Applying to Graduate School in the U.S.A.

(click here if you want to open this page on full screen, e.g. for printing purposes)

On this page you will find the following paragraphs (click to view the paragraph):

INTRODUCTION
WHAT YOU WILL NEED TO DO

DEADLINES OF APPLICATION
QUALITY OF UNIVERSITIES: DOES IT COSMICALLY SPEAKING MATTER?
QUALITY OF UNIVERSITIES: RANKINGS
THE COST OF APPLYING
HOW MANY UNIVERSITIES DO I APPLY TO?
WHICH UNIVERSITIES DO I APPLY TO?
HOW LONG WILL A PH.D. TAKE?
GRE TESTS
HOW IMPORTANT ARE GRE SCORES?
UNIVERSITY SYSTEMS
FINANCING YOUR STUDIES
WHAT QUESTIONS TO ASK
REFERENCES
STATEMENT OF PURPOSE
C.V.
TRANSCRIPT
WHAT TO DO WHEN OFFERS COME IN: DECLINING AN OFFER
MAKING THE FINAL DECISION
LINKS, ADDRESSES, TELEPHONE NUMBERS




INTRODUCTION
This guide should help you apply to graduate courses at American Universities (by which we generally mean Ph.D. courses). As most websites are in English, whoever may be reading this guide can find most of the information about applications elsewhere in English. What you are unlikely to find elsewhere, though, are all of the links and the informal guidelines that I have written for you. They are pretty much all that which I would have liked to have known when I was an undergrad student facing the application processes in the States for a doctorate course in mathematics. I will try to give as much general information as possible, but here and there I will make remarks about specific aspects of interest to those pursuing a mathematics degree.

Whoever has reached this site in the intention of finding information about an MBA (i.e. business studies) or other specific genres of studies (e.g. professional schools), should try to look up and contact directly their Universities of interest.

Regrettably, I am also unable to help you on the application process to undergraduate studies in the States, of which I know virtually nothing. A very instructive and comprehensive guide is: Thomas Sowell: Choosing a College. I understand that generally speaking the following remarks are true about undergraduate studies in the States for Europeans:
(1) it can become an extremely expensive undergraduate course and there is virtually no funding or scholarships;
(2) you will most likely have to study several subjects not directly pertinent to your major subject of interest (for instance, you may major in mathematics, but you may have to take other courses such as philosophy of science or even subjects in the humanities) which means that you may not be specialized in your major subject as you would after a European undergrad course;
(3) remember that there will be early deadlines (1 year before end of high school), you will have to do an English test (TOEFL), you will have to do standardized tests (SAT or similar), and you will need to get an immigration visa if you are not American. Seek elsewhere for further info on undergrad studies in the States.
You may for example like to read the newsgroups on college education (see google newsgroup search), and you will surely find lots of information on the websites of the American institutions of interest (generally speaking, undergraduate studies are referred to "college" and graduate studies to "university", and indeed some schools are called "colleges" because they only do 4-year undergrad courses, whereas other schools are called "universities" because research and graduate studies play an important role).

My personal information is as follows: I have studied mathematics at the University of Cambridge (U.K.) both undergrad and the so-called Part III mathematics course ("CCASM", or "Cambridge Certificate of Advanced Studies in Mathematics" equivalent to a taught Masters course), I did a Master of Science at the University of Chicago, and I am now attending MIT to complete a Ph.D. in pure mathematics. I would summarize my experience with the following assertions:
1) the most important thing is who your advisor is and how much he will help you to get an academic job when you get your Ph.D. If your advisor won't help you find an academic job then even brilliant students will be in trouble.
2) as to rankings: if you are really brilliant, then it won't matter where you go since your publications will speak for themselves, but if you aren't brilliant then it clearly helps to come from a prestigious department.
3) a good and kind advisor at a lesser department is better than a bad or evil advisor at a prestigious department.

As I am European and I studied mathematics at the University of Cambridge, my experience may widely differ from that of, say, an American student coming from an American institution. For instance, I suspect that all issues about funding will greatly differ: a non-American student will generally not have access to American funding external to the university (such as NSF), and he will most likely receive teaching assistantships, research assistantships or fellowships from the university. A non-American will certainly have access to Fulbright scholarships, their only caveat is that you are generally obliged to return for two years to the country issuing the scholarship.

Finally, to avoid all silly emails, I would like to stress that this guide is subjective, so I won't refrain from advising you to prefer some university to another, and I may make biased comments. When guides become too official and objective, they tend to become plain and unhelpful, therefore I hope to have spiced it up with enough personal comments to make it somewhat helpful. I apologize for any mistakes or misconceptions which there may be, and I'd like to recall that this is a non-profit free website which I develop with the sole intention of helping others or of uploading interesting information for everyone on the web.


WHAT YOU WILL NEED TO DO
Here is a quick list of things that you will need to do, in order to apply to a graduate course in the States. I will go into the details of each of these topics later on. You will need:

- three reference letters from your professors
- a Statement of Purpose (an essay describing your intentions at grad school)
- official signed stamped sealed transcripts of your academic results (undergraduate marks)
- take the GRE General test and ask for official scores to be sent to the institutions you apply to.
- you may have to take the GRE Subject test (depending on the grad program and university), and again report the scores officially.
- you may have to take the English language TOEFL test (only non-Americans, but depending on the State sometimes even students from English-speaking countries! e.g. Pennsylvania requires it from all non-Americans)
- various forms which vary from university to university (e.g. personal info, CV-type questions, etc.)

Almost all universities now have online applications. This means you will use the internet to apply formally to the institution you are interested in: name, date of birth, address, institution, undergrad marks, etc. And you will have to pay (the most convenient is Visa Card, but there are several solutions) an application fee which is usually around $60.

You will, however, have plenty of material that needs to be sent by mail (e.g. transcripts and references). You may want to send these things with "certified mail", i.e. "with return receipt". This will confirm that the material has arrived at destination. Some universities even have an online checklist which tells you what material has reached the university (e.g. Princeton keeps such a checklist online). You could also inquire via email, but remember that the admissions offices can be very busy.


DEADLINES OF APPLICATION
The first very important advice is: the application deadlines to universities are rigid and early. The deadlines for American graduate schools vary from university to university, but generally speaking the earliest deadlines are 1 December and the latest are 1 February. So generally speaking, here is a typical timetable:


August

- Look at the university rankings and use them as a list to search the universities' websites. Look up the faculty in your area, write down the names of the professors and their research interests for each university (some sort of summary that you can show to your professors when you ask them for advice and which will help you to make your decisions).

