[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 16 KB, 272x326, poincare2b.jpg [View same] [iqdb] [saucenao] [google]
4573713 No.4573713 [Reply] [Original]

Ask a guy who just passed his PhD candidacy exam in mathematics anything.

>> No.4573716

why does .9999999 = 1?

>> No.4573717

>>4573716

Oh come now, I think we can do better than that

>> No.4573718

How does it feel to know you won't be able to get a job when you finish?

>> No.4573719

What do you think causes brilliant mathematicians to commit suicide?

>> No.4573720

Oh thank you you're just in time. Okay so what's really going on with Jordan canonical form? How do I derive it?

>> No.4573721

What are your papers on?

>> No.4573722

What are you planning to do with the $300,000?

>> No.4573723

What are you planning to do your thesis on?

>> No.4573724

What was your exam on? as in , what subject are you focusing on in math?

and what school are you attending?

>> No.4573725

How do you feel about the sentiments expressed here?
http://www.maa.org/devlin/LockhartsLament.pdf

tl;dr In school we teach children that mathematics is tedious calculation rather than seeing relationships and patterns in logical systems, and we are doing them a monstrous disservice

>> No.4573726

>>4573716
well, .9999999 = 1 is a false statement.
its is equivalent to 1, but it doesnt equal 1.

(x-1) x=1 it'll be 0,

lim(x→0,9999999∞) still wont be 0

>> No.4573730

>>4573721
Geometric structures on manifolds.

>>4573720
Dummit and Foote, Rotman, or Lang are all good references for this iirc, but it's been a few years since my coursework in algebra proper

>>4573719
I'm not entirely familiar with many mathematicians who committed suicide... however I know of quite a few star mathematicians who went 'crazy'. I think it's a mostly that the field attracts those types of individuals that are typically more 'eccentric' than is usual, so it gives the impression that math makes people crazy, when instead I think that some 'crazy' people are drawn to math by its nature.

>> No.4573731

>>4573726
0/10
There are so many offensive errors and abuses of notation in your post

>> No.4573734

>>4573722
Where's this money coming from? =)

>>4573723
>>4573724

Projective structures on manifolds and related moduli problems. I won't say the university because the research field is very narrow and would easily lead to my powerword.

>>4573725
I'll glance at it and get back to you.

>> No.4573736

>>4573731
Best I could do without pen and paper. Still 0,9999999 = 1 is a false statement.

A guy who knew math, would understand what I TRIED to show.

I agree, it was not mathematically correct; more organized mess:P

>> No.4573739

>>4573725

Ah, well while I was TAing I taught some courses that focused on math education, so at least at the level of instructing future elementary school teachers, the emphasis is definitely on teaching kids the 'proper' way of seeing math, essentially as pattern recognition.

Although it's a bit disheartening to know that only a few of those prospective teachers get this message... I literally had a roomful of future teachers ask me what the point of knowing high school level geometry proofs was since they were only going to be teaching elementary school.

Yes... a roomful of future teachers arguing against learning... sometimes I don't want to live on this planet anymore =(

>> No.4573742

How old are you?

>> No.4573744

>>4573742
26

>> No.4573745

What's your IQ?

>> No.4573746

>>4573739
OP, why math?

*not ment to be offensive

>> No.4573757

Pure or applied?

>> No.4573761

>>4573745
I was tested back in 4th grade... it was 169 iirc (would have to call my mom and have her look at the report to be sure)

IQ is pretty much a worthless assessment though... I'll say more about that in a sec.

>>4573746
I originally went into physics, but found that it was the mathematical framework that I was most interested in, so I switched to math.

What's interesting is that my research now is essentially theoretical physics, so I've seemingly made my way back into physics after all.

>>4573757
Pure.

>> No.4573762

>>4573713
WHY AM I SO BAD AT MATH

>> No.4573764

>>4573761
how do you or are you planning to make money?

>> No.4573777

>>4573761
Continuing about IQ...

