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.