- Look up other guides apart from this one (although my guess is that you have seen quite a few guides before you found this one...) and try and make some sense out of all these biased comments.

- Buy a couple of books on the GRE test (for the "General test", and for your "Subject test" e.g. in my case: Mathematics), I will comment more on this later. Practice all the time until your test dates. It is essential that you do well on these tests.

- Write your CV and Statement of Purpose, and keep writing and rewriting them until they are perfect. More on this later.

Early September

- Email the faculty of the universities you are interested in. Ask them for info (see later comments on how to choose a university).

- Telephone the relevant institution that organizes the standardized GRE tests in your region, see www.gre.org (the "General GRE test" comprises English, Math and an Essay; the "Subject GRE test" will be math, physics, etc. depending on what you study). You may also have to apply for the English test called TOEFL (if you are not American, and sometimes even when you are English mother-tongue but non-American!). Make the appointment for early in October. When you arrange your Subject GRE (and only in this case) you will be required to list four universities to which scores will be sent, so you will need to know already four universities to which you will apply. This should not be hard, just mention those places that you really really want to get into. After having taken the test, you can then ask for scores to be sent to other institutions (paying additional fees of course). See comments on GRE/TOEFL later.


End of September
- Order the email comments from faculty. By now you should have a clear idea of where your area of research is represented, who are the good people in your area, and where you should apply to (try and get a list of some twenty places, and reduce down as you go along).

- Contact your own professors, and talk to them about your intentions. Show them the list of professors and universities that you have looked into. You may find that some of your professors will just dismiss you by saying "it's up to you, your decision" and others will go through your list one-by-one and give insightful comments. For example, a couple of my professors sang praises of most of the Chicago faculty, so that helped a lot in my decision of where to go next. It is unlikely that they will say something negative about a professor or a university, so you will have to weigh the words. I mention in passing that your professors' comments should count a million times more than rankings, in case that wasn't clear to you. You might like to discuss your options also with grad students at your university and other colleagues of yours. You will find lots of opinions, the problem is just choosing how much weight to assign to each. Also, show your CV and Statement of purpose to professors, colleagues and friends, and make sure they are perfect.

- You should have a final list of universities to apply to by the end of the month. Apply to a couple more if you are unsure of which ones to pick. Also, you never know if your interest shifts after this last year of university, so have some all-rounded good universities on your list as well.

Early October
- You better be ready for the GRE! Make sure you don't mess up. You will want to have your list of universities ready for the GREs: at the end of them, you will be asked for four universities to which scores will be sent "for free". Additional score reporting is donve via a 'score reporting request form' and you will need to pay a fee for each institution that you want scores to be sent to (something like $15). Note: it takes up to a month for the scores to be sent to an institution (a month from when you took the test).

- You ought to know English, so TOEFL should be easy. The main difficulty here is: don't fall asleep during the test! TOEFL is tremendously long and boring.

End of October
- get all the paperwork done: have a super-polished absolutely perfectly written CV ready, have all relevant forms for each institution printed and compiled (some of these need to be filled in and signed by your referees), make sure your Statement of Purpose is topnotch. More on this later.

- Ask your professors for references. You will need three references. Some universities also want professors to fill out certain additional forms. Some universities want the professors to send the references directly by mail, some give the option of computerized references, other universities want you to send the references in sealed signed envelopes (ask the professor to seal the envelope, sign it across the flap, and ask them to put sellotape on top of the signature: this is a standard procedure).

Early November
- Your references and paperwork should be ready. Last chance to change things.

- Careful about fellowship deadlines for U.S. citizens (e.g. NSF and NPSC graduate fellowships). I am unable to help you with these details, but you will surely find many websites on this matter.

End November
- middle of November: send off everything so that you are sure the mail will reach its destination before the deadline. The worst mailing-scenario is 10 days (from Europe).

December/January
- By this time, everything is done, and you can only wait now...

February
- This is when some good universities send out their first bunch of offers. In general, this means they really want you, and they tend to be good offers. You are not required to decide on the offer until April 15 (the exact day may vary, check the regulations for your year of application). There is a general agreement among U.S.institutions that no one should be forced to make a decision before this date.

March
- Offers will come in until the middle of March, anything after that is because a place has just been freed, or you were on the waiting list or other reasons. When you have made your decision, you should tell your university as soon as possible. Tell all other universities that you regrettably decline their offer.

April
- Careful about the deadline, after the deadline your offer may be withdrawn.

May
- Start loving your new institution, and start hating all the bureaucracy. If you are not American, you will have to ask your university to arrange to obtain the forms required for a "nonimmigrant visa form". Most students come in with an "F1 student visa" (and you will need an I-20 form compiled, signed and stamped by your American institution), other special cases are J1 if you come with certain special scholarships (e.g. Fulbright). You must inquire about these things with your new institution.

June
- You should now have received the forms required to apply for a visa (non-Americans): look up on the Internet where you must go to get your visa (it will depend on where you are resident, not so much your nationality). Call the relevant U.S.embassy and ask for visa services. They will arrange an interview and they will tell you all the things you need to bring and pay.

July
- Get your visa interview done (non-Americans) and get your medical history certified (for insurance purposes, if your university requires it).

August
- Make sure you have your visa (non-Americans), passport, forms, admittance letters, medical history, etc.

September
- The graduate school should start in the middle of September.

QUALITY OF UNIVERSITIES: DOES IT COSMICALLY SPEAKING MATTER?
This seems to be a big business in the States: journals with rankings, websites with rankings, etc. For undergraduate education, I can see the point of helping high-school students to find a good place to study and get a decent education, and in this case rankings can be quite informative. For instance, if you look at the statistics (which I have not and do not intend to!) you will probably find that the students in the top thirty or top twenty universities/colleges will have a far higher rate of students pursuing further studies (Ph.D., MBA, etc.) than at the lower end of the rankings, and you will probably have a correlation between higher salaries and higher ranked schools (although there may be social reasons for this, as top ranked private schools are generally also the most expensive ones).

