/sci/ - Science & Math

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Anonymous Fri May 18 23:09:57 2012 No.4695838 [Reply] [Original]

Sup /sci.

I'm thinking about doing a PhD in mathematics and need your help. I'm approaching my 3rd year of engineering and realized that I hate not knowing the proofs to things.

I'm currently going through Elements to achieve a decent level of mathematical skill and then working up from there to truly understand where Fourier, Gauss, Newton et al were coming from. My "end game" is to master statistics and then apply concepts to quantum mechanics.

Can you guys help me out with a plan for my last 2 years? I've already checked out the sticky and I love it! I'm reading a couple of books on there but I find that school interferes with my education (lol Mark Twain).

Is there a certain order you guys can suggest for me in terms of what to read/what to learn.

I ordered a book from amazon called "Probability Theory: The Logic Of Science" because I heard it's very good but I'm going to finish Elements first.

THANKS!

>>	Anonymous Fri May 18 23:12:42 2012 No.4695846 Learn analysis. Then learn more analysis.

>>	Anonymous Fri May 18 23:14:58 2012 No.4695849 >>4695846 Okay :P Can you pick out any good books from the wiki? I can't differentiate which ones will benefit me the most.

>>	Anonymous Fri May 18 23:15:58 2012 No.4695850 >I'm approaching my 3rd year of engineering and realized that I hate not knowing the proofs to things. me, is that you?

>>	Anonymous Fri May 18 23:16:26 2012 No.4695854 >>4695850 Who? What?

Anonymous Fri May 18 23:21:56 2012 No.4695862

>>4695846
>>4695846
>>4695846
>>4695846
>>4695846
>>4695846

You need -- NEED -- analysis.

In general, Euclid won't help you *that* much with upper math, but it will improve your reasoning.

I'm not too sure if a PhD in Math is what you want, especially since you're aiming for quantum mechanics.

Anonymous Fri May 18 23:22:27 2012 No.4695863

Heh, I'm in the same boat, OP. Although, I've decided that I'm switching programs into math. My recommendations (as was the recommendation of many here and of my new advisor) was to learn analysis as soon as possible. Sign up for some analysis course next year and maybe a course in algebra or probability.

Best of luck, are you going to finish your engineering degree?

>>	Anonymous Fri May 18 23:24:42 2012 No.4695869 >>4695863 I should have read over my post, that was worded horribly.

Anonymous Fri May 18 23:24:56 2012 No.4695871

>>4695863

Thanks a lot to you and >>4695862.

I think I'm going to finish my engineering degree (unless I fail out because I'm honestly at the point where I feel as though everything I'm learning is complete bs).

Analysis seems like such a broad term... what do you learn in an analysis class? Also, can you recommend any books? Thanks!

>>	Anonymous Fri May 18 23:26:26 2012 No.4695877 >>4695850 Doesn't every engineer feel this way at some point?

Anonymous Fri May 18 23:30:26 2012 No.4695889

>>4695871
Analysis is essentially calculus with a lot more rigor. Also, it's usually the introductory subject in which math students first use their proving techniques and begin honing these skills. Most people here will recommend Spivak's calculus.

>>4695877
Perhaps, but I have a hell of a lot more interest in math than in EE; i'd much rather be a professor or a general "math guy" than an engineer.

>>	Anonymous Fri May 18 23:32:56 2012 No.4695893 >>4695877 A friend engineer of mine (boyfriend obviously, cause we're all gay) never has this problem. He also can't understand how mathematicians can find math an sich so interesting without a direct use for it, which I find strange of him.

>>	firefly Fri May 18 23:36:56 2012 No.4695907 >>4695893 You see .. I find that ridiculous. Someone gives you a shovel and you do not care for the thought that somebody put behind creating that shovel and focus your energy on using the shovel as a "tool" instead.

>>	Anonymous Fri May 18 23:38:26 2012 No.4695913 >>4695907 That's precisely what I don't like about engineering There should be a pamphlet, passed out to engineering students at orientation fully explaining this; encouraging them to go into something else if they think this would be a problem.

Anonymous Fri May 18 23:39:26 2012 No.4695915

>>4695871
Analysis is basically calculus, except with much more rigour.

I wouldn't really recommend going straight into an analysis course, especially if you don't have practice with proofs.

Whether or not you know calculus, Spivak is a decent introduction to rigorous math and topics in analysis. As for free options, the Trillia Group (http://www.trillia.com) has some very good introductory material as well as loads of books to choose from in their Online Math section. You should peruse their Basic Concepts of Mathematics book and see what's difficult; their Analysis book is based on the Basics book.

