take all humans and say x and y are related if they live in the same country. What would be the equivalence classes then? For quotient groups, try approaching first from the direction of integers mod n. Then you can generalise it to more complicated cases and eventually reach the point where you are taking the quotients of kernels over images. Can you give an example of a problem most problematic? I believe in you, querido.

>>11743807
I learned the basics from Swan's book on the subject, although it is typewriter stuff. I don't know if it is good all the way through, but the beginning was well-written. This one: https://www.springer.com/gp/book/9783540042457

>>11743853
You need to bang your head against the material until you notice how the situation you are in is suitable for evoking theorem 6.66 etc. Then you apply its claim to move one step forward and recheck your situation. It's obviously not necessarily the only way to proceed. This post is getting algebraic, so let's continue with that. Say you were told to prove that the semidirect product [math]\mathbb{Z}/3\mathbb{Z} \rtimes \mathbb{Z}/2\mathbb{Z}[/math] is isomorphic to the symmetric group of 3 letters. You could construct an explicit isomorphism, or you could use the fact that there are only 2 isomorphism classes for groups of order 6, one for abelian and one for non-abelian groups. Then you would simply note that neither the group in question nor the symmetric group is abelian, from which you would conclude the result. Care to share an example of where you would struggle?

>>11703861
>Did anyone also have trouble understanding Equivalence Classes when they first read about it?
Yes.
>Is it a sign of my brainletness?
I don't know but I am a brainlet.
>Also, what about Quotient Set?
Path components of a space. You will specialise in homotopy theory, will you not? I dare you to say "no" to me.

>>11703865
More like agriculture. My mom comes from a farm, so I guess I inherited her peasantness.