For graduate courses the situation is quite different. If you are a serious scholar then you will already know where some excellent professors in your field are (otherwise ask the professors at your current university), and there is no reason to assume that the best in your field are in Princeton, MIT, Chicago, Berkeley or Harvard! Indeed, if you are a mathematician you should know that certain areas of research are totally absent in some universities and are central in others. For instance, if you want to study abstract functional analysis (Banach algebras) you will seriously consider UCLA (University of California Los Angeles) and you won't even apply to Harvard or MIT. On the other hand, if your interest lies in algebraic geometry, the situation is reversed, and you ought to seriously consider Harvard, Chicago and Princeton, and not so much Californian universities (sometimes it is even true that certain areas of research are better represented only on one of the two coasts!). These remarks about mathematics also make sense in other areas, for instance in economics or philosophy you may want to choose the university also with respect to the line of thought of the institution (e.g. think of the "Chicago school" which revolutionized ideas in macroeconomics).

Another important point to be made is not to be fooled by "name-isis": just because you have heard of Harvard before does not mean that their graduate school in biology is fantastic, it may not be: I have no idea. My point is that it is more likely that you have heard of certain universities from films or from their fantastic football teams, rather than for the current research groups they currently have in your area! So "name-isis" can be a sound way of choosing a university for undergrad studies or if you want to go into business, but if you want to attend graduate school you should consider matters more seriously.

There are certainly better known universities (I don't know if it is because of football clubs or because they have huge marketing teams or because of a self-preservation word-of-mouth information-spreading), for instance most Europeans, not necessarily students, will know: MIT, Harvard, Yale, University of California Berkeley. An example and justification of my previous paragraph is that Europeans know of MIT in particular because of many articles on robotics in popular journals which praised the MIT research teams. This list becomes longer for Europeans undergraduates: they will usually have heard of MIT, Harvard, Yale, Berkeley, Princeton, Stanford, Chicago, Cornell, Caltech, and after that it gets sort of hazy. This is really a pity, since it obviously leaves out very many fine institutions which are certainly on par if not even better in some areas. For instance, Univ. of California Los Angeles, Univ. of Wisconsin, Univ. of Michigan, Brown, Texas-Austin, Penn State, Johns Hopkins, etc. Like a Pavlovian dog, most Europeans will certainly react to the words "Ivy League", far less of them will react if you ask them which universities it comprises (you'll probably get Harvard and Yale out of them, but not more), indeed some even start mentioning Berkeley and Stanford. So, to make this long story short: take your graduate application more seriously than just "I've heard of such-and-such a name before ... ".

My personal experience was as follows: my initial interest was in abstract functional analysis, so after

- discussing the matter with my professors,
- looking up who publishes papers in that area,
- checking the Internet addresses of the mathematics faculty (i.e. the list of professors, their research interests, etc.),
- looking up the speakers of talks and conferences in my area of research,

then and only then could I conclude that some very serious places to consider were Berkeley, UCLA (Los Angeles), Penn State, and Texas-Austin. There are of course some other very good universities in functional analysis, such as Vanderbilt and Texas A&M, which I didn't have on my list. Moreover, contrary to all preconceptions, the faculties of Princeton, Yale, and Harvard, and generally speaking 'the East coast' universities had virtually no abstract functional analysts (here I'm excluding applied functional analysis, which on the other hand is very well-represented there, e.g. the Courant Institute in New York). I was also interested in the interplay of analysis and geometry, and so - again, search the Internet, talk to professors, look up the conferences and who is lecturing - I found that Chicago, Princeton and Berkeley had some of the finest faculty in that area (but don't say "unsurprisingly" - compare this with the functional analysis situation above!).

One of the important advises I can pass onto from those who advised me: do not just apply to Princeton! (and "do not just apply to Ivy Leagues", "do not just apply to Harvard", etc. whatever variant pleases you more). You may think that you are clever, but that is by no means the same as believing that you are cleverer than others. The competition, especially in pure mathematics, is tremendous. In pure mathematics, if you are the best student (and I mean number 1, not 2 or 3), and you have produced some astounding proofs or solutions in your undergrad years, and you have a perfect C.V., and you have perfect GRE test scores, and you have attended a topnotch university, then.... maybe.... and I repeat: maybe, you have a chance of getting into those ivory towers like Princeton and Harvard. But don't even think of setting your hopes on it. This also means, on the other hand, that you should not be discouraged if you do not get into some place. It is inevitably going to happen, in fact it is not a bad sign if it happens because it means you have attempted all ranges of difficulty and you finally got accepted by those programs that expect you to do well in their university. Just because you were not admitted to some university does not mean you were not good enough: for instance, in my year (2003/2004) it was particularly hard to get into the top state universities of California (such as Berkeley, and Los Angeles) because of economical difficulties: the state of California was virtually bankrupt, the state universities were having huge deficits, and so the intake of graduate students was reduced (e.g. by 40% in Berkeley's mathematics department), of which you can bet that foreigners (non-U.S. citizens) were the first to suffer (since these students usually get a $17,000-$20,000 teaching salary per year from the university since they are not entitled to outside U.S.-national funding). So getting into American universities can sometimes be a lottery game. Generally speaking, private universities will have more stable economies, and not have these ridiculous "ups and downs" in the size of intake of grad students (if it was hard to get into Berkeley that year, then halving the intake of students made it even worse). Another thing to remember is that it is much easier to get into graduate school as an American, since many will receive little to no university funding. On the other hand Europeans cost money to the university (they don't pay tuition fees, and they get a salary!). So you may have a university that takes 30 graduate students, and of these, say, 20 are Americans, and only 3 are Europeans. So it's tough competition.

I think it is indispensable that you read the following excellent article from the University of Chicago Magazine:
News you can abuse: a critique of U.S. News rankings and rankings in general.
It is a witty but accurate account on what's behind rankings, and how you should be careful not be mislead by them.