So throughout school, I barely had to put forth any effort at all to do very well up through early graduate level coursework (I had finished 2 years worth of grad coursework while an undergrad). This would be due to my high level of 'intelligence' in the classical sense.

Here's the thing: raw intelligence isn't enough, and in general being a hard worker is FAR, far more important than being 'smart', even in fields like math and physics. I very nearly found myself kicked out of grad school due to my severe laziness and overall lack of any work ethic, together with my severe attention problems.

I had friends who were not as 'smart' as I, but whose path through grad school was much smoother. This is why I think too much importance is placed on being a 'genius' instead of enforcing the mindset in people that through enough hard work, even things like theoretical physics and math become doable. Of course, you're going to have to do less work if you're more 'intelligent', but that's just how it is.

Of course, the greatest mathematicians are both supremely intelligent AND hard working.

>> No.4573782

>>4573777
>high IQ, doesn't think it really means much
>breezed through school until graduate studies at least
>my severe laziness and overall lack of any work ethic, together with my severe attention problems.
Holy shit, are you me? I've avoided actually hitting academic probation and such, but man.

>> No.4573786

>>4573764

Well I plan on going into academia, and of course seeking a tenure-track position at a good university somewhere. Those kinds of positions pay well enough for me to live comfortably. (Decent food + decent home + decent car + badass computer is all I need to be happy in life)

Now, if I was the kind of person who cared much more about money than I do, then yes, getting a PhD in math is not the most efficient path to take, since less or right around the same amount of time invested would've yielded me a law or med degree... but I find both of those fields dreadfully boring, and I don't care about money enough to justify studying them.

Now I do know of some folks who got PhDs in math and went on to work for actuarial firms or Boeing or Lockheed Martin and they now make killer ducats, so it's certainly not impossible to make serious bank with a phd in math. It's just not something I'm interested in.

>> No.4573787

What was your undergrad program like? I'm an EE switching into math next year because that's where my real interest is and I want to go to grad school for it. I've taken calc, diff eqs linear algebra and logic (proofs). I'll be taking the honors courses when I switch.

Did your school offer honors courses/did you take them? What did you all take in undergrad? Any general advice?

>> No.4573796

>>4573782

Yea it's a major problem that people don't realize. I avoided academic probation as well, but I cut everything very close to the limit, i.e. maximum amount of time taken to pass qualifying exams, etc., mostly because of the aforementioned issues and general procrastination of studying.

I think, and this sounds kinda lame, that due to my progression through earlier coursework, I got ready to take qualifying exams and realized I didn't know how to study, since I never had.

Also, because of not being able to focus on anything other than video games for more than ~15 minutes at a time is a serious detriment when you're taking a PhD level exam that requires extreme focus for ~4 hours.

If the exams were in a format of a traditional oral exam I could've easily avoided any issues with passing since my amount of knowledge wasn't an issue... it was more just maintaining enough focus to transcribe that knowledge during the time allowed (well, and motivating myself to study in the first place of course)

>> No.4573801

>>4573777
>So throughout school, I barely had to put forth any effort at all to do very well up through early graduate level coursework

So you're saying even shit like topology, real analysis, geometry and whatever else was childs play to you?

r u a magnet?

>> No.4573816

>>4573787
My undergrad offered honors courses for most of the coursework up through advanced calc (i.e. real analysis) and algebra (group theory, ring theory, modules, galois theory).

In addition to taking the honors courses, you should consider getting through the coursework as fast as you can to allow yourself time to take graduate courses as an undergrad (even possibly taking an extra semester or so to graduate if necessary), because this looks better than anything to prospective grad schools when you're applying. I'd suggest taking possibly a year long grad sequence in either analysis or algebra, since techniques from those two fields are generally applicable to pretty much anything you end up doing. (Even if you're wanting to do applied math)


As for what I took, after the first 'proof' course I had one semester courses in analysis, algebra, then year long honors courses in analysis (so rigorous foundation of real numbers, metric spaces, then real analysis), and algebra, then I took 3 yearlong graduate courses in analysis, PDEs, and Riemannian geometry. I took a few fun grad courses in things like Calculus of Variations. I also took a course in probability and another in numerical analysis, though I hated both of them and this was just to satisfy a requirement to graduate.