Anonymous Fri May 18 23:42:12 2012 No.4695921

>>4695907
wut?
I'm with you. I LOVE rigorous math.
What your describing thought is "Implementation".
It's something that math students don't often come across with because they derive everything from (practically) zero. In the real world implementation is a MUST to get things done even if you don't like it.

>>	firefly Fri May 18 23:46:56 2012 No.4695929 >>4695921 Oh no I know! I'm with you too! I meant to say your friend's idea is ridiculous!

Anonymous Fri May 18 23:48:27 2012 No.4695935

>>4695921
Yes, but in order to best use the shovel (or any tool) you should know something about it--how to best use it, WHY it is best used that way, etc.

I've spent two years in an engineering program, a lot of the problems I've had could've been easily solved had there been more emphasis on the physics or mathematics behind the devices or processes. Instead, they just throw the things at you, tell you to use programs like MATLAB to work essentially like "magic" to give the right answer. It's frustrating for me, but a lot of people don't mind--they'll make fine engineers. It's surely useful to the world, but not what I want from my education. I can figure out the application things on my own, or in a job setting.

>>	firefly Fri May 18 23:48:41 2012 No.4695936 >>4695915 I just read the reviews about this book and I'm going to order it ASAP. Thanks!

>>	firefly Sat May 19 00:03:57 2012 No.4695972 >>4695889 I ordered Spivak's book. I hope that I will enjoy it as much as those who reviewed the book. My school told us to get some crappy Glyn James book that I've despised since day 1.

>>	Anonymous Sat May 19 01:44:11 2012 No.4696213 File: 10 KB, 249x202, 1281925146321.jpg [View same] [iqdb] [saucenao] [google] >>4695838 >>4695838 >engineer >qunatum mechanics NOPE. NOT GONNA FUCKING HAPPEN! You are not smart enought to do quantum mechanics \thread

>>	Anonymous Sat May 19 01:47:56 2012 No.4696225 >>4695838 >Engineer >considers Ph.D in math >wants to study QM Get a Ph.D in physics. Math is math. Physics is physics.

>>	Anonymous Sat May 19 01:48:11 2012 No.4696227 File: 110 KB, 532x800, preach.jpg [View same] [iqdb] [saucenao] [google] >>4696213

>>	Anonymous Sat May 19 01:49:26 2012 No.4696230 >>4695838 You are terrible unqualified for any sort of career in math of physics. I doubt any program would even let you in.

Anonymous Sat May 19 01:51:11 2012 No.4696236

>>4696213
>>4696230
Oh look, summer is here.

Don't listen to these chumps, OP. Just because you studied engineering doesn't mean you found it challenging.

I was a computer science major for four years before graduating with honors in pure mathematics.

>>	Anonymous Sat May 19 01:52:11 2012 No.4696240 File: 20 KB, 471x480, 1269784723757.jpg [View same] [iqdb] [saucenao] [google] >>4695838 You really think you will get into a Phd math program? With just some shitty engineering undergrad degree? ARE YOU FUCKING DELUSIONAL?

Anonymous Sat May 19 01:55:12 2012 No.4696247

>>4696236
It is often the case that comp sci or physics majors switch to math (or visa-verse). There is alot of overlap with the critical thiking skills needed for these majors.

Engineering however, doesn't require critical much thinking skills. OP will not get into a math Phd. He is way out of his league.

Anonymous Sat May 19 01:57:57 2012 No.4696250

>>4696240
He'll get in easily enough. But whether he'll pass the quals is another question entirely.

OP: keep at it. Don't let anyone tell you what you can't do. Fuck these morons, they're just negative assholes that want everyone to feel as bad as they do.
They're bitter because they view themselves as failures in life. Don't become like them.

>>	Anonymous Sat May 19 01:59:26 2012 No.4696256 >>4696240 My Linear Algebra professor got his B.S. in mechanical engineering, M.A. in Math and Ph.D. in Math. Seriously what is wrong with half of the people in this thread?

Anonymous Sat May 19 01:59:57 2012 No.4696257

>>4696247
Sorry, but if you think CS requires critical thinking, then you are deluded. I left the CS major right before graduating because I was disgusted by the lack of intelligence and critical thinking required by any of the courses.

And physics is entirely different. As someone who's worked in a physics lab for over a year now, I can safely say that physics and pure math are pretty much complete opposites.

Honestly, I would bet linguistics or sociology is closer to pure math.

Anonymous Sat May 19 02:02:41 2012 No.4696267
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>>4696250
I don't think you fully realize how little math undergrad engineers learn. Most mathematicans wouldn't even consider that shit real mathematics. OP has NO FUCKING CHANCE of getting into a Math Phd.

HE DOESN'T EVEN KNOW BASIC PROOFS! JESUS FUCKING CHRIST! No credible department in the would would let him in!

