/sci/ - Science & Math

If I want to work in a bank/insurance company with a math degree, what should I study/pursue?

>>6342426
Do you have a small penis?

Also, I should mention a few things to get some preliminary questions out of the way.

My research has primarily been concerned with geometric structures on low-dimensional manifolds, though recently the types of questions I've been looking at have been bleeding over into other, related fields.

I think that math is discovered rather than invented, though I'll admit I don't really give too much of a fuck about foundational/philosophy of math stuff so what I say on topics like these will probably not be too terribly enlightened.

Are you getting $300k starting at any job you want?

>>6342447

>If I want to work in a bank/insurance company with a math degree, what should I study/pursue?

Ultimately it depends on what exactly you want to do. I have some friends who went directly into actuarial work from undergrad... as I recall, there were a few 400 level actuarial math courses offered as part of my undergrad program geared toward those actuary exams.

If you want to be a quant, then typically a PhD in Math or CS is required and it may be helpful if your research/thesis was in a related field, though I knew a guy who was an algebraic geometer who grew tired of academia and went to be a quant at a firm in Chicago with relative ease, and they didn't really care that his research was irrelevant to the job.

Both jobs pay well (my friend started out with ~250k, with much more in bonuses), so if you care about the ducats and don't mind soul-crushingly boring (to me, at least) work, then it's great.

>>6342426

What was your hardest core class?

The algebra sequence here is a pain in the ass for me.

>>6342474

>What was your hardest core class?

I didn't find any of the core classes that I took as grad or undergrad to be too difficult, but some of the topics courses for which there were actually grades were brutal.

The hardest course that I took for which I actually received a bona fide grade was a Calculus of Variations grad course I took as an undergrad. The exams were fucking brutal.

>>6342474

Well, now that I think about it, if your definition of "core" is simply "a course that has an associated qualifying exam", then the hardest core course I took was a graduate ODE sequence.

What opportunities are there for a math PhD asides from quant work or the rare teaching position?

>>6342470
>ducats

you mean you're not paid in pounds of flesh? ;_;

>>6342426
What branch of mathematics is your PhD related to?

What will you do later (inb4 subway)?

>>6342511

>What opportunities are there for a math PhD asides from quant work or the rare teaching position?

If you're the authoritarian sort and don't mind being the embodiment of everything that is terrible about the current state of America, then you could work for the NSA or DoD.

If you're slightly less terrible you could work for Lockheed Martin or Boeing.

There's also plenty of generic high tech industry jobs that you could get with a Math or any other hard science PhD.

>>6342523

>What branch of mathematics is your PhD related to?

See >>6342457

I can go more into detail if you want.

>What will you do later (inb4 subway)?

I will continue to do what I've been doing already for years: research.

I'm currently a post-doc, will eventually seek a tenure-track position at a good university.

>>6342426
List of preferred intro books?
List of just generally good books?

Why doesn't finite differences get more attention? People assume that analysis only covers continuous structures when it also can be applied to discrete structures ie generating functions

Are you ever interested in physical applications of your research in geometric structures on low-dimensional manifolds, or are you content to leave such thoughts to the scientists?
Also, what are manifolds? My math education extends only to diff eq and linear algebra, but I'd like to know what goes on in your niche of the far reaches math.

>>6342521
>If you're the authoritarian sort and don't mind being the embodiment of everything that is terrible about the current state of America, then you could work for the NSA or DoD.

you are an ok guy, anon.

>>6342532

>List of preferred intro books?
>List of just generally good books?

Hatcher's Algebraic Topology is probably the best intro book on the subject. Milnor's Morse Theory is probably one of the overall best math texts ever written. Gromov's Partial Differential Relations is amazing, but almost unreadable. Sharpe's Differential Geometry is a great exposition of the work of Cartan and Ehresmann, and a great overall book for someone interested in geometric structures (even if you're coming to the subject as a physicist). Bridson and Haefliger's Metric Spaces of Non-positive Curvature is the one-in-all reference for the subject. O'Neill's Semi-Riemannian Geometry with Applications to Relativity holds a soft spot in my heart because it was my first proper introduction to differential geometry, and is of interest to the mathematician wanting to learn more about theoretical physics since there are several chapters devoted to relativity calculations.

>>6342555
Thank you anon. This list seems really sincere.

>>6342542

Well, combinatorial arguments are extremely prevalent in more recent research in theoretical physics (at least the part of it that I'm knowledgeable in).

See Kontsevich's solution to the Witten conjecture: it boils down to a counting argument in calculating matrix Airy integrals on ribbon graphs, which reduces almost entirely to the underlying combinatorial structure.

In fact, these arguments are so prevalent that a theoretical physicist friend of mine jokes that the universe is not a manifold, but a graph. (My bet is on orbifold)

>>6342426
I'm researching number theory problems for many years and want to publish an issue that contains some good ideas.

Also I'm paranoid and afraid of plagiarism.

