What do I need to include in a tenure-track assistant professor job application cover letter? I am currently applying for tenure-track assistant professor jobs.
One of the positions requires me to submit a cover letter,
in addition to a CV, research statement, and teaching statement.
(The application is online)
I am thinking of writing the following:


  October 1, 2014
  
  Dear faculty committee
  
  I wish to apply for the faculty position
  in the Department of Mathematics
  at Stanford University.
  Currently, I am a postdoctoral fellow at
  the University of California at Berkeley
  in the Department of Mathematics
  under the supervision of Dr. James Moriarty.
  
  Enclosed are my curriculum vitae, teaching and research statements,
  and two research papers.
  Please do not hesitate to contact me if further information is needed.  
  
  Yours truly, 
  John Watson 
  Department of Mathematics 
  University of California at Berkeley 
  123 4th Street, Box 5678 
  Berkeley, CA 12345-6789 
  (123) 456-7890



What is the purpose of the cover letter?
Is it just to indicate what are the documents included in the application?
I ask this because most of the other positions for which I am applying
don't require a cover letter.
Should I include a brief summary of my research interests and teaching experience, one paragraph each, in the cover letter?


Edit:
In reality, I am not in the field of mathematics,
nor am I a postdoctoral fellow at Berkeley.
The details in my cover letter are fictitious
and meant only to illustrate the structure of the cover letter
which I will write.
I'll be honest about when I read packages (in chemistry). The first thing I look at is the CV. I also skim the cover letter. Then I read the recommendation letters and the research and teaching statements. Depending on the CV and recommendation letters, I may take more or less time on the research/teaching statements - if the candidate seems promising, I'm more thorough.

But if the cover letter is short, not tailored at least some to our department, contains obvious typos, etc. I'll get a bad impression.

Look, anyone applying to a tenure-track position has taken a lot of time to get to this point. You've secured a PhD, possibly gone through a postdoc position, and prepared the whole application.

Why spoil it with a lousy cover letter. Take some time, think up a paragraph or two about a particular department, consider what you might add, and let us know.

This tells me that the candidate is not just blindly sending out a gazillion applications.

I doubt everyone completely rewrites their cover letters for each application (I didn't). But I do want to see that someone has taken the time to carefully craft a paragraph or three about us and how they might fit.

Will we interview someone who seems stellar with a poor cover letter? Probably. But we also get ~100 applications for every opening, so why would you risk it?