QUALITY OF UNIVERSITIES: RANKINGS
To help you get a feeling of what universities are reasonable choices, and to get a general overview of which departments are strong in your area, here is a list of rankings (many of them are for mathematics only, but I will give some links to other subjects as well). There are plenty of websites which warn you against the indiscriminate use of rankings to make your decisions, so I probably don't need to say more than what I have in the previous few paragraphs. In any case, let me summarize once more explicitly here: do not fool yourself in thinking that there is a difference between universities that are just a few places apart (e.g. 6th and 10th). Indeed, in the course of your five years of grad study these places may well change a little. For instance, there has been a critical study of the U.S. News rankings (somewhere on the web) where it was shown that the top ten universities could be arbitrarily shuffled around, depending on how much weight you put on the various indicators (citations per faculty, time to graduate, GRE scores, etc.), and it would not surprise me if you found out that these weights were tweaked to make certain universities rank on top. A similar thing happened in the U.K. with the eternal competition between Cambridge and Oxford: in the The Times Good University Guide (2003) even though Cambridge had better scores in all indicators that had to do with education (teaching assessment, research assessment, entry standards, student: staff ratio, firsts and upper seconds, efficiency graduate destinations) for the first time in a few years Oxford was placed 1st instead of Cambridge. So how is that possible? They had introduced two new indicators: library / computer spending and facilities spending, and these were given enough weight to place Oxford first. You draw your own conclusions!
The danger of having numbered lists (i.e. 1st, 2nd, 3rd, etc.) is that it may give you the illusion that such a numbering is meaningful. In fact, on most official websites of various councils on national research, such as the AMS, you will more often find universities grouped in tens or twenties (especially in "tier groups"). Also, the existence of sometimes widely differing rankings should get you thinking. So read these with a pinch of salt. In fact, I urge you all to read the following article by the great (Chicago) mathematician Saunders Mac Lane, What ranks for research doctoral programs?

The most respected rankings (and those least likely to suffer the bias of marketing and fraud), are those by the National Research Council (NRC), by the title: Research-Doctorate Programs in the United States. These are published by NRC approximately every ten years (1982, 1995 and soon: 2006), which are usually long (two or three year) surveys involving indicators which also take into account a variety of statistics of the faculty's research:

NRC Ranking of Mathematics Programs 1995 and 1982
NRC Ranking of Mathematics Programs 1995 Details
NRC Rankings of all subjects: a huge list compiled by H.J. Newton
NRC Rankings of all subjects: these can also be customized to your own preferences
NRC Rankings of all subjects 1995: This contains the "top 10" in all graduate programs. It is from Berkeley's website as you will surely notice, indeed you may also like to read Berkeley's interesting account on graduate study in the U.S.
Why Graduate Mathematics?: SUNY-Potsdam guide, containing some words of caution about NRC rankings and its methodology

More rankings:
Gourman Rating of the Top 50 Graduate Schools
Gourman Ranking of Graduate Schools in Mathematics
Practical Guide to Ph.D. Admission: contains the 1993 Gourman Report (to view *.ps files go here)
A collection of links from www.phds.org
Massive Graduate FAQ guide: you will find rankings in many areas (also for Canada and the U.K.!)
Philosophical Gourmet: contains general and philosophy rankings
Law rankings

The very questionable U.S. News rankings:
Graduate rankings
Undergraduate rankings (National Universities, not Liberal Arts Colleges)
College rankings (here you find the latest undergraduate rankings)

Here are two very informative guides on why (U.S. News) rankings are questionable:
News you can abuse: published by the University of Chicago Magazine, a critique of U.S. News rankings and rankings in general. It is a witty but accurate account on what's behind rankings, and how you should be careful not be mislead by them.
Brian Leiter: A ranking of U.S.universities by undergraduate educational quality 2001

You should also read the article on rankings by the great mathematician Saunders Mac Lane:
What ranks for research doctoral programs?

The following is useful for mathematicians:
AMS Assistantships and Graduate Fellowships in the Mathematical Sciences (try Google-searching this title to find a more recent edition of this)

I have no idea what the following are, but maybe some of you may find them useful or interesting:
U.S. News rankings of institutions (undergraduate) 1991-2001 (National Universities, not Liberal Arts Colleges)
2001 Lombardi Research Report: The Top American Research Universities (0.5 MB file!): a 150-page statistical analysis, contains lots of data (endowment, SAT scores, etc.).
Princeton Review 1999: Undergraduate Overall Academic Rating
Princeton Review 1999 and 2000: Undergraduate Competitiveness

Only out of interest and curiosity:
One-liner descriptions of the famous institutions (from the Fiske Guide to American Universities and Colleges 2001)
Gourman Rating of the Top 50 non-U.S. Graduate Schools (anyone familiar with Europe will get a laugh out of this one, and in fact this proves how meaningless rankings can be)
Student Reviews of undergraduate life at all institutions
2002 - 2003: Reviews of Universities across the globe, especially U.S.A. (sometimes in French!)
Thomas Sowell: Choosing a College: for undergrad, but contains some interesting ranking tables
Random comments on masters in computer science: and I mean random! This is for amusement only.

For those who are still convinced that rankings should be taken very seriously, you may like to consider the following amusing ranking:
Shanghai Jiao Tong University - Institute of Higher Education: rankings of all world universities
This is interesting because it illustrates the difficulties of creating a meaningful ranking (see the explanation of the methodology).


THE COST OF APPLYING
This is unfortunately not a joke. You will find that the expenses all add up to quite a big figure. Here is an indication:

- application fees: approximately $60 per application
- GRE testing fees: approximately $200 (since you pay for each institution that you report your scores to)
- TOEFL testing fee: approximately like the GRE testing fee
- travelling expenses: if you intend to visit the universities. You may get some/all costs refunded from the institution (ask!). Europeans can expect this to cost around $800.

Note that your university/college may refund some of the costs of applying to graduate school (ask!).


HOW MANY UNIVERSITIES DO I APPLY TO?
Since acceptance to graduate school is competitive and sometimes much like a game of lottery, it is customary to apply to approximately 10 universities, of which

- 2 or 3 will be hard to get into, [e.g. "top 10" universities]
- 3 or 4 you should get into, [e.g. 10-25 in the rankings]
- and 2 or 3 sure-shots. [e.g. low ranking but good in your area]

I hate using the rankings, but I guess I have to give some sort of guideline. Of course it depends on:

- what you want to do afterwards
- how good you are

So for instance, if you go into business it won't matter too much where you go (except if you want to be on the high-end of the scale, in which case you should get an MBA from a "top 5" university, I guess). If you go into academia, it is frightfully important that you keep a clean CV (i.e. top scores, no gaps, top universities, etc.) -- you may complain that this is not essential, and that may well be true, but it still helps!
If you are not so much interested in the high-end, and you are just out to get a good degree and some fun, then forget about rankings and choose a place that you like.


WHICH UNIVERSITIES DO I APPLY TO?

This is the hardest part of the process, and the lengthiest. I took me three months to decide which universities to apply to (after all, you pay $60-$80 per application, and these soon tend to add up to a huge $-figure). Some websites say: scroll along the rankings, pick among the high end, a few on the low end, and then when you get the offers take the highest ranked. It's not as easy as that.

