Math general

a^2 + b^2 = c^2 always helped me out in physics. Highly useful theorem imo

What are some of the most important consequences of your research? Faster hard-drives that can store more bits? Smaller CPUs?

I know this is a lazy question because I could just figure it out with a couple minutes of googling but on the off chance you have a more interesting answer, shoot.

Lads, I need some help.

I'm applying to the honors math program at school and I need to research the research that a potential advisors is doing so that I am prepared to discuss their work and ask them to be my advisor.

Unfortunately, I have only take one quarter of analysis, and I'm expected to apply after I take another quarter of upper div math.

How am I supposed to understand modern math research? How should I go about researching current maths so that I can ask for an advisor? I'm just sort of lost on what I should be doing.

This was discussed in the previous thread.

Topological superconductors are an example of strongly correlated many-body systems, and these are extremely difficult to study and characterize in general. However if there is a systematic way of studying topological superconductors and their behaviour in general using some mathematical machinery (such as braided fusion categories, link invariants, etc.) then we may be able to extend some of the methodology to other closely related strongly-coupled many-body systems, such as the fractional quantum Hall effect and out-of-equilibrium localisation problems. Holographic techniques via AdS/CFT are also being explored (by a faculty I work with closely, in fact) towards this goal.
In the more practical side topological superconductors can be used to produce high Tc superconductors since the topological excitations (vortices, skyrmions, chiral Cooper pairs, etc.) are believed to be topologically protected from thermal fluctuations. In addition they are also (in principle)m believed to be topologically protected from decoherence as well, so there has been work towards using topological excitations as qubits in quantum computers as well.

How do you guys study from textbooks? Do you just read them because you'll remember everything? Take notes? Make diagrams? Capture the main ideas in bullet points? Something else entirely?

What about exercises? Do you usually find them challenging? Do they take a long time even though they're easy?

And in general, what should I expect of myself? I know I should be the one answering that question, but I don't know how, so I want to see what others expect of themselves and other people in general.

Make memes on the internet.

CFT as in conformal field theory? If so, could you elaborate a bit on what courses are necessary to take in late undergrad/early grad school to tackle quantum field theory later on? Topology, analysis? What are the prerequisites that lead to QFT and TQFT?
I'm very interested from what I've seen so far (my analysis I professor work in statistical field theory) and I'd like to get a headstart.

Take notes of everything. I'm pretty much rewriting huge chunks of the book as I go and try to do all the proofs.
It's the only way it can stay with me along the way. If I just try to browse through a book, I read too fast and forget what it's saying from one page to the next. Or I'll understand what's happening but forget it half an hour later.

Take diligent notes, trying to summarize key points. Also work out the proofs and the examples.

Then do the exercises with the notes as a reference.

And how does your note taking process work? What do you write in your notes and what do you leave out? I usually basically get the gist of things while being as complete as possible (so if the book gives a bit of history on a problem, some motivations and tries to tie things together wither other topics from the book, I just leave that out). But I feel like that's hardly the most effective way, couldn't tell you exactly why though.

All I found in that thread were a bunch of categorists circle jerking and posting anime

Yes CFT is conformal field theory. The most important courses to take for QFT is classical field theory, and supplement with a cursory knowledge of the theory of distributions and Lie groups. Functional analysis and topology also help.
For the physical kind of TQFT (Chern-Simons, WZW, etc.) you will need knowledge of manifolds and differential geometry. For the categorical TQFT you need to know a bit of everything in abstract algebra.

>been with girl for several years
>one of these "im a scientist! science is lief" types
>found out yesterday she's taken only up to "calc 2"
couldnt sleep

Drop her user, and search for the mystical math cutie3.14 girlfriend. Godspeed.

Something alone the lines of Landau/Lifschitz volume 2 perhaps? I don't think such a course exists at my university so I might have to make do with self-studying with the help of friends in physics.
Also, what book on QFT would be indicated for someone coming with a mathematics background as opposed to a physics student? The same books that are popular with physics students?

I write all the definitions in full and try to find examples and counterexamples if there are none in the book. For the theorems, I write the statements in full. If the proofs are routine, I just don't write them, but if they're complicated I try to work them out by myself on draft paper or read the proof, then write a neat and succinct summary in my notes.
Don't be afraid of writing too much.

