Best of Luck for your Saturday Exam

amateur · Post by **amateur** » Thu Oct 16, 2008 10:02 am

Best of Luck To All Folks for their exam this Saturday.

Do share with us your experience (Make sure you don't violate any copyrights/ETS Statement of Confidentiality).

Nameless · Post by **Nameless** » Thu Oct 16, 2008 4:11 pm

Best luck for you guys on Saturday exam.
Please share with us your experiences

thanks so much and hope to hear best news from you guys

prce · Post by **prce** » Fri Oct 17, 2008 4:21 am

Couldnt manage to repass all the material for this week exam and also have major problems with the General GRE because of my English, so i have decided to go for next year admisions. However i am taking the exam tomorow just to build experience for the "real" april one.
When you people usualy apply to graduate study? In you last years at the universities or you give yourself a yesr to study?
Yesterday i found an interesting book in .pdf format and since the book is old and almost imposible to find i think its not anethic to post it here for you guys.

Mathematics: Subject Test/Advanced (Graduate Record Examination)
by Morris Bramson

This is the link: http://xinio.info/?http://ifile.it/ws1tgui/mathgre.pdf

If the admin find it unapropriate let him delete the link, and the others contact me on PM.

Best of luck to all of you.

prce · Post by **prce** » Fri Oct 17, 2008 4:28 am

Just for the protocol:

I found the book on Gigapedia.Org which is a wonderfull place and have (i think) the greatest colection of e-books on the net.

kaiserguy · Post by **kaiserguy** » Sat Oct 18, 2008 8:50 am

Well, that was tough. The consolation is that I if I found it tough, I suppose many other people did too. Thanks for all the help and well wishes. I'll post my score when I get it. Hopefully, I won't need to be asking you guys questions again this time next year.

Nameless · Post by **Nameless** » Sat Oct 18, 2008 11:35 am

kaiserguy,

Hope that we will hear the best news from you soon

Could you please post some questions on the test on here ?

thanks and best of lucks for you

prce · Post by **prce** » Sat Oct 18, 2008 3:33 pm

I found the today test not very difficult. I think i did quite well on the computational questions but went on guessing the Abstract Algebra, Complex Analisys and Topology one, and do "manualy" the Number Theory. I have a basis of arround 70% on all the practice tests i have taked but need to do a hard work to re-read the more advanced topics.
Some specific info of the test (hope not going against any thing i signed

):
The test had 2 questions from line and curve integrals, 3 from topology, 1 complex integral.
Just for you to evaluate if its worth studying in depth. Share you experiences please.

orangelights · Post by **orangelights** » Sat Oct 18, 2008 5:50 pm

Yes, the October 18th 2008 GRE Math Subject Test felt somewhat easier than the practice tests in the REA and Princteon Review books. I was was highly encouraged to be fairly sure of 24 of the first 25 problems, but then maybe fatigue set in and I ended up fairly confident on 50 of them and guesing on 5 of them. All in all a good effort though, better than I expected. Who knows when we can call for our scores? I want to determine if I should / have to take the test in November too. I'm just trying to get into some top 50 schools, I figure a score in the 700s should suffice. Lets hear other reactions.
Best,
Orangelights

tohauz · Post by **tohauz** » Sat Oct 18, 2008 6:57 pm

Well, for me it was pretty challenging
Time just flew by
I answered 59 questions and i just don't know what I'm to I get
Hope to get high score.

Nameless · Post by **Nameless** » Sat Oct 18, 2008 6:59 pm

Great to hear good news from you guys

By the way, I think there are many going to take Nov. Exam. I have some questions :

did you cover all review topic before taking the exam? did you encounter any questions which you did not know? and how many questions like that?

thanks and best of luck for all of us for Nov. Exam

tohauz · Post by **tohauz** » Sat Oct 18, 2008 10:22 pm

I think there were 4-5 question from Linear algebra (matrices of course, basis)
3-4 from Abstract Algebra(order of an element, generating element for a cyclic group and so on)
Some questions from advanced calculus, one of them just confused me so much, it seemed like all choices may be correct and at the same time they might me wrong! Can't recall the exact question now
One or two questions were from LOGIC.

