Complex Analysis

>compelx analysis
>not taking Quaternionic analysis

fucking beta cuck brainlets

How the fuck does one even take a derivative there when multiplication is not commutative?

asking a question quick as it is related to the thread.

I'm in a predicament, I am unable to take real analysis next semester as I have another required course I need to take then when it is offered for my degree. The next semester, real analysis isn't offered but complex analysis is. Will I get raped if I take complex analysis before real analysis? Do you even need to take real analysis before complex?

[math]\left( \mathbf C,\, +,\, \times,\, \left| \cdot \right|,\, \tau \,=\, \left\{ A \,\subset\, \mathbf C \mid \forall z\,\in\, A,\, \exists \varepsilon \,>\, 0,\, B_\varepsilon \left( z \right) \,\subset\, A \right\},\, \bigcap_{\begin{array}{c} A \,\sigma \text{-algebra of}\, \mathbf C \\ \tau \,\subset\, A \end{array}} A,\, \ell \right)[/math]-analysis is what happens when you take [math]\left( \mathbf R,\, +,\, \times,\, \leqslant,\, \left| \cdot \right|,\, \tau \,=\, \left\{ A \,\subset\, \mathbf R \mid \forall x\,\in\, A,\, \exists \varepsilon \,>\, 0,\, \left] x \,-\, \varepsilon,\, x \,+\, \varepsilon\right[ \,\subset\, A \right\},\, \bigcap_{\begin{array}{c} A \,\sigma \text{-algebra of}\, \mathbf R \\ \tau \,\subset\, A \end{array}} A,\, \ell \right)[/math]-analysis and add autism to it.

I don't think you do. Haven't taken either, but I have friends that have taken complex without taking real and it didn't sound like what you are worried about is a thing. Iv looked into the kinds of things you would learn in both and it didn't look like they rely on each other.

are you me? have this exact problem at ucsb

Thanks for the input, I'm planning on talking to the professor actually teaching the class when I get back on campus but just wanted some insight so I could plan ahead

Yeah I'm also graduating so I won't have the chance to take it again, shit sucks

>Will I get raped if I take complex analysis before real analysis? Do you even need to take real analysis before complex?
Yes to both.
In complex analysis classes it is assumed that you know how to do analysis and have maturity on it. You can't just go there like that. Everything will seem weird and unmotivated.

this joke wasn't even funny the first time you tried to force it

Scouse?

complex analysis is just multivariable calculus with some stricter definitions
for example, complex differentiation covers multi variable differentiation, but filters out a lot of differentiable functions with the cauchy equation requirements

Your need to feel superior does not obviate the validity of the intermediate rejection by the poster, who I am not, of the still-earlier poster's absurdity.

You've got the lexicon down, now all you need to do is work on sentence structure.

You on theoretical physics? How difficult is "fibred spaces and gauge fields", do you think i can take it in 3rd year BSc, i was offered few classes from MSc and can't decide.

I took complex analysis after real analysis, and no, there isn't any significant overlap in the two courses (in introductory courses at least). However, the arguments used, as the other poster suggested, were often reminiscent of arguments used in real analysis (open sets/balls, epsilon-delta stuff, etc), and often, the lecturer would say "the proof is identical to the real case, QED", which I assume if you didn't take that class, you wouldn't be very satisfied with it.

What I would suggest you do is at least read the first couple of chapters and do the exercises of any real analysis book, like Tao or Pugh. You can skip some parts like constructions of naturals or reals, etc, but at least read through it to understand what's going on.
For example, for Tao Analysis I, try chapters 3,5,6,7,9 (10,11 if you have time too)

Yeah, same guy, don't know how you knew that, but whatever. I was in a somewhat similar situation as you, during my 2nd year I took the grad level topology and smooth manifolds courses so I decided on studying gauge theory my 3rd year and was successful (I mention this as a proof of concept, I'm not amazingly gifted but I did work hard to gain the background material to start). If you're referring to Schuller's videos
youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic
then the material presented here is definitely something a 3rd year can manage, for the most part he goes just in depth enough for a physicist and doesn't assume too much math overhead, though this focuses more on the side of developing the mathematics used in gauge theory than gauge theory itself. If you like I can recommend some books on the subject (or some videos) that can help you learn the topic and/or it's background material. What is your background exactly? It kind of help the me with what I should recommend. But yes a 3rd year is capable of a first course in gauge theory, a lot of the more technical details would come later though, typically during your Phd or masters.

>he doesn't know what a forced meme is
t. wildberger flat-earther

Nice, i hope i have enough background now though i've heard it's one of the more difficult courses. As for my background, i had was home-schooled during highschool and knew significant amount of math as taught on matfyz so i was offered MSc math courses since 2nd semester. But i mostly get classes from math programme, gauge fields are my first MSc class from theoretical physics, i went through NMAG401, NMAG409 and NMAG448 this year for example (A,A,B). If i were to choose between NMAG454 and NTMF022, for the purpose of string theory, which do you think would be better? I would certainly like some good book on the subject, if it supplements or even replaces the reference literature of the course. I went to one of the PhD seminars on string theory (this particular one was on SYM) in 2nd year and unfortunately couldn't keep up, i was missing a lot of the physical and some mathematical background. Basically i want to get into string theory research as soon as i can.