Step 1. So first of all, to decide where to apply to:

- ask your professors: who are the topnotch researchers nowadays? where are they? what do they work on?
- ask some older students: where have your colleagues gone to? what places do you recommend?
- what are my job prospects after going to this university (in academia and in business)? will they help me to find a job? do they care about their students? do they keep a record of their students? do they know where their students went?
- who are the speakers at talks and conferences in my area of interest? look these professors up, look at their CV, their research interest, their past Ph.D. students, where are their Ph.D. students now?
- have a quick look at the rankings to know which universities you want to look up on the Internet, look up their program description: how is it structured? will I have exams? when can I start research? how are research advisers assigned? do I get a teaching assistantship? or a research assistantship? how many hours do I have to teach? how bright will my students be? how bright will my peers be in grad school?
- my area of interest: am I applying to this university because I have heard of its name before and because it has a good reputation or rather because I really think that their research group is exactly what I'm looking for and because they have the faculty I would like to work with? will I have good future prospects in academia or business after this grad course?
- where is the grad school located? will I survive in this huge/tiny town with lots/no distractions for 5 years? do I like this state? does this state like me? [I guess these are the less important questions, but if you have difficulty deciding then you may prefer a sunny paradise on the beach to a cold windy place? well... I chose a cold windy place didn't I?!]

Step 2.
Email the faculty you are interested in. This is a perfectly standard procedure: professors get tons of emails form prospective students. Ask what research they do, and tell them you are interested, etc.etc.
Note: some professors may not reply, maybe they are busy, maybe they are impolite. Who knows. But in any case, email lots of people and you will get a good few replies. I sent out around 5 emails to faculty in about 40 universities. Some places I didn't get answers from (University of Pennsylvania completely ignored me), some other places were extremely helpful and kind (Penn State University, Univ. of California Berkeley), some other places sent back standardized emails and ignored my specific questions, etc. etc. You will get a wide spectrum of replies, which will largely depend on the particular professors you send them to, and you should not judge a university badly just because of a silly reply or no reply at all. I guess I myself gave too much weight to email replies, and I eventually did not apply to those universities which ignored me or sent back standardized replies... but I think I exaggerated in that respect.

Step 3.
Choose at most 10 universities. Make sure you have some hard places and some easy places, so you know that you've tried everything but you are also sure you will get in somewhere.

Let me mention now some general comments that may help you to choose the grad school.

- Find out where the Ph.D. graduates go after the grad course
- Look at which universities get research grants awarded to its faculty and its graduates.
- Talk to as many students and professors as you can, especially those who are active in your area of research.
- This is probably one of the most important decisions of your life, so even if you have to go out of your way to obtain information: it's worth it! When you have narrowed your choices to a few, make an appointment and visit them.
- You may consider visiting the universities that you are interested in and talk to the faculty and grad students there.
- Don't give too much weight to rankings (or you may end up somewhere where you don't have faculty in your area, no matter how famous their football team is). Don't give too little weight to rankings (employment and your future prospects may be adversely affected).
- Many graduate programs admit students to a Ph.D. program, and then examine them after two (or sometimes one) year of graduate courses. Failing these exams may mean that you will not be allowed to continue with your Ph.D. program and will have to leave (usually you are given a Masters degree on leaving). Usually you may repeat this "qualifying exam" if it goes terribly wrong.
- Your adviser (i.e. the professor who will guide you through your Ph.D.) will be the unique most important aspect in your graduate program, so you may even want to let this be the determining factor in your choice of university (what would you do if Newton or Shakespeare were a professor in Alaska?). You may therefore want to email the professors you are interested in, and ask them if they take on new students.

If the above tips are not enough, you may wish to look at the following checklist of criteria to help you choose a Graduate Program:
QuintCareers: Criteria for Choosing a Graduate Program


HOW LONG WILL A PH.D. TAKE?
This depends on your area of research, the university, and your abilities. Generally you should expect it to take 5 years. It may take 4 years if the university allows you to skip grad courses or if you are not required to teach nor take courses. In Europe a Ph.D. generally takes 3 or 4 years since you do nothing except writing and reading for your Ph.D. In the States it is generally 5 or 6 years. This is because you often take advanced graduate courses and because you teach (which is a good thing, since you need this experience eventually).


GRE TESTS
You will find plenty of information on these tests on the ETS website (the organizers of GRE), and in the books that you should buy to practice for these tests (see Amazon.com for reviews on the GRE books). There are two tests:

- General: composed of approx. 30 multiple choice English vocabulary and reading comprehension questions, approx. 30 high-school math questions, and two short essay questions on random topics. The three sections are called verbal, quantitative, and analytical. You can find sample questions, information about testing dates, and registration at www.gre.org. No matter how trivial you find the idea of such a test, you will need a lot of preparation as it is quite time-challenging. The verbal and quantitative sections are marked out of 800, the analytical are out of 6.0 (and marks drop by 0.5 each time). The scoresheet will also say what percentage of students scored below you.

- Subject: this depends on what subject you are required to do (if at all) by your university of interest. Mathematicians do the math test, physicists do the physics test. The mathematics test was 66 multiple-choice questions mostly on calculus, complex analysis and easy algebra, and generally standard first-year undergraduate mathematics (although there is sometimes the odd question that asks about more advanced topics). Mathematics (and probably many other of the subject tests) are scored out of 990. The scoresheet will also say what percentage of students scored below you. Some of the subject tests available are: Biochemistry, Biology, Chemistry, Computer Science, English Literature, Mathematics, Physics, Psychology.

There is no point in writing much about the contents: you will get a content booklet from ETS - Educational Testing Service (the organizers of the GRE) when you register, and you must buy an exercise book for each of these tests: practice, practice, practice.

Note: you may need to take other specific tests, especially if you are going to a professional program. For example:
LSAT: Law School Admission Test (law students)
GMAT: Graduate Management Admission Test (if you do an MBA)
MCAT: Medical College Admission Test (medics!)
VCAT: Veterinary College Admission Test (vets!)
PCAT, AHPAT, DAT, PRAXIS: respectively for pharmacy, health, dental and teaching programs.

Among the English language tests, you will most frequently be asked for:
TOEFL: Test of English as a Foreign Language
TSE: Test for Spoken English
See www.toefl.org.