What is the best safe way to protect my authorship?

>>6342535
Thanks. Have you run into cases when your supervisor / examination committee had absolutely no clue about the correctness of your results?

>>6342546

>Are you ever interested in physical applications of your research in geometric structures on low-dimensional manifolds, or are you content to leave such thoughts to the scientists?

If I'm allowed to cheat and by "physical" assume you literally mean "applications to physics", then the answer is Yes.

I am always excited to learn of some connection between these geometric structure arguments and theoretical physics, and it happens that there is a massive interface between my research and theoretical physics.

When I consider the original motivation for study of these objects, it is definitely baffling and more than a little mysterious that these mathematical concepts which are "dreamed up" essentially "out of nowhere" actually fit into this theoretical physics framework in describing the universe.

I recommend the essay The Unreasonable Effectiveness of Mathematics in the Natural Sciences, which describes exactly this phenomenon.

>>6342554

>you are an ok guy, anon.

Gotta fight the power, man.

Is the tensor product of sigma-algebras an actual tensor product in a similar sense to the one you take between modules/etc..., ie it verifies a similar universal property with some adjustments or something?

>>6342521
>If you want a comfortable and predictable job that won't allow you to experiment or do anything new, then you could work for the NSA or DoD

>>6342575

The arxiv is good for exactly that.

Also, go to conferences, give talks, put your stamp of ownership on your research through this.

>>6342583

>Have you run into cases when your supervisor / examination committee had absolutely no clue about the correctness of your results?

Hah, well one person on my defense committee had no idea what I was talking about, another was only marginally familiar with my area of research, but my adviser and another person on the committee are experts in the field.

If your adviser does his/her job correctly, the defense should essentially be a formality, since it should be up to your adviser to know whether or not your thesis is PhD worthy.

>>6342588

Consult the Book of Armaments... err, I mean Lang's Algebra.

I would go grab it off my bookshelf myself but I'm afraid I would drop it and crush my cat.

I'm taking a degree in biochemistry, but I don't want to spend the rest of my life in that field. I've been thinking of taking a degree in maths after I graduate (I can talk it over with the maths department admission staff - it's a good university) should I do it? I want to work with the abstract.

>>6342588

Actually now that I've thought about it and remembered some analysis, I'm not sure it has a similar universal property.

>>6342608
Also, I realise I'm being vague about my interest in the subject. Let's just say that I'm definitely interested in it.

>>6342608


You're going to have to be pretty motivated to make that switch, but it's doable. You could sit in on some of the core sequences (algebra and analysis mostly) at your university to prepare.

>>6342618
Okay, but how likely am I to become as accomplished as you? I'll be 3-4 years behind my peers. I'll start at age 21-22.

>>6342608

I should mention, I know several people who have switched from math undergrad degrees to graduate degrees in various fields, but the only folks I know who did something other than math during undergrad and switched into a math program were from computer science.

Still, if that's where your interests lie, then you should go for it.

Alright I'm gonna go for it. Is this degree worth what it pays and offers as far as benefits (including insurance) goes?

>>6342597
>The arxiv is good for exactly that.
May I link to arxiv issue like any other issue in solid math journals writing the dissertation? Has arxiv issue the same "power"?

>>6342597
>Hah, well one person on my defense...
Thanks, I'm finishing a PhD, so this is good news.

>tfw adviser tries (and fails) to disprove your theorem by a gorillion pathological numerical examples, because he's too lazy to understand the proof.

>>6342623

3-4 years is irrelevant in the grand scheme of things, and it's not like you're in a race or something. Assuming you won't starve while studying, 3-4 years in order to be happier with your lifelong career is a bargain.

Also, there's no need to think about how "successful" of a mathematician you are (defining a metric that measures such a thing is troublesome), rather (to paraphrase Feynman) just keep learning and learning until you've learned something no one else has learned. That's doing research, and that's what a mathematician does.

>>6342645
That's... inspiring.

Sometimes I feel like I'm the only person who thinks I can do it. Thank you very much.

>>6342642

At my university, one of the people on your committee has to be from outside the department, so the person on my committee that didn't know what I was saying was a physics guy. Other than the two experts, the other guy was chosen because he knew more than anyone else in the department about my research, which turned out to be not so much since he was more on the algebraic side of things.

will the research you're currently conducting ever be credited for a contribution to the invention of a real world application? how much money do you make?

Alright guys, I'm out for a bit to grab some food and such.

I'll check back in on the thread and answer any questions, assuming it's still alive when I get back.

>>6342660
invention is the wrong word, more like conception

Ok, level with me.
What manner of hell did you have to walk through to get that PhD?

I got a question about The Two Children problem.

When we say that at least one of the two children is a boy, the probability of both of them being boys is 1/3.

Now let's say that we are at a friend's house. We know that they have two children. After a while, one of the two children come to sit with us, and that children is a boy. Now is this the same case as before, or is the probability 1/2 here?

