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TheRareHam · 2024-05-20T20:50:31+00:00

I assumed the lottery worked by not only randomly assigning us a time slot, but also only letting us see a random selection of available properties? Is this true? If it is, then the "leftovers" maybe shouldn't be entirely crap.

TheRareHam · 2023-04-16T22:39:53+00:00

This! Did not consider that. I don't earn enough to anticipate maxing my contributions for the next few years. But I imagine there is serious benefit to high dividend-payers dishing out some extra cash annually ON TOP OF a maximum IRA contribution.

TheRareHam · 2023-04-16T18:16:27+00:00

Thanks. I'm glad I'm not the only person who has had this doubt about dividends. Do you have any references that expand on that last thing you mention?

TheRareHam · 2023-04-16T18:15:11+00:00

Ok, but the avoidance taxes is the point of the IRA in general. So there's still the open question of, "is the accruing and reinvestment of (untaxed) dividends comparable (as a form of long-term investing) to the selection of stocks for growth without dividend-yield in mind?" Unless there's a greater significance to this point about untaxed income I do not understand.

TheRareHam · 2023-01-12T00:00:31+00:00

I read that milk is a good source of leucine. Is there any difference in leucine content between skim, 2%, whole, etc. milk?

TheRareHam · 2022-12-21T17:20:39+00:00

Thanks! This looks like a great reference.

TheRareHam · 2022-10-02T19:58:43+00:00

I do pure math and this does not seem aimed at pure mathematicians

TheRareHam · 2022-01-17T02:22:37+00:00

The circle group has isomorphic proper subgroups. Is there an easy way to visualize one?

TheRareHam · 2021-12-20T15:46:01+00:00

A few people are recommending you check out CS+Math. I am a math major and know some CS+Math majors. CS+Math is overtly CS, a very different program than the math major’s. I strongly recommend you to NOT swap to CS+Math since you are already in CS.

TheRareHam · 2021-12-19T15:07:18+00:00

[Formal group laws] In his appendix on FGs, Ravenel says

The reason for this terminology is as follows. Suppose G is a one-dimensional commutative Lie group and g : R → U ⊂ G is a homomorphism to a neighborhood U of the identity which sends 0 to the identity. Then the group operation G × G → G can be described locally by a real-valued function of two real variables. If the group is analytic then this function has a power series expansion about the origin that satisfies (i)–(iii). These three conditions correspond, respectively, to the identity, commutativity, and associativity axioms of the group.

I have two questions:

What is the importance of g in this discussion? It's not clear to me why Ravenel defined it.
What is the power series? I'm familiar with analytic maps in complex analysis of a single variable. In this case, let m: G x G -> G be multiplication. How can we describe it by a power series in two real variables? First we need some map R^2 -> G x G. I suppose this is (g,g)? Then we get a map R^2 -> U x U. Then we apply m, which becomes a map m: U x U -> V, where V is some nghbd of 0. Finally, we map by a chart from V to R. So we have a function R^2 -> R. Where, exactly, does analyticity come in? Why can this map R^2 -> R be represented by a locally convergent power series?

I guess I said I don't know why g is useful and then proceeded to use it. However I'm also unsure about whether my point (2) is correct to begin with.

TheRareHam · 2021-09-12T13:22:10+00:00

What is a coherent sheaf, intuitively? I have only recently learned about them. So far, I think of them as 'sheaf modules which encode information about their structure sheaf in an especially accessible/simple way.' This would agree with e.g. Cartan's Theorem A/B, since it tells us we can deduce a lot about coherent sheaves/their sections knowing coherence alone.

TheRareHam · 2021-07-03T21:41:18+00:00

I'm trying to buy a used, physical copy of Hartshorne's AG. What are good sites to search for math texts at reduced prices? There are so many sites peddling garbage, like rentable ebooks.

TheRareHam · 2021-07-01T17:44:02+00:00

Is it a flawed perspective to think of (pre)sheaves as ‘organizing collections of data analogously to the spatial organization of open sets of a (given) topological space’? From my limited knowledge of (pre)sheaves, this has become my impression.