HOW IMPORTANT ARE GRE SCORES?
Nobody knows. Let me just write that again: nobody knows. You can look anywhere on the web, and you will find one of the following answers:

- the score doesn't matter at all at MIT
- you will need to be in the top 1% to even have a chance to get into the top places
- the scores matter a lot
- you can get into many places even with very low scores

As far as I can tell, all of these statements are false. Of course, you can hunt the web as well, but you will find no answers. The truth, or better: what I believe is close to the truth is as follows:

- different universities give different weight to GRE scores
- a bad GRE score will not help you, and indeed may hurt your application
- don't mess up on the GRE
- verbal/English scores don't matter so much for scientific subjects
- if you have a pile of 500 applications from different universities, and the GRE scores are the only common indicator of all applications, how do you think they will order the pile?
- you really ought to have the maximum score in the General GRE math section if you intend to go to math grad school
- there is no difference between being 97% and 99% in the Subject GRE math section (or at least I would like to meet the mathematician who genuinely believes that these scores distinguish the qualities of two incoming mathematics students)
- some departments may not distinguish significantly between good and great scores, but bad scores may hurt your application

That said, I think the general remark is good to keep in mind: "good scores on GRE won't necessarily help you, but bad scores will hurt you". So if you want to get into a topnotch university, they will expect you to have high scores, but it won't matter how high: what will matter then is that you have very strong references from your professors. On the other hand, bad scores may mean that your application will be ignored (face it: you may have 50 people with almost perfect scores, and all have good references and your application lies in the lower end of the pile... what will happen?). Also, some top universities, can chuck one application into the bin and only read every second application, and still they will get 10 amazing students. So don't expect too much, even with perfect GRE scores.

What are perfect GRE scores for mathematics graduate school? They are: 800/800 in GRE general mathematics, and you should be in the 95% or above in the Subject GRE. This is my subjective guess, so don't take my word for it. You may need 99% or you may need only 90% for it to be considered "perfect". You must certainly not go below 80% in the GRE subject math test if you want to get into a very high ranked school. But I think you could have guessed that yourself, after all 80% means 1 in 5 mathematicians did better than you, whereas with 95% you have 1 in 20. After that it becomes sort of pointless, e.g. 98% would mean what? 1 in 50, and 99%? Do you start distinguishing between someone who made 2 mistakes in 66 exercises with someone who only made 1 mistake? And all this on a silly calculus-and-no-brains-computation-test? There is a myth that some math grad schools on the high-end don't even bother reading your GRE scores and only read the references. I'm not sure if this extreme is true either. It seem dubious at best.

If you are on the high-end of the ladder, there is a general feeling of panic when you get your GRE scores back, along the lines of: "will it matter that I only had 600/800 in the verbal section of the general GRE for a mathematician?" and "Is 98% good enough in the subject math GRE?". I have no idea, but the panic is quite ridiculous. My guess is that provided you don't mess up, the reference letters, your Statement of Purpose and your CV will play the greater role in getting you in or kicked out.

For your amusement, here is an example of how-to-take-GRE-scores-far-too-seriously:
Random comments on masters in computer science: and I mean random!

UNIVERSITY SYSTEMS
Programs of Ph.D. courses can vary. You may have to do one year or even two years of graduate courses at the start. You may then have to take exams! And only after all this will you be allowed to choose an adviser (a Ph.D. supervisor) for a research project. Make sure you know what you are getting into.

For example, in my case (Ph.D. in mathematics), I saw that UCLA and Berkeley required almost two years of graduate courses and then exams in each of them. What annoyed me the most was that some of the courses were really too basic (e.g. "epsilon-delta analysis") and would have been a waste of time. It depends on your level of preparation. Europeans tend to have done some thirty courses in mathematics, whereas some graduates in the States may only have done ten or so. Generally speaking, state universities will start from a lower more basic level, and some may find they're losing a year that way. For example try comparing the Chicago first-year-of-courses with that of some lesser known graduate schools and you will typically see a great difference in difficulty and expectations.

Some Ph.D. programs allow students only to teach example classes (exercise classes, i.e. afternoon-get-together to solve exercises or comment on the course) or some form of surgery hours (or office hours, i.e. students drop by your office/room to ask questions). Other Ph.D. places allow their students to teach entire lecture courses, and even examine their students (within reasonable control, thank goodness). This may be a plus point for the university you choose. For example in Chicago you become a lecturer from the third year of your Ph.D. onwards (in the second year you are an assistant to a professor, and in the first year you have no duties except to pass the grad courses).

Some grad schools have a nasty G.P.A. (grade point average) system, meaning that you get grades for each course, and your stipend (teaching assistantship, research assistantship, etc.) may be taken away if you don't get a certain average. Other universities stop examining their students once they have been admitted (seems more reasonable to me...).

One last remark. You may ask: what is the difference between state and private universities? At undergrad, there may be differences in the sizes of classes and in the quality of your peers (state colleges may be obliged to admit a certain number of state residents). At graduate level, from what I gather, there are less differences: there are some very fine universities in the public group, of which Berkeley in an outstanding example. However you may find, as mentioned before, differences in the economical aspect of things: it is more likely that you will receive fellowships and higher stipends from private institutions than from public ones. Public universities may take in a slightly larger class of students, for example in mathematics UCLA takes in about 50 students and Berkeley usually around 30 or so, whereas private institutions such as Chicago, Princeton and Harvard would take in between 10-15 students. This may make entrance to some private universities more competitive.


FINANCING YOUR STUDIES
American students have innumerable forms of funding, all of which a non-American is not entitled to. I am guessing that any American will know much more about these than I could ever hope to know of. In any case, I understand that something like the NSF fellowship is very prestigious and may well get you into a university even if initially it may have declined your application (ironic?).

For Europeans, and I'm guessing most non-Americans, you will generally, especially in the sciences, receive some form of support if you are doing a Ph.D. (on the other hand, for Masters and MBA's you pay ridiculous quantities of money). The support may be one of the following:

- TA (teaching assistantship): you teach something like 4-8 hours of classes, you may have 2-4 office hours (students seek help or ask questions), and you probably need 10 hours to prepare the work. All in all, especially for visa purposes (non-Americans) you are only allowed to work for a maximum of 20 hours on campus.

- RA (research assistantship): you may be part of a research project, you may assist the professor, or you may receive this money in return for nothing.

- Fellowship: a prestigious way of giving you money.

I understand that it is customary to give graduate students a stipend, since otherwise most foreigners would not be attracted to the States. So you really should expect to receive some sort of funding if you are a foreigner, and you definitely should receive one in mathematics and physics.