>>6342426

Hey OP, i have a few questions.

Can you tell us in detail what happened between slightly before you got accepted to pursue PhD? At top universities you have to do something extraordinary or just achieve something in some field to continue that in a research as a PhD. What is your story? Did you know what specific topic will you research or you just had an interest in a field and you searched for something interesting?

How hard is research? I mean producing Results. How the people handle it around you? I have a little insecurity "ok i'm smart but what if not enough?" i'm not at the top of the class like i don't always understand stuff very fast like a few people. What do you think, Math PhD requires to be really one of the bests?

First year math PhD here, interested in arithmetic geometry.

I would love if you could explain to me, in broad strokes, why is 3 and 4 the dimensions of interest? I have some vague notion that in higher dimensional situations we have enough room to have a successful theory of surgery which, for some reason, often allows us to solve problems there much easier.

>>6342689

Oh, and also, if your'e comfortable, would you mind telling us which institution you graduated from?

>>6342426
Dear OP, has a 30 years old lone amateur any hazzard to make career in mathematics?

>>6342426
what is your favorite equation

How do I into K-theory?

>>6342521
>If you're the authoritarian sort and don't mind being the embodiment of everything that is terrible about the current state of America, then you could work for the NSA or DoD.

>not supporting your country

bravery. ;_;

1. post a picture of your degree.
2. what is your field of study?
3. what undergrad/grad school did you go to?
4. what was your phd years like?
5. what was your thesis defense like? go into detail.
6. who was your advisor?
7. what do you do for work now?
8. were you a child prodigy? did math come naturally to you?
9. how do you study mathematics?
10. how old are you?

What's your IQ?

>>6342732

Not OP. K-theory is a very broad subject. Which type of K-theory?

>>6342740

Not OP. 6 is a little too personal--it wouldn't be hard to identify the OP's identity with that.

>>6342741
topological

>>6342749

Not OP again. I would very much suggest the book by Efton Park. It is certainly not the pinnacle of K-theory (it's all pre-Quillen), but gives an excellent introduction to the subject, while introducing many of the prerequisite notions (that you may or may not already have).

>>6342745
Who cares?

Does OP think we will solve any of the 6 millennium problems soon?

>>6342743
This.
Pls tell us your IQ.
I'm going to guess 135.

Consider a symmetric random walk X of length N*M on an NxM grid. Is there an explicit formula for the probability that X is self-avoiding?

Hey OP, third year here.

The only math that has piqued my interest is general Topology (Separability axioms, Urysohn's Lemma, etc). Does it get better later on? or will I be forced into either Algebraic Topology or Differential Topology? (I already did an introduction to Homotopy theory, not a big fan of it) I'm doing Differential Geometry and it ain't bad, and I'm assuming it's a step towards Differential Topology.

>>6342761
thanks

>>6342659
OP, is there anything you wish you had done or started doing earlier as a grad student?

How many years did it take you to get your PhD?

>>6342426
Hey OP!
1. Should I study/remember every proof we have?
2. Does doing a PhD basically mean you are consciously turning down a higher salary and a more free life in favor of dedicating your life to science?
3. Studying tricks&tips?
4. How long do you study/day, days/week?
5. What was greatest discovery that boosted your studies?

What's a triple integral and why do we need it?

Now that you got your PhD, will you finally get a job and stop shitposting on /sci/?

what field of mathematics is necessarily the trickiest?

By which I mean, if we imagine that a teacher teaching mathematics will usually try to teach mathematics by breaking a proof or construction into a number of smaller, easier to understand steps, where a nicer teacher might break an explanation into a greater number of smaller steps and a tougher teacher might give a more sparse explanation with fewer , large steps that are more difficult to understand, then which field of mathematics do you think necessarily has the largest steps.

i.e. which field of mathematics, if you had to try and explain theorems and their proofs and applications in as many small, easy to understand steps as possible, would you end up with some ideas or steps that are simply irreducible and can't be explained in any simpler terms and you either get it or you don't?

>>6342779

Not OP. I was like you once--I wanted to be a set-theoretic topologist. Then I wanted to be a group theorist. Then I wanted to be a functional analyst. Now I do algebraic geometry. Just try things new, I guarantee you that you will find other things just as interesting (hopefully more so) than topology.

Also, when you say an introduction to homotopy theory, do you mean the end of Munkres? :)

>>6342793
for computing the volume of your coffin for when you finally fucking KILL YOURSELF.

>>6342802
dude, start your own thread. nobody cares about you here.

>>6342795
this is a terrible question and you should feel bad for even asking it.

doubly so for doing so in a math thread. jesus christ can you get any more ill-posed, ill-defined?

>>6342807

Yeah, you're right. Sorry about that!

I hope the thread goes well.

Did you participate in math competitions like IMO or Putnam?
What is your opinion on them? Are they a good indicator of mathematical talent or are they just arbitrary nonsense problems?