Anonymous Sat May 19 02:02:57 2012 No.4696268

>>4696256
He got an M.A. first. Look, I'm the encouraging one here:
>>4696250
>>4696236
>>4696225

But if you think you can go straight from engineering to a Ph.D in mathematics, then you're in for a rude awakening.

Look: I did my undergrad in pure math. I'm starting my master's in physics. Not my Ph.D, my master's.
You know why? Because even though it's not difficult, I haven't had exposure to the subject, and there's no way in hell I'd get through the quals with an bachelor's in number theory and abstract algebra.

>>	Anonymous Sat May 19 02:03:56 2012 No.4696273 >>4696267 I told him to get his master's first. I agree with you, that he wouldn't stand a chance going straight to Ph.D. But that doesn't mean it's not in him. It just means he hasn't had the exposure.

>>	Anonymous Sat May 19 02:04:26 2012 No.4696274 File: 33 KB, 500x372, celebrity-pictures-lady-gaga-eminem-thinking-wtf.jpg [View same] [iqdb] [saucenao] [google] >>4696257 > I would bet linguistics or sociology is closer to pure math

>>	Anonymous Sat May 19 02:05:56 2012 No.4696278 >>4696268 >Got M.A. first Wait, you can skip the masters program and go straight to a Ph.D.? I thought there was no other way... (Undergrad here)

>>	Anonymous Sat May 19 02:06:12 2012 No.4696279 File: 79 KB, 350x385, BestSupportingActor-RobertDowneyJr-TropicThunder15G.jpg [View same] [iqdb] [saucenao] [google] >>4696257 > linguistics or sociology is closer to pure math

>>	Anonymous Sat May 19 02:06:41 2012 No.4696281 >>4696278 Yes. You can go straight to Ph.D. It's becoming more common nowadays, but it's still not super-common.

>>	Anonymous Sat May 19 02:07:26 2012 No.4696282 File: 13 KB, 251x251, wtfamireading.jpg [View same] [iqdb] [saucenao] [google] >>4696257 >Honestly, I would bet linguistics or sociology is closer to pure math.

>>	Anonymous Sat May 19 02:07:41 2012 No.4696284 >>4696274 Than physics? They most certainly are. I can't think of a single thing that overlaps between pure math and physics.

>>	Anonymous Sat May 19 02:08:56 2012 No.4696287 >>4696282 >>4696279 >>4696274 Do you have a point, samefag?

Anonymous Sat May 19 02:10:26 2012 No.4696289
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>>4696257
>ITT: troll tries to convince OP that he can go into math with just an engineering degree

That is some master trolling bro! You are actually gonna fuck up his life.....NICE!

10/10

>>	Anonymous Sat May 19 02:11:11 2012 No.4696291 >>4696289 That's not what I said at all. Do you even know how to read?

>>	Anonymous Sat May 19 02:11:56 2012 No.4696292 File: 100 KB, 392x345, 1267342717763.jpg [View same] [iqdb] [saucenao] [google] >>4696284 >I can't think of a single thing that overlaps between pure math and physics Confirmed troll

>>	Anonymous Sat May 19 02:12:26 2012 No.4696293 >>4696292 Okay. Then list one.

Anonymous Sat May 19 02:12:56 2012 No.4696296

>>4695838

Hey OP firstly do you really like proofs or just don't like engineering. As trust me unless you have studied upto complex analysis I don't think you should do it.

Certainly, I doubt you know what maths is. Trust me I'm studying for an algebraic topology exam in two days.

Just don't bother.

>>	Anonymous Sat May 19 02:14:11 2012 No.4696298 >>4696296 That's funny. I'm studying for a point-set topology exam in two days.

>>	Anonymous Sat May 19 02:15:11 2012 No.4696299 >>4696298 I remember when I was a noob.

>>	Anonymous Sat May 19 02:15:56 2012 No.4696300 >>4696299 It's required for the pure math majors at my school. I find it to be kind of a bullshit course.

>>	Anonymous Sat May 19 02:16:11 2012 No.4696301 >>4696293 Calabi-Yau manifolds I mean, this is not even a fair question, theoretical physics overlaps greatly with ridiculous amounts of pure mathematics, and is more related to pure math than fields like probability and combinatorics.

>>	Anonymous Sat May 19 02:17:27 2012 No.4696306 >>4696301 >manifold >pure math I don't think we're using the same definition anymore.

>>	Anonymous Sat May 19 02:17:56 2012 No.4696305 File: 28 KB, 358x310, 126877739536bbbb8.jpg [View same] [iqdb] [saucenao] [google] >>4696293 >Has never heard of calculus http://en.wikipedia.org/wiki/Lists_of_mathematics_topics

>>	Anonymous Sat May 19 02:18:56 2012 No.4696307 >>4696305 Okay. You're DEFINITELY trolling if you think analysis is pure math.

