Mathematical preparation for postgraduate studies in Linguistics I am an undergraduate student in Mathematics and I would like to continue my postgraduate studies in the harder, more mathematical aspects of Linguistics. What exactly would that include is unknown even to me, but possible areas of interest would include the mathematical aspects of syntax and semantics, as well as computational linguistics, natural language processing, artificial intelligence or machine learning.
As of now, the courses that I have taken have been purely mathematical: real, complex and functional analysis, measure theory, point-set topology, differential equations, group and ring theory, linear algebra. I understand that the analytic courses are not very pertitent in linguistics where data is rarely "continuous" or as nicely behaving as the functions studied in analysis. I would like to hear the community's suggestions about courses that should constitute good preparation for postgraduate studies in the aforementioned areas. The courses need not be mathematical. They can be linguistics, statistics, computer science courses or courses from any other discipline that would best prepare me for the task.
I kindly request that you do not close, delete, flag or anything of the sort, this question. It is quite important for me to read opinions from people who know better than me. If you could somehow promote the question so that I can potentially receive more opinions, this will be greatly appreciated!
UPDATE: If there are other people interested in this question, some more answers have been given here. Moreover, I found this blog, which is extremely rich regarding topics of mathematical and computational linguistics as well as natural language processing. This post as well as this should be of much interest to those in the mathematical side of linguistics.
 A: Theory of computation, formal languages obviously. Other than that...
Get hold of potential thesis advisors, ask them for suggestions to come up to speed in their specific areas. Most (sub)areas are vast enough that you won't find "one size fits all" anyway. And for graduate school level work you'll need to go for recent material, preprints, conferences, that kind of stuff pretty soon (it is said that if some work is done today, it appears in a technical report in a month, in a conference next year, the article is publshed in three years, and included in the textbook in ten).
A: As I mentioned in the comments, I forwarded the question to a linguist I know whose undergraduate degree is in mathematics. This is his response:

I'd take an introduction to linguistics as soon as possible, if you haven't already, to guarantee that you do indeed want to do linguistics, and to help you better identify what area(s) you would be interested in exploring.
Beyond intro, and based on what topics interested you from it, I'd recommend foundational linguistics courses in theoretical syntax, formal semantics (predicate logic, Montague grammar, etc.), and/or phonetics (making concrete measurements of language data and doing all sorts of statistics on those measurements).
Outside of linguistics, again, based on what specifically interests you in linguistics: formal languages, logic and set theory, statistics, programming languages, physics (especially acoustics), cognitive science, natural language processing, machine translation, etc.
It doesn't hurt to beef up your knowledge of a foreign language or two.  Many linguistics grad programs require basic proficiency in one or more foreign languages, and even if they don't, having specific languages you focus on (especially non-Indo-European and/or under-studied languages) will provide you with lots of places to look for research topics where you are already familiar with much of the data.  Don't overlook sign languages!  There's still a lot of linguistics work that needs to be done on them, and anyone who knows both a sign language and linguistics would be a hot commodity.  Throw in some basic knowledge of physics (as it relates to the biomechanics of the human body) and/or computer vision, and you've got decades worth of wide-open research projects just waiting for you.

A: There are a few things you would like to try.
Working in linguistics you will surely work with computers (to test your hypotheses, to gather and manipulate data, to process result statistically). 
That begin said, it is not necessary, but it would be very helpful for you to learn Python and familiarize with Natural Language Toolkit. Good place to start is the NLTK book, full text is available freely online, and is a great source of information (many working examples) on computational linguistics. Even if you won't work as a computational linguist, this area has a great influence nowadays and basic understanding about what and how things are done there is a must.
Of course, probability theory. There are many results that linguists use from there, e.g. Bayesian rules or hidden Markov models.
Naturally, statistics, I suspect this does not need any comments.
Formal languages, including Chomsky hierarchy, formal grammars, automata, also a bit of abstract algebra (e.g. see syntactic monoid). This courses usually contain some information on computability theory (e.g. this) and theory of information (e.g. Kolmogorov complexity), it useful to have some understanding of basic concepts and results in both.
Logic, including predicate calculus, lambda calculus, inference systems. Be aware, that there are (at least) two terms "logic" available: in philosophy and in mathematics. Note, also that mathematical logic is very broad, and, for example, you don't need much model theory (which could a whole domain on its own).
Semantics, including the formal way (e.g. denotational semantics, etc.), but also ontologies and Co.

I know, this is a lot (and still incomplete!), but I just wanted to sketch the area. Most of it you will pick along the way (you don't need everything from the very beginning). Please note, that this is more from computational linguist side, and there is a whole range of themes outside of it which probably will be useful to you. However, it would be best to ask some specialist, why don't you try http://linguistics.stackexchange.com?
Good luck!