>>6342802

Yep, the end of Munkres and a few chapters of Kosniowski's Algebraic Topology.
Anyway thanks for the advice. I'm taking Set Theory next year so I'll see if I enjoy it.

How do you feel about "/sci/ - science & math"? If you were to dictate the content of the board and the behaviour of its posters, what would you change?

Which of the following do you or don't you accept/believe?

- the axiom of choice
- P=NP
- "imaginary" numers
- 0.999... = 1

Do you identify as a nerd or a geek?

did you go through hell to get your PhD or was it an enjoyable journey?

How many digits of pi does a math PhD have to have memorized?

>>6342843

Most important question in this thread.

Is getting a PhD in math harder or easier than a PhD in physics?

Can you drop some mathy buzzwords I could use to impress the plebs?

Do you know calculus?

Is it true that to get a PhD you must choose between math and gf? can't you do both?

>>6342874
Not OP, but as i see on PhD-s it's the opposite, everyone has a gf and usually they are scientist too. Pretty cool,

Please explain partial derivatives to me.

thnx in advance

>>6342426
Is 2+2?

What are the newest cutting edge research theories on division by zero? Are we coming closer to solving the ancient mystery?

>>6342874

You know what's interesting? I've noticed that despite the fact that the world is full of unsavory, unappealing people, the vast majority of adults I come in contact with are married, or have been married.

Are you actualy going to contribute something useful to society? You are obviously gifted, you can do something not many other people can. Please don't wast it at some shit hole like an investment bank

>>6342426
I have a couple of questions:
What books can you recommend on the following subjects (ranging from introductory to all the way up):

>Analysis
>Linear Algebra

a nice answer would be something like this for instance:
Analysis: Spivak Calculus -> Baby Rudin -> Royden -> Big Rudin
But recommend anything you genuinely consider worth recommending! I'm reasonably smart, btw.

After those two subjects I have to deal with in uni as a physicist, is there anything else you think is a great read and worth checking out? I can find interest for everything.

That said, I'm very interested in geomtry - all kinds of geometry. Especially manifolds seem interesting, but I'm still wearing babby shoes. Anything you can recommend on that?

Thanks a lot <3

What is your stance on the philosophy of mathematics?
In your opinion, what is the ontological status of mathematical entities?

I'm a social science major and I'm struggling with precalc. ;(

What can I do? Can you recommend a book on precalc?

My main problem are logarithms. When I see a logarithm, I am too scared to attempt solving the equation.

>>6342901
>social science

please get the fuck out and never come back you stupid fuck

>>6342808
what's ill defined?

no need to get butthurt, kid

Is 155 IQ good enough for math? Or should I stick with something less challenging like e.g. physics?

>>6342907
>...something less challenging like e.g. physics.
Different anon, but I don't think you have to worry about it.

>>6342904
Hey, it's still science. My only problem is the math.

Is 37.256 a nice number? If that number appeared in the solution to an equation, would it make you feel good, bad, or indifferent?

>>6342907
>like e.g.

also
>pic related

and online IQ tests don't count

>>6342917
>Hey, it's still science.
No, it's not. Get the fuck out.

>>6342924
>No, it's not.
lolwut? Social SCIENCE has science in its name. How can you say it isn't science?

>>6342924
I never mentioned online IQ tests. Please work on your reading comprehension.

>>6342521
>embodiment of EVERYTHING that is terrible about the current state of America

1. There are other terrible things not embodied in these somewhat inconsequential government programs
2. It's the US, not "America"; you're confusing /sci/'s Bolivian population

>>6342426

Does the set which contains all sets that contain themselves contain itself?

>>6342931
>Social SCIENCE has science in its name. How can you say it isn't science?
Killer WHALE has whale in its name. How can you say they ain't whales?

>>6342934
I never claimed you mentioned online IQ tests. Please work on your reading comprehension.

>>6342931
This a fault of the English language, because words don't define themselves. Words get their meanings from agreement.
In german science is Wissenschaft, which literally means creating knowledge. But here is the problem, you guys do not knowledge. For if you did you would have to be able to predict the future, like we guys in physics do.

If I throw a rock with a certain mass, at a single angle, with a certain speed, etc I can predict where it will land.

You fucking mental midgets do nothing but jerk to the retards you worship who also accomplished nothing. If it was an actual science there would always be only ONE theory for every aspect, only one solution. But clearly there is not, so it's not a science. It's a religion, really.

Now fuck off you simpleton.

>>6342962
>you guys do not create knowledge*

>at a certain angle*

so many mistakes, it's already 1am here. long story short, go fuck yourself

>>6342962
>In german science is Wissenschaft

Geisteswissenschaften sind auch Wissenschaften.

>>6342962
You shouldn't be that arrogant and derisive when you don't know what you're talking about. Have you ever even read anything about social sciences?

>>6342426
Can you post your dissertation?

