/sci/ - Science & Math

I'm starting my first introductory physics course this coming fall semester. I haven't had a physics course since highschool and I have since forgotten everything. I'm 25. Is there anything I should know before going in? I really want to dedicate my entire being to this.

>>11894404
To put it more shortly: A mere bijection is not enough, but it also has to respect whatever structure there is. Since the model stuff is a bit rusty, I'll explain my algebraic counter-example a bit better. If we let f: N -> Z be an isomorphism, then there has to be a natural number n such that f(n) = -2, but this forces 2+n=0, and this is not the case for any natural number. Have fun learning!

>>11867069
In the categories (or at least most of them) he is doing stuff in, they are the same. I see it as a thing that is analogous to the fact that the group of quaternions is not abelian itself but any of its proper subgroups is. In this case you restrict the category of topological spaces to a proper subcategory and get something extra like non-surjective epis. Do I remember correctly that Weibel actually has epimorphisms and epis as two separate concepts but then proves that they are actually equivalent? I have this vague memory, but I really can't remember if it was him and how the definitions were. Probably like if e is an epi and fe = 0, then f=0, or something like that. It's been ages since I read his book. I did it touch it last year, though, as my office mate had it in a pile over my books!

>>11867103
Cheap wine from Lidl, several times a week.

Someone may find this link worth checking out
https://www.lancaster.ac.uk/maths/study/phd/math-sci-studentships-2020/#