The most common funding in the sciences is the teaching assistantship, which almost always involves a tuition waiver (you pay no university fees) and a reasonable salary (which should cover housing and living expenses). In exchange you are required to teach classes, or mark/grade papers. Alternatively an assistantship may involve helping faculty in a research project. It may also involve office hours (i.e. consultation hours for undergrad students). These activities usually take up between 10-15 hours and never more than 20 hours per week. Some universities, such as Chicago, often give summer support for Ph.D. students.

Unfortunately I cannot provide any help on fellowships specific to United States citizens, however, check out these websites:
National Science Foundation
National Physical Science Consortium
NOTE: these fellowships are usually due early in November! So be careful about deadlines.


WHAT QUESTIONS TO ASK
Questions for professors on the research:
- what are the strong fields of research of this department?
- which professors will be taking on new students? in what areas?
- when and how do you choose your advisor?
- how does the research group compare with other institutions?

Questions for professors on the graduate program:
- how many graduates are accepted each year? (i.e. what is the size of the entering class?)
- how many of these in average will complete the program? (i.e. what is the dropout rate?)
- what is the average time to obtain a Ph.D.?
- how many students will be in my entering class?
- what is the typical form of support? (TA/RA/fellowship?)
- what is the typical stipend?
- how many working hours per week is expected for a TA/RA?
- is the TA/RA guaranteed for the entire time, or is it on a year by year basis? what would disqualify you?
- do TAs lecture or just hold example classes and office hours? what type of courses do you teach?

Questions for current graduate students
- what is the academic social environment like? do students work together?
- is the atmosphere highly competitive?
- what are the professors like? in what areas do graduates usually go?
- are students satisfied with their research advisor?
- how frequently is the advisor available?


REFERENCES
Make sure you choose your three references wisely. Don't choose a famous professor just because they are famous: it's useless if they don't know you (unless of course your results are so extremely outstanding that they will know of you). So it is more sensible to ask references from the professors you have worked with and that know you well, and also that you think will take care in writing a decent reference (not just any old brief comment). It is unfortunately a subtle aspect of the application, since it is likely to be the most important and telling element about your abilities and at the same time it may not be entirely correct (some professors may exaggerate your abilities, others may not review them with enough enthusiasm).

These letters are extremely important and should tell whether you are suitable and skilled enough to attend the graduate program. You should give your professors your Statement of Purpose, C.V. and a copy of your transcripts, so that they have all of your details in front of them.

You are usually asked on the application if you want to waive your right to see the letters submitted on your behalf. You must waive your right to inspect the letters! If you do not waive your right, it may seriously adversely affect your application (because it basically means you don't trust your professor's judgement).


STATEMENT OF PURPOSE
Also known as Letter of Intent. The statement of purpose should be an essay about why you want to attend graduate school. Do not make it too long: mine was about two pages and I don't see a good reason for it to be any longer in general, in fact if it is long it is probably too wordy or you have written about too many secondary aspects of yourself. I'm told that Americans like a simple 3-part layout: a strong introduction, a cogent body, and a strong conclusion. I stress that the beginning and ending should strike the reader (along the lines of "catch their attention" and "make them remember reading your statement"). So my advice on the three sections is:

- the first paragraph should immediately mention: how good you are (what grades - e.g. say "I belong to the top 5% of my class" - what university, what subject area). Make sure this first paragraph is interesting and terrific. You have to catch the reader's immediate attention.
- the body should (briefly!) review what you have done in your undergrad years (courses, projects, awards, prizes) and why you are interested in your subject (mention, of course, any papers you have written). It is up to you on what facts you want to put weight. Mention why you want to study at this particular university (are there any professors or research groups you would like to work with? why?). Mention why you would make a difference and why they should offer you a place.
- the finishing paragraph should be some conclusion about why you are good enough for the program, and why the institution would profit from admitting you. Make sure your last sentence is snappy.

There is no point in me telling you what I think you should say. This essay is really about you: your style and thought should be somehow represented in this essay. This means two things: don't make this essay banal, and don't make it artificial. If you ask a counseling service at your university, they will probably produce an artificial essay for you. I don't know if that helps, I personally think that an experienced professor will spot it miles away and that can adversely affect your application.

Also: this essay will most likely not make that much of a difference, provided it is a serious well-written essay. The motto is again: "a bad statement will hurt you, a good one won't make much of a difference". So don't mess it up, but also don't think this will have the importance of, say, your results and reference letters.

On the web you will find many companies that will help you write this statement in return for large sums of money. This all seems morally wrong to me, so I don't recommend it. However, these companies often have sample essays online, for example the following Medical School Statement. I haven't found any outstanding essays online, so don't take online statements of purpose as "ultimate guides". You can also buy books, some with really stupid titles like "the essays that will get you into the Ivies" or similar. I don't know if they are any good, but you could have a look at them in bookshops.

If you start your essay with << When I was five, I went to the baker with my dad and I realized he got back the wrong change. I knew then that I wanted to become a mathematician >>, then it is unlikely anyone will take you seriously. Also, starting an essay in this way means that you won't strike the reader with anything factual. If your university results were good (say a perfect G.P.A.), then that's the first thing you should mention, together with your university's name and area of interest. A note especially for Europeans: don't be self-deprecating, and don't say "I hope to do this" or "I might like to do that", you should be definite and say "I want to do this", "I intend to do this", and "I am planning to do that". Avoid flattery, clichés, hesitant remarks, boasting, etc. Be cogent, clear, and straightforward. Show enthusiasm for your research interest, that is after all what you intend to do for the next five years. You may like to highlight particular aspects of your field that particularly stimulated you, some important reading that have formed you academically, and try to infer that you have sharp analytical skills and that you are creative (but don't boast and don't be flowery). It is usual to rewrite this statement many times (in fact it is a good idea to restart from scratch after your first few drafts).

The main point about this essay is to show that you are a serious and interested student, so market yourself well on this aspect. Enough said: it's up to you to sell yourself well.

For a checklist of tips on writing this essay, go here.


