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How can I know which mathematical field each country or university is the best in these days? For example, I've already heard that in my country there isn't so much research in algebra and my university is great in geometry.

I wanna know this because I have family in Germany and France (Paris and Toulose) and I have to choose my field of interest in this semester, I like so many things in mathematics and this information would help me to pick one.

Thanks in advance.

user42912
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    Well instead of picking your field of specialization based on where the "best" university is located, how about choosing your field based on what you like and what interests you. I am assuming you are looking for graduate studies. If so, I can assure you that if you end up in the "wrong" field which you are not very passionate about then you will be very miserable and unhappy and may not even finish and drop out. As for actually answering your question, it is far too broad, completely subjective, and opinion-based. Not the right kind of question to ask here. – Fixed Point Jul 30 '13 at 07:47
  • @FixedPoint that's my question, I wanted to know if I can know this objectively. – user42912 Jul 30 '13 at 07:51
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    I would say that it doesn't matter much whenever a country or even a university is good or bad in some domain. However, if you insist on this perspective, then the most important is the person you are going to work with. Of course, a university that is good at something is bound to have some good people there, but it is those people you need to find, not the place. – dtldarek Jul 30 '13 at 07:51
  • @FixedPoint Speaking of the mathematical subjects, I agree with you, I wouldn't choose a field which I hate. However, This kind of information I would like to know, there are a lot of things that counts, but I shall take account of this information. – user42912 Jul 30 '13 at 07:55
  • @dtldarek yes, it's true, good remark. – user42912 Jul 30 '13 at 07:56
  • @user42912 How can one answer this objectively? First how do you rate universities? Second how do you compare them against one another and rank them? I can tell you that one university is excellent in Numerics and no doubt someone else will disagree with me. And let's say even if you do find a "best" university in something, that doesn't mean it is the right choice for you. You may end up with an adviser who you really hate, someone who is a jerk, and enslaves you. There are plenty of problems you can run into like dltdarek points out. – Fixed Point Jul 30 '13 at 07:57
  • Having spend years in grad school and having witnessed plenty of demise and suffering of other grad students around me, the two most important things are first carefully picking the right field you are interested in and then very very very carefully picking the adviser who will have great control over you grad school life and life immediately afterwards. Looking at "best" schools is sooooo high-school. As for some concrete advice, visiting campuses, meeting professors and meeting their grad students will help you more than "the school's name". – Fixed Point Jul 30 '13 at 08:02
  • @FixedPoint For computer science there is the dblp database, given a mapping from names to universities (this is not easy, but you can pick only these which interest you) you could count the number of papers in good conferences and journals (again, what is good here). This is not objective very much, but it's as close as one can get (of course, if paper-counting is any measure to you). The problem is, I don't know whether there is a similar database for mathematics. Anyway, I would not base my pick on that. – dtldarek Jul 30 '13 at 08:03
  • Thank you @FixedPoint for the advise – user42912 Jul 30 '13 at 08:08
  • Well paper counting is one metric. There are plenty of "problems" with that metric. What are "good conferences and journals"? Who decides which are included? How do you weight them? Is one paper in a "really good journal" worth more than a hundred papers in the "fifth-best journal"? Is this the only metric? Do you count the number of nobel laureates/field medalists? Do you look at the size of the department faculty and grad students, student/teacher ratio, funding, their success rate and drop out rate? And then how to combine them to get one metric and then how to compare different schools? – Fixed Point Jul 30 '13 at 08:09
  • @FixedPoint that's why I thought this isn't so subjective: http://www.lefigaro.fr/sciences/2009/03/27/01008-20090327ARTFIG00006-pourquoi-la-france-est-une-terre-de-mathematiques-.php?page=&pagination=17 – user42912 Jul 30 '13 at 08:10
  • it says: "Alors que les Américains sont souvent amenés de travailler dans des domaines très reconnus et balisés, comme les équations aux dérivées partielles, omniprésentes dans la modélisation, les Français peuvent travailler dans des domaines apparemment plus farfelus, comme la théorie des nœuds, ou même les pliages de feuilles de papier. C'est aussi ce qui fait leur originalité." – user42912 Jul 30 '13 at 08:11
  • @FixedPoint thank you for your advice, I'm going to visit the campus of some universities these days. – user42912 Jul 30 '13 at 08:12
  • @FixedPoint I would like to know how can I have access to this data: "Do you look at the size of the department faculty and grad students, student/teacher ratio, funding, their success rate and drop out rate?" – user42912 Jul 30 '13 at 08:15
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    Translating from French, that very quote seems entirely subjective. I don't think it is true but anyway I didn't mean to come out so strong. I have seen plenty of my friends and fellow grad students having problems (some quite serious) with their schools/depts/advisers/funding/etc. so just wanted to give you a fair warning. The "name" of the school and what it is "best" at are not the most important things to consider when picking a grad school. They should be considered but they shouldn't be the primary factors. – Fixed Point Jul 30 '13 at 08:20

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