Well good luck guys. I wish info above will be helpful

orangelights · Post by **orangelights** » Sat Oct 18, 2008 11:19 pm

I recomend going through the whole Princeton Review book the night before, not doing any problems, but just absorbing the facts they present. I knew I wasn't going to relearn DiffyQ in one night, it turned out to be much more useful to scan for facts to use as references. The test was very fair, I think I got a raw score between 40 and 50 which will get me in somewhere on my 15 school list so life goes on. Tohauz, congrats on answering 59 questions, I'm sure you did fine / better than me and there will be a place for you in a good program. Out of curiosity, what's your math area of interest?
Good luck future test takers,
Orangelights

tohauz · Post by **tohauz** » Sat Oct 18, 2008 11:31 pm

to orangelights:
I want to do some applied and/or computational math
what about you?

orangelights · Post by **orangelights** » Sat Oct 18, 2008 11:36 pm

Tohauz,
Discrete math, so Combinatorics and Graph Theory, though I did like Numerical Analysis and Probability, I'm kindof in the intersection of pure and applied. Mostly I'm applying to pure programs, but I'm looking at John Hopkins applied.
Go Red Sox

Orangelights

kaiserguy · Post by **kaiserguy** » Sun Oct 19, 2008 10:33 am

I think I messed up on time managment. It took me 1.5 hours to get through the first 33 quesitons. It usually takes me closer to an hour. Towards the end I had to skip quesitons because it would have taken too long to get the right answer. I was getting scores in the mid 80 percentiles in the sample tests and was hoping for a score in the 90s, but there's no way I got that. I'm applying to some top schools e.g. Cornell, Berkeley, Caltech, etc. Would a 70 score be good enough for them?

tohauz · Post by **tohauz** » Sun Oct 19, 2008 11:02 am

TO kaiserguy:
As i know for Berkley you need at least 80%.
I 've read this on their website

Nameless · Post by **Nameless** » Sun Oct 19, 2008 11:05 am

kaiserguy :Wow, I guess your profile must be above outstanding. I have never dreamed about such schools.

to get an admission to such schools, you must be excellent. I know one of my friend, he got 77% for GRE maths but still had an admission to Gatech

best luck for you

blp · Post by **blp** » Sun Oct 19, 2008 11:33 am

I thought that the test was a lot more time consuming than the practice tests. However, one person on the test told me that about 10 questions were identical compared to the November test a year ago.

I'm also applying to top 20 schools only and was hoping for a result somewhere in the 90%+ range. I had got around 94% on each of the old practice test, but on the older test from the 80s I got 66 questions correct, but the tests have gotten harder since. However, I messed up pretty badly yesterday after being incredibly stressed. I answered around 55 questions without guessing on any of them, but I know that I answered wrong on the first question and was extremely sloppy on one other and I think I added a few fractions incorrectly in some others. I had a nightmare experience on of the problems that was converted to an integral of the form:

20 - integral = ?

However, I managed to write

20 - integral = 10 - integral

after the first equal sign and tried to redo the exercise LOTS of times and each and every time I had written the same thing down getting an answer that was off by ten and way too small. Never actually got the answer right, so left it unanswered and was totally panicked after it which messed up the rest of the test.

The battery on my watch also stopped working during the test... talk about bad luck and stupidity for not changing the batteries! NOTE TO EVERYONE ELSE: CHANGE BATTERIES ON YOUR WATCH BEFORE THE TEST!!! I'm going to take it again next month though. Just hoping that there's room at my testing location for stand by testing.

tohauz · Post by **tohauz** » Sun Oct 19, 2008 11:57 am

damn, i couldn't do the second problem
I've already found one mistake
i'm checking my solutions now by doing the problems i can recall

kaiserguy · Post by **kaiserguy** » Sun Oct 19, 2008 12:09 pm

People from my college before have gone to Cornell, Berkeley and Stanford. I was told I was good enough to get into those schools. I have reasonable research experience but my poor GRE will probably be my undoing. It's okay though as Cambridge is my first choice. I too found the questions extremely time consuming. There was one question I think I spent close to 10 minutes on. That was an extremely bad idea and cost me dearly.

blp · Post by **blp** » Sun Oct 19, 2008 3:54 pm

The GRE seems to test as much how good you are taking tests than the actual math after you have reached a certain level. The point with it is pretty much that those who get top scores are certainly good, but it doesn't mean that those get worse scores are bad. That's where all the recommendations come in to play.