>> No.4573823

>>4573801

It was all child's play until it reached a point where my weaknesses in attention span and inability to prepare more than a few days in advance caused me issue; namely, these big exams designed to test knowledge of a subject covering huge amounts of material typically covered by a year long course in some topic.

That's not to say it was all 'easy'... there was a lot of frantic last-minute studying that I had to do (i remember a couple of complex analysis and algebraic topology exams in particular), but it always worked for me and I always managed to do well in my courses.

It stopped working at the qualifying exams, however.

>> No.4573828

congrats on your qual, dude. was it harder/easier than you expected?

>> No.4573840

>>4573828

It was more or less as I expected.

I had been to a few candidacy talks for my friends so I pretty much knew how things went.

It was nothing compared to the written quals... those were things straight out of a Lovecraftian nightmare. I swear I think those exams could easily give a person PTSD

>> No.4573856

EE undergrad here. I don't "get" dif eq. I got an A in ODE, i can solve problems with 2nd order DE straight or with laplace with no real problems. But it doesn't make sense to me in the same way that calc does. Is there something I could do to get a more intuitive feel for diffy q?

>> No.4573878

>>4573856
Disclaimer: I know very little about ODEs


Coming from engineering, maybe PDEs would feel more intuitive for you?

In most applications, some phenomenon you want to model is going to be described by some PDE or a system of PDEs coming from physics. Maybe seeing the derivation of these equations from the physics side of things would provide more motivation?

I realize that there exist similar examples in ODE theory but because ODEs are 1 dimensional sometimes the situation where they arise is made so simple that it can be hard to see what's going on.

I know very little about dynamical systems/ODE theory though, so I'm sure someone with a strong background in that stuff could give you many motivating examples of ODEs.

>> No.4573892

How important are lower division course grades? I've actually published some very small research in physics, but I got 3 Cs in lower division (weed out?) courses related to physics. i also haven't taken any graduate courses.

are those cons going to weigh heavily against me if i apply to engineering/applied math/physics grad schools?

>> No.4573901

>>4573856
best way to understand ordinary differential equations is to take a vibrations class.

unfortunately, being a EE i imagine that it is neither a requirement nor would it count as a technical elective.

>> No.4573908

>>4573892

If you've done any kind of research, that's more important than pretty much anything else on your application. If you can get 3 good letters of recommendation from the best professors you can, that should be enough to outweigh a few bad grades. You should try to take some grad coursework if possible though.

Be prepared to be rejected by plenty of schools though... I had what most would consider an excellent resume, yet I applied to ~12 schools and only got into 3 of them. Granted a few of those rejections were Princeton, MIT, Brown, etc. but even some of my 'safer' schools rejected me.

This happened to everyone I knew when it came time to apply for grad school... they were routinely rejected by a school only later to be accepted into a better program. You just never know with grad school applications, and the whole process is somewhat nightmarish anyway.

>> No.4573917

OP, give some advice to a future algebraist

>> No.4573918

>>4573892

Oh and I should also say:

GRE scores are only important insofar as you make better than the grad school's cutoff. I literally fell asleep during my gre math section and had to do most of that portion of the test in about 3 minutes, and so my GRE math score wasn't even that exceptional, lol (which you'd think would be an auto death sentence when applying to a math program since the GRE math is like middle school tier material). But it's precisely because math depts. know that the GRE is fucking worthless that they don't really care too much about it... even with a bad score I was able to get a nice fellowship at a top 15 math program.

>> No.4573920

>>4573918
What are you going to do now? Finished with academia?

>> No.4573925

>>4573917

Learn representation theory asap... its range of applications are absolutely ridiculous, and from that subject alone you will be able to know lots about many fields of current research.

Arguably its the most ubiquitous of all the fields other than the super-vague classifications like 'analysis' or 'algebra'.