>>6342973
You can't even get logarithms right. They are literally as easy as addition and multiplication. Is your IQ 90?

>>6342970
Du widersprichst mir nicht.

>>6342907

I'm one of the math students in these threads.
I honestly wouldn't put any mind on "IQ". Math is all about practice. The more you do proofs, and the more you meditate on the subject matter, the better you are at it. Sure, some people are naturally better than others with this stuff, but if they were the only ones studying the subject, there'd be a lot fewer mathematicians.

>>6342962
Solving too many equations must have damaged your brain. Did you go crazy because your intro level physics classes were too hard for you? Everything you said in your post is wrong and horribly ignorant.

>>6342973
Have social sciences ever actually made any contribution to ... anything?

>>6342931
>this is what social science majors actually believe

>>6342980
Logarithms are hard. I bet you can't solve them either.

>>6342981
Like every science social science explains things.

>>6342980
You are proud of knowing logarithms? Hahaha, my sides. This is getting more and more hilarious. How old are you?

>>6342983
Thanks for the laugh, kiddo

I'm gonna take a wild guess here and assert you're at least one of the following
(a) female
(b) raised be a single mom
(c) you have daddy issues
(d) you're gay

Now fuck off and on your way out take a look at that chart
>>6342924
and realize where I'm located and where your waste of time is located

>>6342987
What things?

>>6342986
Not that guy, but sorry but they really aren't

>>6342983
>feeding the yuro trolls anything but their semen ration

>>6342993

Ok, you know what, pure math isn't for you.
Wanna know why? Cause once you get out of first year, you'll start wondering what's the use of all the math you're learning, all the abstract arguments and proofs and all the arbitrary assumptions and conditions, and you'll find it pointless and stupid.
Stick to physics.

>>6342993
>using "female" as an insult

Watch out guys, we're dealing with a professional /r9k/ "feel" poster over here. And I bet the guy is still wondering why he doesn't get laid.

>>6343000
Butthurt female detected.

>>6343002
>implying there are non-females on sci

>>6343000
I didn't use any of this as an insult, I'm simply showing this little kid that I see through these >muh social science morons like a thin sheet of glass.

I'm bisexual myself and I never been to r9gay

>>6342999
I wish I could bring a counter argument, but I'm still waiting on the actual argument

>>6342993
Not that guy (or girl), but how does the fact that he (she) was raised by a single mom/has daddy issues/is gay affect in any way he (she) says? That has nothing to do with the discussion about how you're a moron

Finally a good thread on /sci/ and you turn it into a giant shitfest.

>he meant logarithms over Lie groups

>>6343015
it doesn't have anything to do with it, but I know at least one of those assumptions is to be true, probably 2 or 3 even

ofc you can't see how I arrived at these assumptions, but that would be because you aren't as smart as me

>>6343018
Thanks, asshole. You ruined the joke.

>>6343017
Dis. ask/answer or STFU!

>>6343019
Toppest lel. What's your level of education, kid? Pop sci videos on youtube?

>>6343019
>implying

>>6343032
We both know I'm right, but it's okay shorty, I don't mean to hurt your feelings

just do me a favor and never call it a science again, it rustles my jimmies
*hug*

>>6343038
Too bad, scientific truth doesn't care about your jimmies. If the existence of social SCIENCE hurts your feelings, you better stay away from the science board.

>>6343025
backtoreddit.jpg

>>6343038
I'm not the guy who said social science was real science. Can't you follow a discussion moron?

>>6343041
>implying all memes come from reddit

Rage faces were invented on 4chan, newfag.

OP here, I'll go back and look at some of the questions and answer what I can.

Caveat: IQ circlejerking is stupid and in my experience is mostly engaged in by people unable to actually accomplish anything of note, and so evidently the next best thing is to hang on to a number while repeating softly 'm-muh IQ, muh fugga'

People may be shocked to learn that being a successful mathematician relies entirely on your ability to do good research (in which I am including the ability to effectively communicate one's research and one's ability to interact in a fruitful way with one's peers). Doing good research requires hard work. Some people work less hard, or work less. But when reading someone's research, something that never crosses my mind is whether or not the person arrived at his conclusions through sheer outstanding stroke of genius, or whether it was a painstaking gradual process of hard work. I literally do not give a fuck; I care only for the quality of the results, and every mathematician I've known in any capacity feels the same way.

tl;dr if you want to fellate each other over your IQ scores instead of talking about mathematics, then you've come to the wrong place, motherfucker.

>>6343053
>Rage faces were invented
No, they were discovered

>>6342660

>will the research you're currently conducting ever be credited for a contribution to the invention of a real world application?

If theoretical physics counts as "real world", then the answer is definitely yes, since it already has applications.

If not, then I would only say that it is possible, since I'm not comfortable in saying that even the most seemingly esoteric mathematical result won't someday be applied in some "real" way.

>how much money do you make?

