Can you say more about what you mean about home ownership being a lifestyle as opposed to an investment?
I'm guessing what you mean is that houses require upkeep and they also come with certain benefits (e.g. more freedom with what you do with the house), but I'm wondering if you meant something different?
Possibly a long shot, but I was wondering if you knew of any sources of the CDC also taking this stance?
I have a vague memory that they also made similar statements, but I tried to find evidence of that recently and couldn’t find a source. I’d appreciate anybody that could link me to a source if they have it on hand / find one.
Many people don’t have any financial role models in their lives, especially at young ages. It’s not like the school systems teach children about saving, and especially not in the more underfunded districts.
I’m much more inclined to blame maladaptive behaviors on systemic failures to educate people and to provide them opportunity than I am to blame individuals.
Sure, in every system with live agents there will be bad actors and those with poor behavior, but when the system is overrun with examples of this, perhaps it’s the system we should be looking at, not individuals.
I like terminal based music players when I’m doing work exactly because the terminal already feels like work, so it doesn’t feel as much like Tidal or Bandcamp or SoundCloud are open in the background and something I could get distracted by. For keeping it out of sight, tmux or any terminal multiplexer is great at that.
I agree with the idea that fines based on the number of users affected makes a lot of sense. One question I have is how would you propose that number be calculated? In truth, I think the company whose data has been leaked should know exactly how many records have been leaked, but per-individual based fines create an incentive for them to underreport this number. Do you think that’s a problem, and if so, is there a good answer for how society could get an honest answer as to how many individuals are affected in a breach?
Yes, elliptic curves are huge in cryptography, but they are also mathematically significant. They are the degree three nonsingular algebraic plane curves with at least one rational point. This makes them essentially "one step up" from the conic sections. The conic sections, of course, are well understood including the parametrization of their rational points. However, elliptic curves are much more subtle! We do not even have proven algorithms for determining the size of any elliptic curve's set of rational points, and in specific the algebraic rank of that set. The Birch and Swinnerton-Dyer conjecture is one of the millennium prize problems, and it relates elliptic curves' algebraic ranks to their analytic ranks. Elliptic curves are also very related to modular forms, and this connection is part of the theory that allowed Andrew Wiles to prove Fermat's Last Theorem. In the study of the rational solutions to integer polynomial equations, i.e. Diophantine Analysis, elliptic curves are one of the next stepping stones that must be more thoroughly understood before we can have a more complete understanding of polynomials in general. Their applications in cryptography and integer factorization are huge in applied mathematics, but they are also incredibly important subjects to fields like algebraic geometry, diophantine analysis, and of course, number theory.
I don't know your situation, but have you thought about part-time remote work? Or just part-time work in general? Every job post seems to be looking for people who can work with React. If you're looking for remote work, web dev is def the place to be.
a rather interesting aspect of the taxicab number story is that ramanujan had been looking at "near misses" to the fermat equation, and this was the first values of one of the infinite families of near misses he had constructed. The story is often dramatized to make it sound like Ramanujan just knew about all the cubes and their sums and he pulled this out of thin air on the spot, but the truth is probably that he had worked enough with these equations to recognize the number when Hardy mentioned it.
Abstract algebra is often about studying structure on sets. That usually takes the form of studying operator(s) with certain properties and the elements that they work with. Some early examples that students see are things like rotations/reflections of n-gons, modular arithmetic, polynomials, matrix spaces, and fields.
It is different from regular algebra in the sense that often one starts with a set and operation one supposes to have a particular kind of property (perhaps it's a group, or perhaps it's a field, or perhaps it's a certain kind of field (maybe separable, or local, or ...)). Then from these assumptions one proves facts about the assumed algebraic structure.
It's different in that often particular elements aren't of much interest, and it's not as tied down to a particular context.
I'm guessing what you mean is that houses require upkeep and they also come with certain benefits (e.g. more freedom with what you do with the house), but I'm wondering if you meant something different?