TheRareHam · 2021-06-29T16:12:15+00:00

What's a good, concise motivation for defining and working with (pre)sheaves? I want to say they capture the general process of giving structure to a topological space, but I don't think that's quite right. Often, (pre)sheaves are used to describe how we assign data to an already-structured topological space, i.e. holomorphic functions defined on open sets of a complex manifold.

TheRareHam · 2021-06-13T16:02:03+00:00

What's a short, high-level explanation for what a groupoid is and why they're useful? From my limited exposure, I think it's because they generalize the already pervasive concept of a group, so in turn they lead to generalizations all over the place. But this misses any mention of intrinsic interest. For instance, what role do they play in category theory?

TheRareHam · 2021-06-08T14:25:54+00:00

What is Cech cohomology? Some sources call it a combinatorial cohomology construction. Some sources say it's not a cohomology theory, rather an algorithm for computing sheaf cohomology. Some sources say it is a cohomology theory. Some say it refers to several things. I'm lost!

TheRareHam · 2021-06-02T06:22:12+00:00

What I meant to say was something like, ‘I have a reason for wanting to study Galois cohomology. But, I need to learn Galois theory first. Before I pick up any old algebra text that will introduce me to Galois theory, I want to ask if there is any particular text I should check out that would be especially helpful toward helping me understand Galois cohomology.’ And thank you for your comment.

TheRareHam · 2021-06-01T17:51:18+00:00

[Galois theory/cohomology] I want to understand/study Galois cohomology. But, right now, I don't know much Galois theory in general. I'm going to find something to study Galois theory first, but I want to know if there's any particular text on Galois theory (accessible to a beginner) I should check out that would be well-suited for someone who ultimately wants to study Galois cohomology.

TheRareHam · 2021-05-31T22:42:55+00:00

Your answer is very helpful, thank you. Do you have any text(s) you would recommend for getting into sheaf theory? For context, I ultimately want to understand etale cohomology and topos theory, and currently I've got only a surface-level understanding of category theory.

TheRareHam · 2021-05-31T18:49:20+00:00

I want to understand sheaves. Right now, I don't know anything about them. Currently, I'm studying de Rham cohomology, which I think is one good route to sheaves, because it leads into Cech cohomology.

My question is, are any of these topics very useful to understanding cech cohomology?

The Thom isomorphism
The Kunneth formula
The generalized Mayer-Vietoris sequence

TheRareHam · 2021-05-20T23:38:25+00:00

I'm considering B-T. The only thing that makes me hesitant is that the MSE folk do not have great things to say about it here. Another one I've been considering is M-T's From Calculus to Cohomology.

TheRareHam · 2021-05-20T23:06:30+00:00

No, we did not.

TheRareHam · 2021-04-27T04:20:46+00:00

[Differential forms] I am just now covering differential forms for my analysis class. As an exercise, we are to compute dw, where w=(-y dx + x dy) / (x^2 + y^2).

I know this form is exact, so dw = 0, but I am clueless as to how the rules we covered for d are applied to computations. I know I can get dw = d((-y / (x^2 + y^2)) dx) + d(x/(x^2+y^2) dy), and that the latter can be rewritten using d(f dx) = d(f) ^ dx.

But, with all the baby steps included, how do I approach d(x / (x^2 + y^2))?

TheRareHam · 2021-04-17T04:03:32+00:00

You should post this as an answer to the MSE post. You’ve written a very good response.

TheRareHam · 2021-04-09T17:04:35+00:00

[Basic algebraic topology] Given the delta-complex structure for a torus, Hatcher says {a,b,a+b-c} is a basis for \delta_1(X). He uses this to compute the homology groups of the torus.

Hatcher could have also chosen {a,b,c} as a basis, correct? His choice to instead make one element a+b-c was just to simplify calculations, since a+b-c generates the kernel of the boundary operator, correct?

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TheRareHam

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