I think my appointment (post-doc) is currently like ~50k USD, which is like obscene wealth compared to how impoverished I was during grad school.

>>6343059
>something that never crosses my mind is whether or not the person arrived at his conclusions through sheer outstanding stroke of genius

All you proved with that post is how shallow you are. You read the papers and you're struggling to comprehend the contents. I on the other hand can and do appreciate the authors' thought processes.

>>6343069
>I've seen everything, I've seen it all
http://www.youtube.com/watch?v=Fg_cwI1Xj4M

>>6342740
>>6342740
>>6342740
>>6342740
OP, please answer this.

I just bought a study guide to retake the SAT's.

Why does it tell me how to eliminate answers and not solve them?

>>6343076
>OP, please *ignore this [retarded, irrelevant question]

ftfy

>>6342426

What is your ethnicity?
Where did you do your PhD?
Have you always been good at maths?
How did you get so good?
Why maths?

>>6342673

>What manner of hell did you have to walk through to get that PhD?

Heh, I'll say that if you're not a transcendent genius nor exceptionally lucky, then you need to learn how to accept a good deal of failure to succeed in a good grad program in math.

>>6342682

>Can you tell us in detail what happened between slightly before you got accepted to pursue PhD?

During undergrad I already knew I wanted to pursue a PhD, so I blazed through my undergrad program in 2 years and then spent the majority of my last 2 years of undergrad taking graduate level courses. After that, I went through the painful process of applying to a bunch of grad schools and then went to the best program with the best offer.

>How hard is research?

It can be very hard... I was recently stuck for months on what seemed to be a trivial detail, but was much more subtle and involved than I originally thought. That said, there is nothing more rewarding than the feeling of actually making progress.

>I have a little insecurity "ok i'm smart but what if not enough?

I had this EXACT feeling before I went to grad school. I worried that I would reach a point in my math education where I would no longer be able to continue... essentially that past that point I would no longer be "smart enough" to comprehend the subject.

I can gladly report that no such barrier exists: If you're willing to work hard enough, you don't have to worry about such a knowledge barrier.


>>6342717

>what is your favorite equation

The Monge-Ampere equation.

>>6342740

1. No
2. Geometric structures on manifolds
3. Too easy to be powerworded because of smallness of my field.
4. Varied wildly; lots of failure at first, followed by lots of success. Also, typical grad student poverty.
5. By the time I defended I had already given several talks on my research at various conferences, so it was just going through the motions mostly.
6. Too easy to be powerworded
7. I have a post-doc position, where I do the same research I've been doing for the last few years
8.I was in several gifted programs as a child, and was certainly more advanced than my peers throughout grade school. I also have severe attention problems and cannot remain focused an a single task that exceeds 10-15 minutes in duration with a few notable exceptions, math somewhat being one of them.
9. I didn't study until grad school, and even then I had some weird method of writing out material I deemed to be important by hand, then understanding it fully through staring at it.
10. I'm 28.

>>6343105
>I didn't study until grad school, and even then I had some weird method of writing out material I deemed to be important by hand, then understanding it fully through staring at it.

This is total bullshit.

>I can gladly report that no such barrier exists: If you're willing to work hard enough, you don't have to worry about such a knowledge barrier.

Says the guy who could apparently stare at something and then get it.

>10. I'm 28.
Let's assume that even though you say you're smarter than all your peers and you breezed through university in 2 years, you still entered undergrad at the average age of 17.
So you got your bachelors at 19.
It took you 9 years to get your PHD? LMAO.

>1. No
OP is a troll. Carry on, everyone.

How do you enjoy math?
Can anybody be interested in math?
Why do you like math?

Is quantization a functor?
Do you watch youtube?

>>6342768

>Does OP think we will solve any of the 6 millennium problems soon?

I have no idea regarding the current state of those problems, since none of them are really close to my research interests at all. Always interesting to check in on every few years, though!

>>6342774

I'm awful at probability and know virtually nothing about it.

>>6342784

>OP, is there anything you wish you had done or started doing earlier as a grad student?

I wish I had been a little more social in the department early in my grad studies... it would have helped my overall mood during a tough first year.

>>6342787
>How many years did it take you to get your PhD?

6.5 years

>>6342789

1. No, because not every proof is worth remembering, especially if you have time constraints. For the purpose of studying, try to focus on proofs via methods that may have applications to other questions outside that particular proof.

2. Not necessarily... on one hand, you can get a PhD in math and go into industry and make some serious ducats, or you can go into academia and make far less, while living a much more free life.

3. I'm a terrible person to ask for help studying because my own study habits were strange and inconsistent.

4. Some days I do no research at all... on others, I spend every waking moment thinking about it. I like to take gaming breaks often because I find it puts my mind in a state more receptive to research.

5. Probably what I mentioned earlier, where I realized that if I worked hard enough I could understand (at least at the level of consumption) anything.