Does anyone in this thread know of a good Latex editor/writing tool ? I'm going to have to write a paper and I'd rather make it as easy on myself as possible. The only Latex I know is from posting here.

texmaker

You could always use Overleaf to do the formatting of the paper.

LL is great if you want to feel like a retard. But I learned classical field theory and QM from LL as well and I am a retard so you may be able to do it too.
There are a few standard texts on QFT (Schrednicki, Schroeder, Bjorken and Drell, etc.) for physics students, and they all have some level of handwaving. This is inevitable since they all need to cover some form of Feynman diagrams and the functional integrals in their generating functionals are far from rigorously defined. Those books are good if you're fine with that but if you're not then I'd suggest you start with them and then move on to books on non-perturbative approaches in QFT.

good book on lambda calculus ??

>the proof is trivial

Thanks for your help, do you have a recommendation for a non-pertubative approach to QFT?

Strocchi, Swieca, Streater, Wightman.

I was supposed to do an independent study of modular forms with a professor next quarter, but I've lost all drive and passion for mathematics. I feel like up until now I've given up the most important things in life in a pursuit of absolute truth. It's similar to the way Grothendieck abandoned math because he felt "spiritually impoverished". (Of course, I'm nowhere near as driven or intelligent as he was.) I'm wondering if anyone else knows this feel.

A clear goal helps to remotivate. I've been close to giving up a lot of times, but always just having some concrete thing to achieve has always given me back my will to study more.

i know that feel

Thank you so much, you helped me more than you probably think. Here's a cute Wakaba for you.

What is this warm fuzzy feeling inside me?

>strongly correlated many-body systems
>protected from thermal fluctuations
>(believed to be) protected from decoherence as well

Thank you for taking the time to respond. I'm sure you have better things to do than answer our trivial questions. Much appreciated.

Texmaker, like said

I just started using LaTeX and these were also helpful to get started.

youtube.com/watch?v=rT5kIQ-JHhw
tex.stackexchange.com/

I personally use TeXworks. It's flexible but more bare-boned than other editors. I'm also looking into using emacs for typesetting.
>I'm sure you have better things to do than answer our trivial questions
I wrote that up within minutes because I've worked so closely with it. It's no sweat.

Math Major Physics Minor here,

Is this decision a terrible mistake?

Is there any supplementary reading I should be taking in order to learn faster? I'm just taking Calc 1 now and feel like I get all the material and want to learn more.

I am reading pic related.

No one has ever read it, the most anyone reads of ancient geometry is Elements. :(

>reading non-existent books
next level

Pic

numberphile's new video

very humble guy, i like him :) no homo

youtube.com/watch?v=MXJ-zpJeY3E&feature=youtu.be

Currently reading elementary number theory by David Burton, really enjoying it so far...

Just make sure you get your integrations and derivations down for now. Calc 2 and 3 all rely on you really knowing this shit. Is there a reason you're taking physics as a minor? I'd consider maybe cs instead if you're not completely sure.

can second - i took thermophysics for giggles and it'd have majorly helped to be fluent in manipulating derivatives, integrals, doing derivations of that sort

All I ever needed in my MIT physics class was y=mx+b, where'd you learn that one?

Because my school doesn't offer a Physics major and I do not have the capability to transfer. (For my own sanity, finances, and due to my gpa.)

I just really enjoy physics.

I think I have to take a few CSCI classes for my math degree, actually. Should be good

Yeah a few friends of mine actually ended up dropping thermo because of that.
If you enjoy it then go for it.

You're not going to understand their research. They're not going to expect you to.

>Math major
>Taking calc 1
Isn't it a bit early to have settled on a major?

could use a bita help with M_{e

I'm in my second year and had to declare something

How does someone make it to second year before taking calc 1 and still get enrolled into a math major and physics minor? What did you do in first year?

General education and precalculus

Your pic reminded me just how little I remember from linear algebra.

I seriously hope you had a fucking wild year of partying.

mostly LAN parties

oof

holy shit,nice time get

You made me get all introspective and realize I basically did nothing but play video games my freshman year. Wew lad im depressed now

Find [math]U[/math] such that [math]U^{T}\mathcal{D}U = \mathcal{B}[/math] then calculate [math]U^{T}TU[/math].