>> No.4573928

>>4573920

No, once I graduate I plan on seeking a tenure-track position at some university... so my plan is to stay in academia.

The lifestyle I like to lead doesn't lend itself well to industry, but to me it's worth the reduced pay in order to have a lot more freedom in work hours.

>> No.4573931

>>4573928
Fair enough, good luck to you and congrats.

>> No.4573940

>>4573931

Much thanks =)

>> No.4573959

You seem nice, so I'll ask what is probably a stupid question-

I only really 'realised' that I liked math towards the end of highschool. I'm now studying a degree that's basically combined math and computer science- I went in for the computer science, but I am honestly liking the math a bit better. Problem is, I only really get average/slightly above average marks, (which sometimes might have something to with my less-than-great math foundation in highschool, but I've almost completely overcome that now).
Anyway, I'm starting to have thoughts about perhaps majoring in math (probably applied) and maybe doing some postgrad stuff. Do you think that with my grades and late-blooming interest in math that I could perhaps make it, or is it really only for the more intelligent ones that can get their shit together and put in the hard work as well?

>> No.4573969
File: 24 KB, 819x460, problem8math.png [View same] [iqdb] [saucenao] [google]
4573969

askin

>> No.4573977

>>4573959

I was also a late bloomer with respect to math interest.

First of all, I went to public high school in east TN, i.e. my high school was a complete joke. I was good at math always, but I hated it for the most part. In fact, I hated it so much that the only reason I took AP Calc my senior year (the only AP course offered at my high school), it was only so that I could get the AP credit and never have to take another math course.

Fortunately for me, the teacher was the best teacher I had throughout high school, and made me immediately decide to go into physics at uni. I then shifted from physics to math, and here I am.

So it's definitely possible to overcome a poor/late blooming math background and do post-grad work. I suspect as much is true for any field, if you;re willing to put in the work to make up for your lack of a strong starting point.

>> No.4573991

>>4573977
Thanks so much. Actually, our stories are kind of similar in the HS regard! All the best for the future.

>> No.4574017

>>4573977
>>4573959
lol.
I didn't decide to do math until my junior year of college, and even then I had to spend more time on my other major (physics) and couldn't focus on math at all.
Now I'm going into math for a PhD. Fuck being too late.

>> No.4574259

>>4573713
What is the most important advice you can give to a freshly enrolled PhD candidate in mathematics like myself?

By the way, are you from the former Soviet Union?

>> No.4574271

OP, are there actually any jobs for a math major?

>> No.4574272

>>4574271
There's always quantitative finance.

>> No.4574343

>>4573959

Dude you are a complete copy of me.

I don't know to go math or not because it's much time. Currently i'm finishing my engi BSc, but if i want to go math it's +3 years and the math MSc more... and the problem i would like to get a PhD. i think i'm late with the math, i should have done it paralel with my BSc but i fucked up...

I think i'll do the masters and after if i'm still wanting to go math i'll do it. It's a very sad story we have such a short life. It's even more worse when you haven't got 120+ IQ so you get slower things. add some ADD and deep procrastination and you get constant depression of your miserable life... im a fucking retard :(

>> No.4574371

>>4574343

Get out of here you subhuman.

>> No.4574397

>>4573713
Why is math starting to get a bit racist these days like science?

>> No.4574613

If you can't find a job, will you consider becoming a full time paid personal tutor to people on /sci/ while making math lecture videos that resemble those from khanacademy?

>> No.4574630

Well all I can say is congrats on your achievement

>> No.4574642

>>4573713
what subjects were the most enjoyable for you / what did you hate? What was your minor?
Do you do math in your free time, like solving putnam problems?
also
>Projective structures on manifolds
has this real life applications or is it mostly math for the math's sake

>> No.4574663

>>4573725

>"mathematicians conceived of black holes long before astronomers actually found any"

John Michell was a geologist

>> No.4574836

Are you still here OP?

>> No.4574867

>>4574642

It has applications to physics and engineering, as well as pure maths.