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AKG

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AKG

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- #2

Pengwuino

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- #3

JasonRox

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Pure Mathematics? Applied?

We need details.

We need details.

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AKG

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What is your dissertation on?

(On what mathematical topic?)

(On what mathematical topic?)

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A dissertation is usually something written in, not before, grad school...

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matt grime

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(nb I've chosen to omit Princeton from a classification since I don't konw much about the place, or more importantly I don't know what the intearction between the Department and IAS is like.)

The UK is much much different. As it stands there is little if anything in the way of graduate lectures in the UK; you just get on with your work. That is changing to reflect the knock on effect in changes in degrees, but right now you need to look carefully at your options here (not least for the funding). Cambridge is about the only place with the facility for graduate lectures (when you are able to participate in part III courses). Other places are trying to catch up, but it is a difficult thing to do because British mathematics departments are very small places. A typical department (ie not one of Cambridge, Oxford, Warwick, Imperial Durham, or Bristol) might have only a dozen PhD students if that, so don't be sucked in by one of the British univeristy's webpage which states them to be 'the best place for post-graduate study according to a recent survey' (of postgraduates).

(As a sample, Sheffield has 18 pure maths PhD students, exeter has 13 [in all areas of maths] any single London College might well be small, but they are all part of a larger organization and often have intercollegiate collaboration)

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AKG

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Thanks matt. What is IAS?

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AKG

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I believe IAS stands for the Institue for Advanced Study, at Princeton.

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- #12

matt grime

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If you like functional analysis and can stomach somewhere (small than) the size of Berkeley without the back up of the City 6 stops down the BART then Penn State has some great people to work with (Roe, Higson and Baum, for instance).

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Go to Berkeley. Say hi when you drop by too :)

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cogito² said:

Yeah (next year I will be a junior)

Well I do not want to derail this thread, so to the original threadmaker, I would like to wish good luck in whichever place you decide to go to.

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Hi,people.

I am a student in China.I am a freshman.

I find algebra and foundations of math (mainly set theory and logic for the moment) so fantastic to me.And I learn fast and have a strong willing to do math research after undergraduate study.

I wish I could go to Berkeley for graduate study and I wish you Berkeley guys could help me.

What text books are being used for the undergraduate students?What quality do I have to have to be admitted to the graduate school at Berkeley?Is it harder for a non-US student to be admitted?

Any guidance will be appreciated.

- #18

mathwonk

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In the old days places like Princeton expected you to finish in 2-3 years which is very fast for most people. Harvard may have allowed 4. Other places may allow more.

The key thing is finding the right relationship with an advisor. And these people change. One of my friends studied with Curt McMullen at Berkeley in topology but McMullen is now at Harvard after receiving the Fields medal.

I studied at Utah and found the ideal advisor for me in Herb Clemens, and Clemens is now in Ohio. In general, with the influx of superb foreign born mathematicians over the last decades, virtually all US math departments seem to be getting better and better faculty.

The locale is relevant to some extent. A place like Berkeley is exciting but for some much too expensive and hectic. Last time i was there the grad students were striking for higher wages and the place was shut down, and there was a lot of strife.

Wonderful as the mathematics is, my wife and I dclined to go to Columbia because raising kids in NYC seemed such a challenge. I suspect Michigan is a good choice, and Ann Arbor is a lovely little town.

But there are lots of options. It is useful to have financial support, helpful faculty, and a student body that supports each other and interacts mathematically.

And you might be surprized at what leads to success. Some of the strongest faculty our Univ has hired went to Yale, Berkeley, Princeton, MIT, but others have gone to North Carolina, Brandeis, Utah, Queens in Ontario,...

I suggest looking at the webpages of the deprtments to see who is there and what their interests are.

- #19

mathwonk

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another thing to do is try to get an idea of the prelim requirerments, how many prelims you must pass, how long you have to pass them, what they look like.

some of this information is also available on websites under information dfor students. e.g. at UGA the website has a section called info for grad students, including prelim syllabi.

here is an old one from UGA in algebra:

some of this information is also available on websites under information dfor students. e.g. at UGA the website has a section called info for grad students, including prelim syllabi.

here is an old one from UGA in algebra:

Last edited:

- #20

mathwonk

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UNDERGRADUATE MATERIAL

Group Theory:

subgroups

quotient groups

Lagrange's Theorem

fundamental homomorphism theorems

group actions with applications to the structure of groups such as the Sylow Theorems

group constructions

such as:

[free groups

generators and relations]

direct [and\0 \0s\0e\0m\0i\0-\0d\0i\0r\0e\0c\0t\0] \0p\0r\0o\0d\0u\0c\0t\0s\0

\0s\0t\0r\0u\0c\0t\0u\0r\0e\0s\0 \0o\0f\0 \0s\0p\0e\0c\0i\0a\0l\0 \0t\0y\0p\0e\0s\0 \0o\0f\0 \0g\0r\0o\0u\0p\0s\0