Its good to reflect man

Il faut faire des maths si tu veux faire des maths pures, donc inscris toi au cours par correspondance de l3 de math de l'upmc...

How do I learn Inter-Universal Teichmuller Theory?

maths.nottingham.ac.uk/personal/ibf/notesoniut.pdf
>3. STUDYING IUT AND RELATED ASPECTS

>Teenage math autists bow to Mochizuki
>In contact with frobenoids
>Rumoured to possess mathematical abilities
>Solved the ABC conjecture with an iron, but indecipherable proof
>Direct descendant of Minoru Mochizuki
>Will bankroll the first cities in between universes (Mochizukugrad will be be the first city)
>Owns basically every IUT research facility on Earth
>First designer babies will be Mochizuki Babies
>Said to have 200+ IQ
>Ancient Indian scriptures tell of one angel who will descend upon the Earth and will bring an era of enlightenment and unprecedented technological progress with them
>This is Mochizuki
>Owns Femtobot R&D labs around the world
>You likely have Shinichibots inside you right now
>In regular communication with the Archangel Grothendieck, forwarding the proofs of God to the book
>Learned fluent Algebraic Geometry in under a week
>Invented Inter-Universal Teichmuller Theory, a complex field of mathematics which only he can comprehend fully
>This ingenious development proved to be the last piece in the puzzle of time travel
>This lead to the design and construction of the first time machine through a joint effort between himself, Lockheed and the CIA
>Nation states entrust their proof reserves with the twins. There are no proofs in Ft. Knox, only Ft. Mochizuki

Oh fuggg....It's true...the prophecy's come true...

Fucking kek

imo, coming in to a non-introductory physics class from a pure math perspective leaves you scratching your head at the derivations: for every 1 new symbol that's mentioned, there's like 5 ways it can be written in terms of 10 others. having your head on with the dimensional meaning of everything you're doing is important and if that guy enjoys physics and has interest/background in it then he'll steer clear of most of those pitfalls. but otherwise, without some physical perspective, doing something like deriving say the density of energy function can seem like totally arbitrary manipulations of symbols-- almost like writing the theorem after writing its proof.

Okay Veeky Forums, Math plebe here but I feel like I just got jipped on my Calculus 1 Midterm. I got asked

"Define, using limits, what it means for a function 'g' to be continuous at 'a'."

So I read define and saw it as "Give me a verbal answer as to how to define continuity at g." So I wrote something along the lines of "The limits as you approach 'a' from either side are the same and g(a) is defined." But then I read "using limits" and so I wrote out the formulaic version of lim x->a- g(x) = lim x->a+ g(x) and where g(x) is defined.

Am I stupidly dense or does this feel like the question is worded weird?

I can do the maths just fine for calculating continuity and derivations and all that jazz, but it's hard to answer a question when I don't know what the question is asking. Does that make any sense? I couldn't tell if he wanted a verbal answer or a formulaic answer and I'm not sure if it's because of my stupidity or the way the question was written.

I am not smart enough to know how stupid I am so I don't need to be railed on about "omg this problem is so simple." Thanks.

It sounds like you just can't handle reading, dude. That was a perfectly reasonably worded question and then you started adding more words to it.

Okay I'm probably just autistic, thanks!

Since I feel like actually being helpful, a problem with undergrads (which you'll grow out of) is this weird discomfort with notation. The notation is totally irrelevant. The equations say the exact same thing you could say in words, and oftentimes people will use words. We like equations because they fit those long sentences into a compact form.

I didn't particularly mind the notation, mind. I just literally didn't understand which of the two he was asking for.

But in general, I should just go with equations because they're concise? Cool deal, thanks user.

>the vectors have arrows on top of them
is this high school LA?

what the fuck do you do? bold font them?
sounds like more effort than drawing a line on paper

You use letters. Like this:
Let v be in R^n (or whatever you say in English for it is an element of it) Then v is a vector in your sense

I guess I'll just do my best to understand the general idea of what they're trying to do?

I just don't want to look like an unprepared doofus when I ask someone to be my advisor

I mean at least from my personal experience my calculus profs all referenced what we were doing to physics.