Looked through the course materials for each class, by and by I'd say take NTMF022 simply due to the fact that a proper understanding of gauge theory will be far more useful (you haven't listed what physics you know, I'm guess qft since its pretty core to gauge theory and building up to string theory) and there are various supplements to learn the mathematics (a set of lectures I am found of are Ooguri's lectures).
youtube.com/playlist?list=PL7aXC0jU4Qk7K778c5nmgQImd6VKKFMYu
He covers a lot of what you're gonna want from the mathematics side (always with an eye towards physics though) so you could probably just watch those to gain some bearing with the mathematics needed for string theory. Some books that I feel cover the topic of gauge theory and/or the mathematics behind it well without assuming too much are Baez, Naber (two volumes), Nakahara, Jost, Westenholz, Nash (two volumes), Choquet-Bruhat (two volumes), Grockeler, Weinberg (3 volumes), Aitchison (two volumes), Padmanabhan. Katz also has a pretty accessible book into tqft's and string theory, clay math also has two mirror symmetry monographs that are quite nice, plus there's Deligne's two texts. All of these are at varying levels of difficulty and style so pick a few you like, though be sure to have the necessary physics/math prerequisites, research is a lot of fun but if you fuck up your fundamentals then it'll leave you an ultimately weaker researcher.

Thank you a lot, user. My physics is lacking, i've only been through Landau and two other russian books about QFT specifically, so i'd better catch up on physics and slow down with math courses for now.

Have you been through all ten volumes of Landau? If so that'd be give you more physics knowledge that than the typical 1st year grad student in physics.

because of my complex analysis course i can evaluate integrals on the real line in minutes that would be impossible/take you hours

I can evaluate laplace transforms you couldln't even look at

it literally applies to everything, its like learning what calculus SHOULD be.

Only up to vol. 5, i feel like i'm far from grad students in physics. I want to do the rest, but don't have any free time at all. The two hours i don't study, i go to gym. The only free time apart from that is when i'm on a toilet and i usually waste it on Veeky Forums. I want to finish Landau when i'm done with my thesis, or before depending on difficulty. Which book would you highlight for string theory? Is Motl's list accurate?

I looked at Motl's list and he gets most of the usual reads down, I'd suggest Zwiebach's book first if only for the fact that you seem to have not taken a class in particle physics and qft yet and it might help solidify intuitions about the subject, plus the mathematical overhead for other string books is pretty big, I'm pretty sure most math grad students couldn't read one unless they were already working in geometry. It's also an easy read so it should fit better in you schedule. If you find it too easy I'd suggest Dine as it connects particle physics to string theory and it's many applications or Schwartz and Becker for more modern topics. Polchinski and Green are both also worth looking at, but maybe not to learn from for the first time as they aren't the mot pedagogical books imo, they do contain other material not covered in the other books. To cover the math for string theory this lecture series should get you close to where you need to be
youtube.com/playlist?list=PL7aXC0jU4Qk7K778c5nmgQImd6VKKFMYu
Hell, that's what the lectures were made for

Thanks again for the help, i've ordered Naber and Zwiebach and i'll watch the lectures whenever i can (is there a set of excercises with each one?). You seem to know a lot about it, are you a PhD here?

I took it in undergrad last semester using that text. Great class, but that text is shit.

If you're doing statistics outside of engineering and physics, you won't get much out of it but it is usually fairly rigorous. Learning how to prove problems in complex can help you see things more clearly when you're coding, or w/e in your job.

The lectures have short problems given to the students. I hope you checked out the contents of each book before ordering them, you do know there are websites like lib gen where you can basically download them all for free, right (hell some can be found via a google search)?
cquest-studygroup.wikispaces.com/file/view/A First Course in String Theory.pdf
Not saying it's the right the thing to do, more so that texts are expensive and you should only get the ones that'll be really useful for you so it might be useful to know what's good for you prior to buying. I'm actually going into my 4th year, the reason I know a decent amount of qft/particle physics is that I work in a group that studies lattice gauge theory so it was mandatory to learn it. As for knowing some string theory, really I'm just fascinated by the amount of new tools and ideas that come from the subject and feel that alone makes it worth studying (I actually started from Zweibach and katz and then moved onto Dine and the Mirror symmetry monograph. I've pursued the other string texts I mentioned but never had a great deal of time to really get into the meat of some of them, especially Deligne's). I should also mention some nice advanced topics in qft/string theory lectures available on youtube.
static.ias.edu/pitp/2015/schedule.html
static.ias.edu/pitp/2014/schedule.html
sns.ias.edu/pitp2/2010files/schedule2010_v2.html
sns.ias.edu/pitp2/2008files/schedule2008_v2.html

en.wikipedia.org/wiki/Quaternionic_analysis#The_G.C3.A2teaux_derivative_for_quaternions

Ah, almost forgot the some of the best lecture videos, good old perimeter
perimeterinstitute.ca/training/perimeter-scholars-international/psi-lectures
They got every kind of field of theoretical physics you could want, these were basically what helped me get through a lot of the material.