The EEB department does not have a core set of courses that everyone should take, and each student's plan of study is determined through consultation with their graduate advisory committee (who must sign off on the plan, ideally during the student's 2nd or 3rd semester). The following, however, are key courses that I would expect most PhD students in my lab to take at some point. MS students probably would not have time to take all of these courses, but should, at a minimum, expect to take at least one of the ecology courses, conservation biology, and as much statistics as you can fit in.
EEB 5301 Population and Community Ecology
EEB 5302 Organisms and Ecosystems
EEB 5310 Conservation Biology
EEB 5335W Vertebrate Social Behavior
EEB 5449 Evolution
STAT 5005: Introduction to Applied Statistics. If you've not had a course like this one, then you should take this as soon as possible after getting to UConn.
STAT 5315/5515: Analysis of Experiments/Design of Experiments. Most students in my lab group should plan on taking these two courses, unless they have had graduate level stats before. The courses can be taken in either order. 342 focuses more on regression, while 343 focuses more on ANOVA-type analyses. Before taking them it would be a good idea to talk to other EEB students about their content.
STAT 5505/5605: Applied Statistics I and II. This two course sequence (starts in fall semester) provides more advanced graduate statistics with a greater emphasis on theory. They need to be taken in sequence. PhD students in my lab group should seriously consider taking these classes, especially if their thesis work has a large math component.
The following 1 credit seminar courses are also likely to be very relevant to most students working in our lab group:
EEB 6480 Seminar in Vertebrate Biology
EEB 5369 Current Topics in Biodiversity
EEB 5895 Invest. Spec. Topics. The ornithology group also conducts a weekly lab meeting class every semester in which we discuss current research activities within and outside of the lab. Everyone engaged in research within the group should participate. To enroll you will need to get a permission number from Chris or Margaret.