C.V.
You may wish to send a Curriculum Vitae (C.V.) together with your application. I will not go into the details of writing a C.V. as there are plenty of reasonably good websites about this (for example here and here), and you can consult your professors and colleagues about this. However, generally the following is advisable:

- it should not be too long (for an undergrad, three pages is already almost too much, some employers even advise 1-page C.V.s, which then makes it into a cramming exercise).
- for grad school, I would leave out the chitchat about the sports and activities that you enjoy (that's more for undergrad applications), unless you feel that leisure activities play an important role in your application.
- you should have the following sections in your C.V.: [name/personal info/contact info], Education, Awards/Prizes, Relevant Experience / Skills, Languages, Work Experience, Computer Skills. Of course it depends on who will have to read the C.V. and what the strong points in your application are.
- make sure the layout is clean and easily visible. One should be able to glance at your C.V. and catch the salient points at once (so use 'boldface' to highlight your results or the year/date, etc.).
- The typesetting must be flawless (same fonts and same fontsize for similar things, correct alignments, etc.).
- Don't write too much, it has to be a summary of the most important events in your career.

Many universities have counseling services to help you write a C.V. (and a Statement of Purpose), and you should look up some books on writing C.V.s (check your library?) and have a look around the net to see how people write C.V.s. Indeed, look at the Curricula professors put up on their websites!

For your amusement, here is a how-not-to-example: Res Gestae.


TRANSCRIPT
These should comprise: what subjects you have studied (titles of courses, duration of courses, who taught the courses) and your marks (G.P.A. or class or whatever your institution uses). You may like to include an explanation if you feel that the institution you are applying to may not understand your university's scoring system.

Transcripts must be official. This means the relevant authority in your university has compiled and signed your scores. It is advisable that these scores are put in an envelope and sealed, and ask the authority to sign (and stamp) across the flap and sellotape the flap. This is a standard procedure to show that the scores are authentic and that you have not opened the envelope. (a similar procedure should be used for the reference letters). You may also want to include a list of courses that you are currently taking and will attend in the present year, and let the authority confirm that you are taking whatever degree you will obtain that year.


WHAT TO DO WHEN OFFERS COME IN: DECLINING AN OFFER
After submission of all of your material, you will have to wait for replies which may reach you any time between the beginning of February and April 15. The common agreement among U.S.institutions is that you need not make your final decision until April 15, but there is also an unwritten polite agreement with the student that you should contact all those universities which have given you an offer which you decided to decline: something along the lines of

<< Dear ...,

I thank you for the offer to attend the graduate program at ... .
Regrettably, I have decided to decline the offer.

Sincerely,
... >>


Depending on how well you know the graduate admissions tutor, you may wish to add reasons for your decisions or inform them where you have decided to attend. That's up to you.


MAKING THE FINAL DECISION
After all offers have come in (if any university insists, you may wish to advise them that you are still waiting for all offers to come in), you must take this decision very seriously. It's not about letting a ranking decide for you! Here are some tips to help you decide:

- professional opinion of the universities,
- the financial package
- the strength of the research group you are interested in
- the size of the grad school (if you don't know what area you will go into, a large school is probably better)
- the number of incoming students (do you prefer to be one in 50 or one in 15?)
- the grad courses offered (this will also tell you which areas are stronger in the department)
- the faculty (this is very important if you already know who you want to work with)

What your professors advise you to do is much more important than what a ranking says, since a professor will know the quality of the current faculty and may be able to advise you specifically in your area of mathematics (would you go to Chicago or Berkeley to study algebra? how about Lie groups? a ranking won't help you in that decision). On the other hand, the rankings are not entirely insignificant: you must not start distinguishing between 6th and 10th, but widely differing rankings will make a difference in your professional opportunities. A similar remark goes for financial packages: small differences, say between $18,000 and $19,000, are irrelevant, since the costs of living will anyway differ between cities (incidentally, in cities like New York and Chicago you will obviously be spending much more than in small towns). However, if one university offers you a generous teaching assistantship and a fellowship, and another only offers you a low assistantship, then this should certainly influence your decision. However, don't let high stipends tempt you if the quality of the universities differ widely.

If you really can't decide, then the following details may help you:

- cultural and political environment
- location and weather: would you miss winter in California ;-)?


LINKS, ADDRESSES, TELEPHONE NUMBERS

Testing Services
GRE website
TOEFL website
ETS - Educational Testing Service: the organizers of GRE, TOEFL, etc.

Guides like this one
Natalia Lukina's Homepage: an excellent thorough guide
Applying to Graduate School: the excellent Chicago guide
Graduate Schools and Fellowships in Mathematics: the excellent Harvard guide
Kyle Kneisl: Applying to Graduate School
Doug Faires: A Graduate School Primer
Mihai Budiu: Practical Guide to Ph.D. Admission (to view *.ps files go here)
Beliot College Graduate School Planning Guide: in a useful checklist format
About: links to guides on choosing a Graduate School
About: links to guides on Graduate School
Thomas Sowell: Choosing a College: this is for undergrad only, but very interesting
QuintCareers: Criteria for Choosing a Graduate Program
Harvard Guide to Applying to Graduate School: a huge guide on all aspects
Excerpts from The Grad School Handbook by R. Jerrard
The Philosophical Gourmet Report: some general concepts, and a lot on philosophy programs

Beware of rankings articles
News you can abuse
What ranks for research doctoral programs?

FAQ guides
Massive Graduate FAQ guide: posted on the soc.college.gradinfo newsgroup, it contains information about rankings (USA, Canada, UK), Standard Tests (GRE, GMAT, MCAT, LSAT, TOEFL), Scholarships and Funding issues, general advice on grad school, etc.

Graduate Mathematics in particular
Why Graduate Mathematics?: the excellent SUNY-Potsdam guide
Graduate Schools and Fellowships in Mathematics: the excellent Harvard guide
The AMS guide

General remarks about entering Graduate School
The Chicago Guide to Your Academic Career

Newsgroups and student comments
The Princeton Review: usually has heated discussion groups
Also try the newsgroups via google groups searches
StudentsReview: it's undegrad, but it has many interesting comments about each university
MAA Online: How to Choose a Graduate School: students recount their experience
College Confidential: Undergrad, but the discussions are still interesting

Reknown guides, from which I could never find any useful information
Peterson's Education Center
Princeton Review
Kaplan Online
Gradschools.com

C.V. guides
Beloit College: Resumé and cover letter guide
UPenn: Resume resources
Search Google for "Career Services" of universities (they always have C.V. guides)

A comparison with Italy
Lorenzo Marrucci, L'università negli Stati Uniti d'America in una prospettiva comparata con l'Italia, Marzo 2003



Comments, criticism, and corrections:
Please send comments, criticism and corrections to









Copyright © 2001 Alexander F. Ritter
(ask for permission if you would like to reproduce any material found on my site)

Subliminal Nonsense