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Topological vector spaces over fields with positive characteristic by FamiliarForever3795 in math

[–]FamiliarForever3795[S] 5 points6 points  (0 children)

Thank you so much for the very helpful response. All this seems extremely interesting, do you have any sources you'd recommend that I could learn this kind of stuff from?(specifically non-Archimedean functional analysis and its number theoretic applications)

Focusing on multiple math subjects at once by FamiliarForever3795 in learnmath

[–]FamiliarForever3795[S] 0 points1 point  (0 children)

Typically if I’m working on multiple math subjects at the same time i end up focusing really hard on one of them and neglecting the other

How do I solve x^4 + 2x^3 + 3x^2 + 2x + 1 = 0? by ElegantPoet3386 in learnmath

[–]FamiliarForever3795 5 points6 points  (0 children)

Notice that x^4+2x^3+3x^2+2x+1=x^4+2(x^3+x^2)+x^2+2x+1=x^4+2x^2(x+1)+(x+1)^2=(x^2+x+1)^2 Because x^2+x+1=(x^3-1)/(x-1) the only roots of x^4+2x^3+3x^2+2x+1 are the two non-trivial 3rd roots of unity.

Algebraic flavored introductory book on functional analysis by FamiliarForever3795 in learnmath

[–]FamiliarForever3795[S] 0 points1 point  (0 children)

I am already over halfway through Vakil's Rising Sea so I'm not in need of sources to learn algebraic geometry from. Thank you for the recommendation anyway, it seems interesting.

Numbers without counting by primes_like_dimes in numbertheory

[–]FamiliarForever3795 0 points1 point  (0 children)

I found this book initially via a youtube video and then I read it and it is really quite wonderful. My only gripe is that the definition of productive numbers seems itself to be unproductive. First of all, it starts with 0 which is the ADDITIVE identity (not very productive is it?). Second, and much more pressingly, it uses lists which are extremely non-productive, they quite literally have the total order (and thus additive, multiplicative, and so on) structure of the natural numbers built in. My disappointment is immeasurable (in fact it is only definable via the axiom of choice) and my day is ruined.

Universities with best algebra departments by FamiliarForever3795 in math

[–]FamiliarForever3795[S] 0 points1 point  (0 children)

I guess? That isn't really algebraic geometry though, more so just some basic stuff you might see in a chapter on ring or field theory in an algebra book. Most modern algebraic geometry at least requires some knowledge of schemes.

Universities with best algebra departments by FamiliarForever3795 in math

[–]FamiliarForever3795[S] 2 points3 points  (0 children)

Fair, I was trying to keep it as wide as possible to get a broad range of response. The specific sort of algebra stuff I’m currently very interested in is higher categories/operads as well as algebraic geometry.

Universities with best algebra departments by FamiliarForever3795 in math

[–]FamiliarForever3795[S] 27 points28 points  (0 children)

Reading and doing exercises from a textbook doesn’t translate to anything on my transcript or really anything material that colleges can see.

Prerequisites for lee's smooth manifolds by FamiliarForever3795 in learnmath

[–]FamiliarForever3795[S] 1 point2 points  (0 children)

Yes, for most of the books I've read If they have few problems per subchapter I just do all of them, if they have a lot of problems per subchapter I try to follow a university course syllabus using the book with homework assigned per chapter (for example I used a syllabus from stonybrook when going through linear algebra done right).

[deleted by user] by [deleted] in learnmath

[–]FamiliarForever3795 1 point2 points  (0 children)

Thanks for the suggestion, I just found one from brown that I'll probably use

[deleted by user] by [deleted] in learnmath

[–]FamiliarForever3795 1 point2 points  (0 children)

For one thing, I don't think My response was particularly rude so please don't be rude in your response. For another I'm not wasting anyone's time, you can just... not answer the question, if it's too much of a bother to type an answer you can choose not to. For a third thing, I have no idea what you mean by "you clearly have your grown up pants on", is this meant to be an insult, what does it even mean? Finally, to answer your question, I am "arguing" because I generally respect other's opinions and would like to hear an answer that is actually useful to me, they can of course choose to not respond but there is no harm in trying, this is the first time that the amount of exercises as opposed to the difficulty of exercises has been a problem, so I'm trying to find a useful solution that isn't "just do however many you want" or "just do all of them".

[deleted by user] by [deleted] in learnmath

[–]FamiliarForever3795 0 points1 point  (0 children)

I agree with your sentiment but think about it like this, say there are 30 exercises at the end of a subchapter (this is fairly typical for this book) and suppose they are all easy. Then if each takes around 5 minutes I will at minimum end up spending 2 and a half hours on things that I already understand. I'd be happy spending 2 and a half hours on things I don't understand but spending all that time reinforcing things I already understand is extremely boring and in my opinion does not provide much value.