>>6343118

I spent 4 years in undergrad, and got my PhD in 6.5 years. My thesis was finished 2 years ago, and I've been publishing papers since. I only graduated recently because 1) a position that I knew about from earlier opened up and more importantly 2) I had to wait on my wife to finish her PhD as well.

>>6343145

Married an educated woman. You will divorce quickly. Plus are you white?

>>6343146

>You will divorce quickly.

Shiiiiiit I've been married for 6 years.

>Plus are you white?

Yes. American, even.

>>6342426
Are arithmetic operations just special cases of functions with two variables?

Alright guys I'm out for a bit again.

Same deal as last time.

does your wife know you post here?

Fow did you get to 4chan in the first place?
For /b/?
For nakes wemin?

>>6342426
how do you feel about Newton? Do you think Leibniz is solely responsible for the invention of Calculus?

wtf would you need a PhD in mathematics for? What are you gonna do, invent a new number?

>>6343060
I haven't laughed for days. Thanks anon

what's the best way to teach myself single variable calc by september

>>6343243
That's subjective

>>6343243
if you need that long to learn it you're a retard.

>>6343243
What do you know now?

how is your cryptography fu? What branches overlap with it?
How is statistics not bullshit?

what dissuaded you from being an actuary?

If I were to play cards (poker, blackjack) vs you, how fucked am I

>>6342426
Hi, retardfag here, but how do you actually stand the dry text of textbooks that you can actually manage to learn something from such books, and the way most authors go about it they seem to overcomplicate the process in which they solve the equation and the subject becomes arcane.

>>6343481
> what dissuaded you from being an actuary?

probably because that's the most boring job ever. I'd rather sell ice cream on the beach than be an actuary.

>>6343814
This, so much.

>>6343243
that shit takes 2 weeks at the most to learn.

>>6343826
>but muh shekels

OP, silly non-math related question, but how did you meet your wife? Even worse, how do you make friends? I am in grad-school (for physics related field) and it seems there's no easy answer to these problems.

>>6343059
> Caveat: IQ circlejerking is stupid and in my experience is mostly engaged in by people unable to actually accomplish anything of note, and so evidently the next best thing is to hang on to a number while repeating softly 'm-muh IQ, muh fugga'
mah nigga

>>6343118
>>I didn't study until grad school, and even then I had some weird method of writing out material I deemed to be important by hand, then understanding it fully through staring at it.
> This is total bullshit.
That's how I used to study in school, I see no fundamental problems here. Together with actually solving stuff, this is still my best approach.

OP what are you doing now? Are you a professor?

>>6344902
read the thread, he's doing a post-doc

Something maybe related with your research element; I am trying to prove the distance of a point in n dimensions from a geometrical object represented with a first degree equation with n variables and one constant number. I gave my proof to one mathematician that teaches me and is obviously underskilled by a lot, and he said he didn't understand a point where I took a paralel vector in n dimensions with start a constant point namely the O(0,0,0,0,..,0) and he doesnt understand how something can be paralel in more than 2,3 dimensions. When I thought about it, I found it common sense and self explaining. But his remark problematized me and made me wonder if I have to prove that the vector I took is actually paralel and is allowed to be paralel in n dimensions. What do you have to say?

The formula I derived works for 1,2,3 dimensions, dont know how I find the real distance for more to check if I get the same result though.

Been trying to self-learn mathematics for a while now, but just can't

>Am I too stupid for Mathematics, should I just do manual labor until I die?

Do you smoke? Why do all the mathematicians I know smoke or the elder ones have recently quit?

>>6344972
OP please help

>>6344969
just stop using the word paralel and start using linear dependent. Same thing.

Mathematics grad student here. I'd like to do research in algebra, as it is what I'm most interested about (and also where I got the best results). What are the research opportunities in algebra in your country ? Where I study (France) I have the feeling there are so few tenures that the only guys having a decent shot at research in algebra are freaks.

Congratulations on the PHD! I remember being in your thread when you were finishing it. Any tips for a math undergrad in his first year who eventually wants to do a PHD? Studying tips/module choices etc?

What's the state of the private sector in regards to doing pure research in things like Math and CS? Are there many opportunities similar to what Bell Labs used to be like? I've heard Microsoft still does a lot of hard research, but that not many other major companies do. Any knowledge on this? I'm going for a CS degree, and thinking about doing a PhD after I finish my undergrad, but if I can get into research elsewhere, I'd rather do that.

>>6343172
As someone who is looking to be applying to statistics and biostatistics graduate school next year, do you have any advice?

What would you have done differently if you were given the chance to redo your application?

>>6342654
I can totally picture some physics guy sitting there, wondering what the fuck are all those drawings about

>>6342901

in pre cal logs are literally plugging the numbers and putting in log values, dude

another one is just switching the things around to its correct place (kind of like 5x + 5 = 25 where you isolate the x)

go to the lectures and then read the book 20-30 minutes and do the practice problems over and over again

do not memorize pre cal (unless it's the babby shit), just practice over and over

>>6344972
Not OP but you can't self learn math. You have to be very gifted to teach yourself in such a delicate area, you need at least a mentor.

