It's definitely possible to learn them together in parallel, I know one person who has done it, but it's really not a good idea because the amount you'll learn is very little
you won't have a very firm understanding of QFT if you learn QM in parallel
you could probably get away with knowing harmonic oscillator, Fermi's golden rule, and knowing how to get irreps of rotation group using raising and lowering operators
but I still concur wholeheartedly with @ACuriousMind
What do you mean "am I done"? Have you shown the existence of such an $n$? (It's somewhat obvious, but I'd have had to calculate it explicitly in my first analysis course)
This approach seems to not give a proper bound for $n$, it's probably too tight - use $\frac{n-j}{n}\epsilon < \epsilon$ first and then say that for any $\epsilon'$, you choose $\epsilon = \epsilon'/2$. This gives $\sum_{i = 1}^{j-1} \frac{\lvert a_i - a \rvert}{n} < \epsilon'/2$, which has a proper bound.
I recall struggling with my first $\epsilon$-$\delta$ proofs as well, you should get used to this stuff after you've seen it hundreds of times in slight variations :P
@0celo7 that's because QM and GR are really easy when it comes to textbook problems
analysis is a whole different beast
it's to be expected
user54412
5:28 AM
@0celo7 I also suggest Carothers. It's a nice casual book that still hits all the important points.
user54412
It's also memorably quotable. Not only is "sets are not doors!" in the index, it doesn't hesitate to conclude proofs with things like "hit it with Fatou!"
@0celo7 sometimes what physicists mistake for a proof is rather something else, such as intuition...and intuition is important, but easier than a proof ;-P
@0celo7 the implicit question is, how well do you trust future-Microsoft to correctly decide what is a pirated game and what isn't? Or what counts as unauthorized hardware and what doesn't? Bear in mind that this article comes from the perspective of people who don't have that trust, or at least don't take it for granted.
Also it's privacy advocates, not piracy advocates.
@Slereah : when you read Einstein and Rosen's wormhole paper it's nothing like what you thought it was. It's about representing a particle as a "bridge" between two sheets. It isn't about wormholes as they're discussed today.
@Slereah : some authors appeal to Einstein's authority whilst saying something very different, or even flatly contradicting him. Wheeler didn't understand the difference between curved spacetime and curved space. If he had, he wouldn't have talked about the geon. He would have talked about the electron.
@ACuriousMind So after close discussion with my honors mentor (who is a super cool chemical engi/math double major), we figured out that the course that uses that book is actually the second analysis course. The first one has course description: "Introduction to the theory of the real number system. Limits of sequences and functions of a real variable."
That makes me feel a lot better because I can't handle Jost yet.
So next year I'll do Analysis 1 and some other class...have to decide between Topology and Abstract Algebra most likely.
@Slereah No, you can't choose a phase because the whole expression is meant to be real. The $\mathrm{i}$ only ever appears because physicists have a fetish for self-adjoint operators-
do they take 4 years of math? I know you are required to take 2, but everyone I know who took a full 4 remembers how to do algebra and some basic trigonometry
@ChrisWhite Just like true world-history-ignorant Americans. Sounds about right.
Does anybody know what the status of Hawking's Chronology Projection Conjecture is? Is it accepted as possibly likely, or is it considered dubious?
Someone on Worldbuilding tried to invoke it to make wormholes possible (ignoring some other issues) and I'm trying to shoot it down.
user54412
I've always held the unwavering view that wormholes are like unicorns -- it's hard to mathematically disprove their existence, but a scientist shouldn't go around with even the slightest doubt that they don't exist, since they're just a figment of sci-fi/fantasy writers' imaginations.
user54412
That said, there are scientists with lower standards than me for believing in theories that just sound cool to them.
When a question comes up in the re-open queue because it was edited, the default is to show the side-by-side comparison of the pre- and post- edit. There is another 'tab' available that will show the question as it appears after the edit. The view highlighting the changes is fine, and probably wh...
@ChrisWhite have mixed feelings on it. think there is some near-scapegoating going on about them. personally regard them as innovative & pioneering into terra incognita. recognize they are highly controversial. they seem to "split opinion".
user54412
Well, I guess they can't be as bad as Mars One. It's not like they're actively trying to kill people.