BTW, does anyone of you know when we get to know our raw scores? Do we have to wait for the actual scores being released?

orangelights · Post by **orangelights** » Mon Oct 20, 2008 12:04 am

Yeah its my feeling that a result below 80th percentile won't get you into a top 15 school. You never know, maybe you're above 80th percentile. This talk about actual test problems has started to scare me. Honestly I can only remember about 5 problems. Yeah when is the first possible time to hear our results?

tohauz · Post by **tohauz** » Mon Oct 20, 2008 12:30 am

SO, as I understand now the tests we're given were different from each other? I think mine of average diffuclty , i.e. B.
As for the raw scores, will we be able to see them online?

tohauz · Post by **tohauz** » Mon Oct 20, 2008 10:14 pm

TO PPL who took the test on 10.18.08
could somebody pls pm me the statement of the problem about epsilon-delta, where we're asked to find equivalnet statement to that given one.? i do remember all the 5 choices, but can't recall the exact problem
thx

chenxuwen · Post by **chenxuwen** » Tue Oct 21, 2008 9:50 am

I know that problem.

For any e>0, there exists a delta>0 st. for any d(x,1)>delta, d(f(x),f(1))>e. Problem is get a equivalent statement of this.

Answer is the limit is infinity as d(x,0) goes to infinity.
The other answer (unboundness) is not equivalent.

The whole exam is too consuming, I gave up a lot of integrals. I think I can get 57s right.

tohauz · Post by **tohauz** » Tue Oct 21, 2008 9:55 am

well i chose unboundedness
thx

amateur · Post by **amateur** » Tue Oct 21, 2008 11:45 am

I didn't give that test, so sorry to interrupt your discussion, but doesn't
f(x) = arctan(x) satisfy the statement of the question as you wrote it but lim x-> infinity f(x) = PI/2 ?

EDIT: Ok for e = PI/4 no value of delta exists. (That is, for e = PI/4, no matter how large a value of delta is chosen, the statement d(x, 1) > delta => d(f(x), f(1)) > e is violated (As its contrapositive d(f(x), f(1)) <= e => d(x, 1) <= delta is violated.

Am I right?

Amateur

chenxuwen · Post by **chenxuwen** » Tue Oct 21, 2008 1:00 pm

amateur

that's for any e.
i.e. just let e=100, 10000, 1000000, and so on, you see the answer.

chenxuwen · Post by **chenxuwen** » Tue Oct 21, 2008 1:02 pm

I guess that's a tricky one. Since epsion always going to zero. But this one is letting epsilon go to infinity.

In fact, d(f(x),0) >= e + d(f(1),0) by triangles inequality. then we see this is extractly equivalent to f going to infinity.

This also impies f is unbounded, but not equivalent.

Nameless · Post by **Nameless** » Tue Oct 21, 2008 1:13 pm

For any e>0, there exists a delta>0 st. for any d(x,1)>delta, d(f(x),f(1))>e.

Is the question : " find the equivalent statement for above statement ?"

Based on the statement, I guest f(x) --------->infinity when x!= 1

Is it correct ?

PS. Could you guys , who took the test last Saturday, try to remember the questions and post them on here so that we can discuss PLEASE ?:D

chenxuwen · Post by **chenxuwen** » Tue Oct 21, 2008 2:25 pm

I guest f(x) --------->infinity when x!= 1
What does this mean?

Nameless · Post by **Nameless** » Tue Oct 21, 2008 4:00 pm

I guest f(x) --------->infinity when x!= 1
What does this mean?

I mean based on your the statement above, we can construct a function f(x) that goes to infinity when x!=1 and f(x) can be any thing when x=1

blp · Post by **blp** » Tue Oct 21, 2008 4:11 pm

We're not allowed to post questions by the NDA we signed, so I would not start posting questions. I think the best way would be to exchange them by private messages between those who actually took the test...

