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    Programs Math PhD shorter than physics PhD?

    Conjecture: Math PhD is generally(with appropriate definition of generally) shorter in duration than physics PhD. (PhD programmes in US is under consideration and universities in question are say top 10) Anyone with proof? I have an impression that math PhD is normally ~4 years whereas...
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    Math and physics program

    Ambitious but realistic? That is indeed an ambitious plan and I have nothing against your willingness and motivation to commit yourself to indulge in such courses but it does raise few questions... 1. Is it a realistic plan? Many of the courses you listed are quite advanced both in...
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    Masters necessary/unnecessary?

    In commonwealth education system we have BSc(3 years and equivalent to US BA 4 year system) --> BSc Honours (1 year of taking 'graduate' papers and we do a small research project) --> Masters (can take at most 2 graduate papers and we do a thesis) --> PhD (thesis) Now, from my understanding...
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    Masters necessary/unnecessary?

    I had hard time deciding over math or physics and now I am faced with another hard decision... Based on advices that I get, it's half half. Surely there are goods and bads for both options and if that's the case I might as well flip a coin and decide...
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    Masters necessary/unnecessary?

    Option 1: BSc(with Honours) (4 years) ---> PhD(overseas) Option 2: BSc(with Honours) (4 years) ---> MSc (1 year) ---> PhD(overseas) Until now I was considering taking option 1, but when I talked with my supervisor recently he advised me option2 with his reasons being: 1. For someone...
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    Meaning of 'Canonical'

    V is a canonical vector space, and so is V* above sentence still confuses me because how could you incorporate the meaning: 'without any choices having to be made' or 'independent of any choices made' then? i.e. V is a vector space without any choices of basis having to be made? is that...
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    Meaning of 'Canonical'

    I'm not exactly sure if this is the right place to post this, but assuming it is, what is the meaning of 'canonical'? Someone told me that roughly speaking, it means "given from God" or something like that, when I look up wikipedia it says "standard" etc, I read from books that it means...
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    Schools Seeking some info on MIT math graduate school

    you are saying top 20-25 schools are unreachable? are you saying this on your behalf or mine?
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    Schools Seeking some info on MIT math graduate school

    I thought Princeton and Harvard is beyond reach for ordinary people and I guess I should add MIT to the list. This makes me wonder, what schools 'are' reachable? Say, Stanford, Caltech etc? or they too are up there?
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    Schools Seeking some info on MIT math graduate school

    mathwonk, thank you for your suggestion of contacting listed people, however I noticed that all of them have somewhat different research interest to mine so I'm thinking of contacting department secretary first to guide me to correct person.
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    Schools Seeking some info on MIT math graduate school

    i see Thank you for your replies. mathwonk said "maybe good showing on the Putnam exam, would be nice." Unfortunately I'm not US resident and such competition is not very active in this country. To be honest that sort of thing is what I think will hurt my chances mostly because I came...
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    Schools Seeking some info on MIT math graduate school

    thanks for that info Thanks for that info I'm waiting for their reply at the moment, I think they are still on holidays I'm quite surprised that penn state university requires rather high scores, I guess I'm not very wrong in presuming that MIT probably requires say 3.9+gpa and 900+ gre...
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    Schools Seeking some info on MIT math graduate school

    Google is quite useless in seeking such information so let me try it here, in case anyone knows any others who got into MIT math graduate school etc The sort of information I'm seeking here is 1)expected GPA 2)expected GRE(subject) Also, do you have to be one of those gifted genius who...
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    Is Hom(Lambda^k(V),Lambda^(k+1)(V)) and element of End(Lambda(V))?

    I agree with matt grime Yes I agree with what matt grime said, When I carefully read the text again it said, "Let V-->Hom(Lambda^kV, Lambda^(k+1)V) be the action of V on LambdaV" and since action of V on LambdaV is precisely the homomorphism between V and End(LambdaV) I can see that an...
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    Is Hom(Lambda^k(V),Lambda^(k+1)(V)) and element of End(Lambda(V))?

