Creating a Computational Linguistics College Degree?

$random_var asks: "I am an undergraduate student currently studying Bioengineering. However, I am growing more and more interested in programming and linguistics, which leads me to think that I should define my own major, Computational Linguistics [mit.edu], which google defines as 'a field concerned with the processing of natural language by computers.' When I present my proposal for this degree to the school's advising staff, I would like to have a complete list of all of the topics this major should cover. Having only little experience with computer science and engineering, I'm not sure what parts of that field I should include. Beyond the basic lower-division courses, what specific fields of computer science do you think should be emphasized in a practical undergraduate study of Computational Linguistics?"