As questions usually show up again on the tests, it's not actually in our own interest to share them to the world and give others an unfair advantage.

tohauz · Post by **tohauz** » Tue Oct 21, 2008 9:06 pm

I Fully support what BLP said

blp · Post by **blp** » Wed Oct 22, 2008 11:46 am

BTW, about the exercise you already posted. I was in a complete state of panic during that exercise and never managed to even read past the first answer choice, so I have no idea what the choices were. However, if it was given in exactly that way, then a function like

f(x)=(-1)^[x]*x (where [x] means the closest integer)

satisfies the condition, but it doesn't diverge to infinity as it keeps changing the sign between intervals of length one.

lime · Post by **lime** » Wed Oct 22, 2008 1:46 pm

but it doesn't diverge to infinity

Yes it does.

blp · Post by **blp** » Wed Oct 22, 2008 2:44 pm

Well, the way I've been taught is that a function diverges in that case, it's not said to diverge to infinity. The term diverges to infinity has been reserved for the cases that there's in an M>0 such that f(x)>M for all x reasonably close to whatever the limit is taken to mean. Similarly for the term diverges to the negative infinity.

I actually just looked up in Rudin, and I can't see a definition of "diverges to infinity" that would correspond to your interpretation. I'm actually quite amazed that ETS uses a question like this in the first place. Assuming that the problem didn't state that the absolute value diverges to infinity, which is equivalent.

EDIT: I take the symbol f(x)->\pm\infty to mean that either f(x)->\infty OR f(x)->-\infty. So my function doesn't fill the condition f(x)->\pm\infty, because neither of these conditions are fulfilled.

amateur · Post by **amateur** » Wed Oct 22, 2008 2:53 pm

Nice try, BLP.

The function f(x) = (-1)^[x]*x, is technically not a function as

f(5/2) = (-1)^[5/2]*5/2 = -5/2 if you consider the nearest integer to be 3
f(5/2) = (-1)^[5/2]*5/2 = +5/2 if you consider the nearest integer to be 2

Even if we fix the function by changing the word "nearest integer" with "floor" or "ceiling" function, it would still be discontinuous and so not make a very good counterexample to the
unbounded function claim.

If we consider f(x) = x sin x, where x is real and in radians, then although the function is unbounded, continuous and keeps fluctuating between -infinity and +infinity, but according to the statement of the question as posted here,

For any e>0, there exists a delta>0 st. for any d(x,1)>delta, d(f(x),f(1))>e. Problem is get a equivalent statement of this.

Try e = 800, delta = 1000, So let x = 1 + 1000 = 1001.

Then although d[ f(1001) - f(1) ] = 920.06911 > 800,

but for x = 1002

(Recall that the question says for any x such that d(x, 1) > delta)

d[ f(1002) - f(1) ] = 166.75 < e

and for x = 1005.31, d[ f(1005.31) - f(1) ] = 0.352

Infact d[ f(x) - f(1) ] can be made arbitrarily small by choosing x such that sin x = 0.

So the claim that f is unbounded does not satisfy the statement of the problem.

blp · Post by **blp** » Wed Oct 22, 2008 2:56 pm

There was no assumption that the function should be continuous (actually one of the answer choices was that the functions is NOT continuous!). And what I defined is definitely a function. Usually [x] is meant to round upwards when between to whole numbers, so it is well defined, but you can choose either way; it doesn't matter.

chenxuwen · Post by **chenxuwen** » Wed Oct 22, 2008 3:22 pm

I guess you guys can just write it out.
The def of d(f(x),0) converges to infinity is
For any e>0, there exits a delta, s.t.
d(f(x),0)>e, for all d(x,0)>delta.

So use triangle's inequality, we have this implie d(f(x),0) goes to infinity as d(x,0) goest to infinity.

In fact, y=x satisfies conditions.

blp · Post by **blp** » Wed Oct 22, 2008 3:26 pm

Ok, I didn't read the first post with the original statement, because what you wrote actually corresponds to the absolute value.