    Sorry I don't know how to write in symbols so I'm using Latex codes, anyway, the question is as in title: Is an element of Hom(Lambda^k(V),Lambda^(k+1)(V)) and element of End(Lambda(V))? In words, is an element of the homomorphism between k th grade exterior algebra over V and k+1 th...
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    Question on quaternions

    I read in some text the following: Quaternion algebra becomes a normed vector(linear) space with appropriate norm ...(blah blah)... Also since every element has a multiplicative inverse it is a field. Now, what I find confusing is that according to above a mathematical object called...
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    Clifford algebra isomorphic to tensor algebra or exterior algebra?

    Unfortunately there seems to be a misprint in the paper I'm reading which is an introduction to clifford algebra, it says:(I highlighted in red possible misprint, either one of them has to be true misprint if you know what I mean) The Clifford algebra C(V) is isomorphic to the tensor algebra...
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    Difference between algebra and module?

    Obviously having been assigned two different terms indicates these two objects are different but as far as I know, algebra: vector space with the multiplication which takes two elements in vector space and give another in vector space module: vector space over ring(extending from field)...
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    Graded algebra - Z_2 grading?

    I see, thank you for that information. The example I have here is tensor algebra which it says has Z_2 grading. So I guess Z_2 grading divides tensor algebra into T+ and T- where elements of T+ has even degrees(including 0) and elements of T- has odd degrees? Now I'm thinking if any other...
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    Graded algebra - Z_2 grading?

    Hello, I think I have an idea of what graded algebra means but when people say it has Z_2 grading etc I'm puzzled. Could someone please help me out? By 'Z' I mean integers and '_2' means mod 2.
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    Question and answer on 'not exact' forms

    Thank you for your explanation, but all the things you wrote down I already understand. My specific question was interpreting the solution that lecturer wrote down, I'll write down again, suppose w=df where f is smooth on R^2\{0}. On R dp=df implies d(p-f) is constant. This contradicts that f...
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    Spivak calculus on manifolds solutions? (someone asked this b4 and got ignored)

    Does anyone know if there's worked out solution to the problems in spivak's calculus on manifolds? It's awfully easy to get stuck in the problems and for some of them I don't even know where to start... Also, if there isn't any, any good problem and 'SOLUTION' source for analysis on manifolds...
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    Question and answer on 'not exact' forms

    The question is: Show that on R^2\{0} (without zero), let w=(xdy-ydx)/(x^2+y^2) and show (a) closed (b) not exact. (a) is straightforward, and for (b), the following is the solution lecturer provided. Firstly convert to polar coordinates letting x=rcos(p) y=rsin(p) where p is supposed...
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    For x∈R^n define g:R->R by g(t)=f(tx) g'(t)?

    Have to use chain rule, so I was thinking, if we let u(t)=tx where x is the vector, then g(t)=f(u(t)) so dg(t)/dt=d(f u)(t)/dt=(df(t)/dt)u(t)+f(t)(du(t)/dt) but then I don't know what to do...
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    Statistical mechanics question

    x is supposed to be multiplication N number of molecules k Boltzmann's constant T temperature in kelvin Cv heat capacity
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    Statistical mechanics question

    Below 0.6K the heat capacity of liquid He is well represented by the equation Cv=(9.819 x 10^-3 K^-3)NkT^3 Given that transverse shear waves cannot propagate in a liquid, predict the phonon contribution to the heat capacity of He from the data c=238 m/s (speed of sound in liquid He) p=0.145...
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    I thought w(f) where w=dual vector f=vector is Reals?

    But lecturer said today that it's a function. So for example he said, if we have w x f where x is supposed to be tensor product, then w(f) x f can be written w(f)f without tensor product sign because w(f) is just a function...
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    Meaning of integrating exterior forms

    I don't think there are experts who can answer your nor my question.. sad.. T_T
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    Cartan forms and structure equations

    omg.. nobody answering... there aren't many people who understand these stuff eh?:rolleyes:
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    Cartan forms and structure equations

    Could someone explain these two concepts? What I need is the big picture of 'why' we need this, roughly 'what' these equations mean, 'where' its used etc Thanks in advance
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