>>6345288
>Not OP but you can't self learn math. You have to be very gifted to teach yourself in such a delicate area, you need at least a mentor.

Ramanujan would like a word with you

>>6345288
Not really, you just have to be very determined. There's more than enough material out there nowadays.

Problem is that a lot of people either try to do things that are too difficult right off the bat or they just don't want to invest the time and work into it that it requires.

>>6345306

Yes. But he is not Ramanujan. That's what i'm talking about. If you want to make your way alone from elementary math to cutting-edge math you have to be very-very talented. You can find tons of information on the internet, but the QUALITY of most are bad.

>>6345319

Ok. If you are determined as fuck AND you are not a genius you can self learn math... just give it enough time... your life...

Does math get more exciting?

I'm a senior in HS looking to major in math currently taking Vector Calc and it just seems so boring right now... it may just be my professor though

>>6345355
>Ok. If you are determined as fuck AND you are not a genius you can self learn math... just give it enough time... your life...
You've basically described what pure math majors do.

>>6345408
Different math majors are into different things. Like everyone is expected to have some level of basic understanding in several branches of math but once you're out there working as a mathematician you generally focus on whatever branches interest you. Why do you find vector calculus boring? What do you like about math?

How much you make?

>>6345425

I fade in and out of attention in the class so this may be incorrect but it seems like very little changes from concept to concept, as if I'm just learning the same thing over and over with very slight variation

>>6345434
Well calculus classes are more or less like that. You have to keep in mind that they're not really geared at math majors, they're geared at general students.

Perhaps you may be interested in tasting some different branches of mathematics? There's many threads here where anon's post textbooks for other topics. In many of them you don't even need calculus as a pre-req. You may need a more thorough understanding of maps, functions, relations, sets, mathematical logic, proofs, and general abstractions. I've picked up my knowledge from lots of different textbooks and courses, perhaps another anon can suggest a good textbook for jumping into real math.

>>6345306
you don't think ramanujan is in the "very gifted" category?

>>6345434

Since you're in HS, I assume your vector calc class isn't doing any proofs.
Maybe once you encounter proofs your motivation will kick in. I know mine did.

>>6342426
Is computer science a branch of mathematics?

>>6345584
no

>>6345585
I was asking OP, silly goose

>>6342426
perhaps you can help me.
I'm trying to find the proper way to express the formula for the following situation.

The action involved is found in an electronic amplifier device called a traveling wave tube. It amplifies by the interaction of a beam of electons moving axially down a helical coil. a small signal is injected at one end of the coil and the signal is amplifed by the DC electron beam while traveling down the helix and is "picked up" at the far end of the coil.

I do not have a good grasp of the complex math involved but I do realize that it will need to account for the total current of the beam, the alignment of the beam with the helix axis. The helix parameters of axial length, diameter, number of turns and cross section of conductor.

thank you for any consideration you give this post.

Do you think it's important to attend lectures? Why?

I am 20 years old and I have been a NEET since I left school nearly 1 and a half years ago. I was in the top set but I was a delinquent and as a result got worthless grades. I want to do something worthwhile with my life just like you. In your honest opinion, is it too late for me?

>>6345710
>20 years old
>too late for anything

>>6345710
Not OP, but I failed out of 9th grade, dropped out, and spent several years of my life fucking off as a deliquent. I used to be top-class material and participated in math competitions throughout middle school.

I got back into school at the age of 22 after taking my GED, aced all of my classes, and earned a job as a writing and eventually math tutor.

I'm doing research this summer over singular value decomposition, I'm about to complete my bachelor's in math, and I'm about to start my graduate for PhD.

It's not too late. I just had to become independent, save up money, and actually give a fuck about my future.

>>6345710
No. I've dropped out of university, worked for half a year, NEETed for 1.5 years, and am now studying again (now math). If you don't have to pay outrageous tuition fees, go for it.

>>6342555
what about just generally good books?
(i thought the guy who asked this wanted to know else you read that is not math related)

>>6345786
>>6345710

Why is sci filled with dropouts?

why does 1+1=2? a friend of mine just learned that in class, said it was hard, but couldn't explain it to me correctly

Do you take any drugs?
What study methods did you use throughout undergrad/grad?
For example, I attend the lectures, make really scruffy notes throw them away, and just reread the lecture notes before exam time. This is doesn't really get me anywhere though.

Also how do you go about learning theorems definitions and proofs?

It was asked already but you missed it.
Have you participated in IMO and Putnam?
Do you think they are a good prediction of somebody's success as a mathematician?

>>6346294
because we define the netural numbers and + this way.

>>6342426
pics with timestamp or it didn't happen

Has OP forsaken us?

>>6342737
>equating your country with state apparatus