\0 \0s\0u\0c\0h\0 \0a\0s\0:\0

\0p\0-\0g\0r\0o\0u\0p\0s\0

\0[s\0o\0l\0v\0a\0b\0l\0e\0 \0g\0r\0\0\0o\0\0\0u\0\0\0p\0\0\0s\0]\0\0\0

\0\0\0d\0\0\0i\0\0\0h\0\0\0e\0\0\0d\0\0\0r\0\0\0a\0\0\0l\0\0\0,\0\0\0 \0\0\0s\0\0\0y\0\0\0m\0\0\0m\0\0\0e\0\0\0t\0\0\0r\0\0\0i\0\0\0c\0\0\0 \0\0\0a\0\0\0n\0\0\0d\0\0\0 \0\0\0a\0\0\0l\0\0\0t\0\0\0e\0\0\0r\0\0\0n\0\0\0a\0\0\0t\0\0\0i\0\0\0n\0\0\0g\0\0\0 \0\0\0g\0\0\0r\0\0\0o\0\0\0u\0\0\0p\0\0\0s\0\0,\0 \0c\0y\0c\0l\0e\0 \0d\0e\0c\0o\0m\0p\0o\0s\0i\0t\0i\0o\0n\0s\0\0\0

\0\0\0T\0\0\0h\0\0\0e\0\0\0 \0\0\0s\0\0\0i\0\0\0m\0\0\0p\0\0\0l\0\0\0i\0\0\0c\0\0\0i\0\0\0t\0\0\0y\0\0\0 \0\0\0o\0\0\0f\0\0\0 \0\0\0 \0\0\0A\0\0\0n\0\0\0,\0\0\0 \0\0\0f\0\0\0o\0\0\0r\0\0\0 \0\0\0n\0\0\0 \0\0\0> \0\0\04\0\0\0\0

\0

\0L\0i\0n\0e\0a\0r\0 \0A\0l\0g\0e\0b\0r\0a\0:\0

determinants, \0

eigenvalues and eigenvectors

Cayley-Hamilton Theorem

canonical forms for matrices

l\0i\0n\0e\0a\0r\0 \0g\0r\0o\0u\0p\0s\0 \0(\0G\0L\0n\0 \0,\0 \0S\0L\0n\0,\0 \0O\0n\0,\0 \0U\0n\0\0)\0

dual spaces: definition, dual bases, pull back, double duals.

finite-dimensional spectral theorem

GRADUATE MATERIAL (MATH 8000)

Foundations:

Zorn's Lemma and its uses in various existence theorems such as that of a basis for a vector space [or the algebraic closure of a field], and existence of maximal ideals.

T\0h\0e\0o\0r\0y\0 \0o\0f\0 \0R\0i\0n\0g\0s\0 \0a\0n\0d\0 \0M\0odules

basic properties of ideals and quotient rings

fundamental homomorphism theorems for rings and modules

characterizations and properties of special domains

such as:

EUCLIDEAN IMPLIES PID IMPLIES UFD

classification of finitely generated modules over Eucl dom

applications to the structure of

finitely generated abelian groups and

canonical forms of matrices

[Noetherian rings and modules]

[tensor products of vector spaces]

Field Theory:

algebraic [and transcendental] extensions of fields

fundamental theorem of Galois theory

properties of finite fields

separable [and inseparable] extensions

computations of Galois groups of polynomials

of small degree and cyclotomic polynomials

[elementary symmetric functions]

[solvability of polynomials by radicals]

References

[1] Thomas W. Hungerford, Algebra, Springer, New York, 1974.

[2] Kenneth Hoffman and Ray Kunze, Linear Algebra, Prentice-Hall, 1961.

[3] Nathan Jacobson, Basic Algebra 1, W.H. Freeman, San Francisco, 1974.

[4] Nathan Jacobson, Basic Algebra 2, W. H. Freeman, San Francisco, 1980.

[5] Serge Lang, Algebra, Addison Wesley, Reading Mass., 1970

- #21

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Many of the answers you're looking for can be found by fishing around on their home pageGreenApple said:Hi,people.

I am a student in China.I am a freshman.

I find algebra and foundations of math (mainly set theory and logic for the moment) so fantastic to me.And I learn fast and have a strong willing to do math research after undergraduate study.

I wish I could go to Berkeley for graduate study and I wish you Berkeley guys could help me.

What text books are being used for the undergraduate students?What quality do I have to have to be admitted to the graduate school at Berkeley?Is it harder for a non-US student to be admitted?

Any guidance will be appreciated.

http://math.berkeley.edu

you can find a book listing by clicking on "courses" and selecting a particular semester or looking in the course archives.

Under the "Graduate" Section you can find a lot of useful information about the admissions process and what their looking for in a candidate.

- #22

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Thanks for all your help.All the informations are usefull to me.

- #23

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Oops didn't notice this. Send me a message next year and we can kick it.BryanP said:Yeah (next year I will be a junior)

Well I do not want to derail this thread, so to the original threadmaker, I would like to wish good luck in whichever place you decide to go to.

Also if anyone else has anymore international information I'm still all ears. :D

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