Honestly, that's probably out of reach. They won't think you're an idiot. You should talk about what you've learned and what excited you most, and then they can describe some facet of what they like that relates.

>researching
Nil and void, like my soul
>studying
Abstract Algebra from a Category Theoretical perspective
>book recommendations
Algebra: Chapter 0, understandable to undergrads who aren't brainlets yet contains lots of interesting material

[math] \int_0^\infty x^{S-1}e^{-A\,x}\dfrac{1-(Z\,e^{-x})^M}{1-(Z\,e^{-x})}{\mathrm d}x = \Gamma(S)\sum_{n=0}^{M-1}\, \dfrac{Z^n}{(n+A)^s} [/math]

That's a cool identity but check this bad boy out.

[math]3\sum_{n=1}^\infty \frac{1}{4^n}=1[/math]

Slow week.
Anybody else smokes?

i'm a retard

[math](n-1)\sum_{k=1}^\infty \frac{1}{n^k}=1[/math]

[math] \dfrac{1}{1-q} = \sum_{k=0}^{\infty} q^k [/math]

eh?
Yes, I'm jelly.
You made me jelly. Mad jelly.
I'm gonna show you

[math] [n]_q := \sum_{k=0}^{n-1} q^k [/math]

[math] [n]_1 := \sum_{k=0}^{n-1} 1 = n [/math]

[math] \dfrac{1}{1-q} \int f(x) d_q x := x \sum_{k=0}^{\infty} q^k f(q^k x) [/math]

[math] \int x^m d_q x = \dfrac{x^{m+1}}{[m]_q} [/math]

[math] \left(\dfrac{d}{dx}\right)_q f(x) := \dfrac{f(qx)-f(x)}{qx-x} [/math]

[math] \left(\dfrac{d}{dx}\right)_q \, x^m = [m]_q\, x^{m-1} [/math]

[math] e_q(x) = \sum_{n=0}^\infty \dfrac{x^n}{[n]_q!} [/math]

[math] \left(\dfrac{d}{dx}\right)_q \, e_q(x) = e_q(x) [/math]

Alright, thanks. I'll do my best. Hopefully I get an interesting project and a cool advisor

I fairly intensely disliked Aluffi when I tried to read it
I don't know if people here genuinely like it or if it's just memed because muh categories

You're not learning "Abstract Algebra from a Category Theoretical perspective", you're learning foundational algebra with occasional breaks to rephrase everything in very (very) primitive category language which serves no purpose other than ramping up the pretension for 3/4 of the book

Not to mention his writing style is aids

*pushes glasses up*

Nice try kid...

Did you know that [math]\sum_{n=1}^\infty \frac{1}{n^x}[/math] converges when [math]x \geq \sqrt2[/math]?

...that's what I thought.

*unzips notebook*

For all functions [math] f [math],

[math] \int_{- \sqrt{2} }^\sqrt{2} f(x^2) \dfrac{1}{1 + {\mathrm e}^{x^2\sin(x)}}\,{\mathrm d}x = \int_0^\sqrt{2} f(x^2) \,{\mathrm d}x [/math]

For all functions [math] f [/math],

[math] \int_{- \sqrt{2} }^\sqrt{2} f(x^2) \dfrac{1}{1 + {\mathrm e}^{x^2\sin(x)}}\,{\mathrm d}x = \int_0^\sqrt{2} f(x^2) \,{\mathrm d}x [/math]

I need a good elementary algebra book, but with more elaborated set of exercises.
Schaum and Khan Academy are easy

Brainlet here
I was exploring different things you can do with absolute values when I found out this problem

Does the following evaluate to 1,-1, both, or undefined?

[eqn]\lim_{k \to \infty} f(x) = \frac{|sin(kx)|}{sin(kx)}[/eqn]

How hard do you want?

Andreescu has at least one problem book for everything you could do within the bounds of high school math to know and they're mostly very well chosen. But they're tough.

If you just want not baby tier it's probably enough to just work through that Lang meme book

Go through Gelfand or something similar.

It's not defined. A limit cannot evaluate to "both"; limits are always unique. There's either one or none.

Roughly speaking the problem is that no matter how big k gets, it doesn't help the values of f get any closer to each other; f never stops oscillating between -1 and 1. Since your values aren't approaching any one number, there's no limit.