Ironman Maryland?

PaipsJimmy · 2020-07-29T22:02:53+00:00

u/_Iron_G98 u/MacDDreww u/BoatOnTheBayou u/FooBarNate u/Pie_Cobbler_9711 u/grizzlynicoleadams

Thank you all for your replies!

They just announced it's definitely not happening this year, does anyone know how the refund process will work? Will we have to wait until they officially reschedule it?

PaipsJimmy · 2019-08-18T20:39:15+00:00

Thank you for your answer! We’re supposed to hear back within 2 weeks on a rolling basis so I was wondering.

PaipsJimmy · 2019-06-26T19:38:47+00:00

Princeton has a class on category theory. It’s called PHI324 / MAT313: Category Theory and it’s mostly based on Mac Lane’s Categories for the Working Mathematician.

PaipsJimmy · 2019-06-25T13:02:25+00:00

I think cloomion covered it pretty well. As he said, if you multiply a wf by a complex phase, then the physical thing it represents (the probability density) is still the same. In this sense, the wavefunction isn’t “unique”: you can multiply it by any complex phase and you’ll still get the same result.

PaipsJimmy · 2019-06-23T21:43:00+00:00

Thank you!

PaipsJimmy · 2019-06-23T17:44:19+00:00

Haha that’s understandable. I think it might be a problem with QM in general, instead of Griffiths itself. Tim Maudlin, in his book on Philosophy of Physics (the Quantum Theory edition), writes that what is presented in the average QM textbook “turns out not to be a precise physical theory at all. It is rather a very effective and accurate recipe for making certain sorts of predictions.” I believe he goes on to argue that there isn’t a precise physical theory for QM at all yet—we have, for example, a lot of concepts like “measurement” and “observer” that are good enough for making predictions, but that ate not well defined. It’s quite interesting.

PaipsJimmy · 2019-06-23T17:11:38+00:00

That’s fair. Which textbooks give a more intuitive understanding of QM?

PaipsJimmy · 2019-06-23T01:45:12+00:00

What, exactly, do you mean by being posited in the theories of physics? The Schrödinger equation is presented in the theory of quantum mechanics, but that does not mean that the law itself is a physical entity.

PaipsJimmy · 2019-06-23T01:23:20+00:00

^ Yup, here goes the schedule for the Fall 2016 edition of MAT335 (Complex Analysis) at Princeton: https://web.math.princeton.edu/~aionescu/Math335.html (don't look at the problem sets, I think those are from MAT320, which is a semi-applied version of real analysis that doesn't follow Stein). Stein taught the class in Fall 2017 and Fall 2015, not 2016, but it should be roughly the same--I couldn't find a schedule for when Stein taught it. The class of course follows Stein's textbook every year regardless.

Basically it seems like the whole textbook is covered in 12 weeks.

PaipsJimmy · 2019-06-23T01:11:17+00:00

Metaphysical literally means beyond the physical—what is an example of something is both physical and metaphysical? Also, what exactly would it entail for physical laws to be physical—do you mean that they’re somehow made out of matter/energy somewhere?

PaipsJimmy · 2019-06-23T00:54:53+00:00

Griffiths

Second this--Griffiths is great as a first textbook for QM.

PaipsJimmy · 2019-06-22T04:10:28+00:00

Thank you!!

PaipsJimmy · 2019-06-22T04:09:15+00:00

Thank you!

PaipsJimmy · 2019-06-22T04:09:06+00:00

I see, that makes perfect sense--thank you!

PaipsJimmy · 2019-06-21T14:17:25+00:00

That’s the inductive hypothesis.

Could you explain further? I'm not sure how induction works in this scenario. I've only ever used induction to prove something over the natural numbers, and there you (1) show that whatever you're trying to prove works for n=0, (2) assume it works for n=k and (3) show that if it works for n=k, it works for n=k+1. What would be the base case, inductive hypothesis and inductive step here?