>>	Anonymous Sat May 19 02:19:42 2012 No.4696310 >>4696306 what are you even on about

Anonymous Sat May 19 02:20:56 2012 No.4696313

>>4696305

I understand Manifolds as I'm an Algebraic Topology PhD student.

You are deluding yourself. The definition of manifolds that is used is way different to what Mathematician consider a manifold.

Not only that, but Calabi-yau stuff is closer to magic than Maths.

>>	Anonymous Sat May 19 02:21:41 2012 No.4696314 File: 31 KB, 265x350, 70870871094641.jpg [View same] [iqdb] [saucenao] [google] >>4696307 >implying you can't do analysis for the sake of analysis knowledge alone I think you need to look up the definition of pure math

>>	Anonymous Sat May 19 02:22:41 2012 No.4696316 >>4696310 I dunno. I guess my definition of pure math might just be too strict compared to most other people's?

>>	Anonymous Sat May 19 02:23:41 2012 No.4696319 >>4696314 Okay. Now you're just trolling to hide your butthurt. This is ridiculous. I'm going to sleep.

>>	Anonymous Sat May 19 02:24:57 2012 No.4696321 >>4696313 If you had a course in complex manifolds, there's nothing magic about calabi-yau manifolds. But sure, Mr Algebraic Topology PhD student, tell me more about how I am deluding myself

>>	Anonymous Sat May 19 02:26:41 2012 No.4696323 >>4696316 Your definition of pure math is just wrong then

Anonymous Sat May 19 02:28:56 2012 No.4696326

>>4696321
http://en.wikipedia.org/wiki/Calabi%E2%80%93Yau_manifold

Many different definitions.

Superstring theory assumption in them.

No mathematical proofs.

Not magic?

Cool story troll. Personally, I have never seen a paper written by a Mathematician on this subject. I've even read that big three page book on it titled mirror symmetries.

>>	Anonymous Sat May 19 02:31:11 2012 No.4696329 >>4696293 vectorial calculus

Anonymous Sat May 19 02:32:56 2012 No.4696332

>>4696313
Okay, you are clearly talking shit now. I attended a joint physics and math conference just a few weeks ago, and many of the talks were about Calabi-Yau manifolds. Most of them from mathematicians, and some from physicists. Some physicist talked about generalized complex geometry over projective varieties, is that "pure math" enough for you? Another research topic presented was investigations into minimal surfaces in hyperbolic spaces, can you guess whether that was pure math or physics? While its true that physicists and mathematicians use different words and styles, they often research very similar things nowadays.

Anonymous Sat May 19 02:36:12 2012 No.4696335

>>4696326
>Cool story troll. Personally, I have never seen a paper written by a Mathematician on this subject.
Maybe that's why you think they're magic? I mean, your ignorance is pretty obvious here.

A Calabi-Yau manifold is a compact Kaehler manifold whose canonical bundle is trivial. - this is from the wikipedia page you googled five minutes ago.
Here's an article with a bunch of sources on purely mathematical (Algebraic geometry and complex analysis, for the most part) aspects of Calabi-Yau theory
http://www.scholarpedia.org/article/Calabi-Yau_manifold

Go back to studying AlgTop.

Anonymous Sat May 19 02:38:41 2012 No.4696340

>>4696326
Both Calabi and Yau are mathematicians, you know. Calabi discovered these manifolds long before string theorists got interested in them, and Yau proved an important theorem about them, also before they got any use in string theory. If you check the references on the wiki page you get a whole bunch of math papers on the subject. But I guess you are just trolling.

>>	Anonymous Sat May 19 02:39:26 2012 No.4696342 >My "end game" is to master statistics and then apply concepts to quantum mechanics. Then major in Mathematical Physics, you silly git. You will not learn a lick of QM in a pure math program.

Anonymous Sat May 19 03:29:26 2012 No.4696430

I used to think the whole summer thing was a joke, then I saw this thread. OP: I have a friend doing what you want but he had to go via a masters in math first. If you're really wanting to do statistical quantum mechanics you will have to learn a lot of statistics, which means a lot of probability theory, which means a lot of analysis.

terence tao has a good blog (sometimes) about measure theory. Otherwise, stop reading elements immediately, that won't help you in the slightest. Do real analysis up to fubini-tonelli theorem (which will cover lebesgue measure theory ) then do complex analysis. Don't touch probability theory until you've learned measure theory as you will onlly have to relearn it anyway. good luck

captcha inuanus squire

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