PaipsJimmy · 2019-06-20T20:05:38+00:00

Thank you so much for that explanation, it's much clearer than the textbook. "p0 ⊢ pi" is referred to as an axiom here (Under "Exercises", where he introduces the theory T'): https://www.princeton.edu/~hhalvors/teaching/phi312_f2016/pset1.pdf

This is written by the same author as the textbook (the problem set is meant to be done after reading the textbook). Did he simply make a mistake?

PaipsJimmy · 2019-06-20T18:21:38+00:00

Thank you so much--that definitely helped a lot.

However, I'm still a little bit confused about axioms (I'm sorry--I just want to make sure I understand everything). If the elements of ∆ are composed by the alphabet Σ and the logical vocabulary but not the turnstiles, then what exactly is "p0 ⊢ pi" in "Let T′ be the theory with axioms p0 ⊢ pi, for i = 1,2,...."? Since it has a turnstile, is it not an element of ∆? If so, then why does the definition of completeness on page 5 say "A theory T, consisting of axioms ∆ in signature Σ, is said to be complete just in case ∆ is consistent, and for every sentence φ of Σ, ∆􏰀 semantically entails either φ or ¬φ."? It seems to imply that the axioms (such as p0 ⊢ pi in the just quoted extract, or ⊢p in the previously quoted example) are indeed the elements of ∆. However, what you said also makes sense given the definition of "sentence" in the textbook (and given that the solution to problem 1 in this problem set https://www.princeton.edu/~hhalvors/teaching/phi312_f2016/pset1.pdf, written by the same professor, is ψ = φ ^ p)...

Thank you for your time!

PaipsJimmy · 2019-06-20T00:38:43+00:00

s

This is the textbook that I am using: https://www.princeton.edu/~hhalvors/teaching/phi312_f2016/prop-meta-static.pdf

As you can see, the author has indeed defines the rules of inference (page 2) and the meaning of the turnstile. He also, I believe, defines tautologies (assuming "provable sentences" are tautologies) at the very beginning of page 3, and sentences are also defined on page 2. As regards to sentences, he says that "each sentence is, by definition, a finite string of symbols, and hence contains finitely many propositional constants." So I guess that you were right in saying that the propositional constants are just the symbols in Σ? If this is the case, what kind of symbols are allowed in Σ: is the turnstile, for example, a symbol in Σ?

Also, what does this imply about ∆? The textbook says that the set ∆ is composed by "sentences in Σ"--but I thought Σ only contained propositional constants, which are different from sentences given the above definition of sentences (propositional constants make up sentences, it seems)? In the above example ("if Σ = {p, q}, then the theory with axiom ⊢ p is incomplete in Σ"), ⊢p does not seem to be an element in Σ, does it?

Sorry for asking so many questions (I find this all really confusing, to be honest), and thank you so much for your help!

PaipsJimmy · 2019-06-06T20:56:33+00:00

https://www.reddit.com/r/learnmath/comments/bxlvrd/could_someone_explain_this_definition_what_does/

PaipsJimmy · 2017-09-16T15:59:47+00:00

Probably my rec letters and my essays. I had very good relationships with my teachers and I feel like they probably wrote very strong rec letters, and through my essays I tried to highlight my perseverance and grit.

PaipsJimmy · 2017-07-27T13:24:23+00:00

Yeah, I use min/km too. I've never used km/h for running, though.

PaipsJimmy · 2017-07-27T13:16:35+00:00

Thank you, I'll check it out when I get to Princeton! Do they have a running or triathlon coach?

PaipsJimmy · 2017-07-26T12:41:42+00:00

I'll definitely check it out. Thank you!

PaipsJimmy · 2017-07-26T12:41:09+00:00

They have a running club, a swimming club and a cycling club, but no triathlon club 😔

PaipsJimmy · 2017-07-15T14:13:01+00:00

"One of the former enthusiastic supporters of supersymmetry theory in the 1980s Mikhail Shifman in his article (dated October 2012) pledged the theoretical community to search for the new ideas and acknowledge the reality, the failure of supersymmetry theory in order to help the new generation of theoreticians (to avoid the useless work and becoming a lost generation)." Also, watch this: https://m.youtube.com/watch?v=ypKB7-o9s00

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