The US National Science Foundation (NSF) funds a number of programs offering research experiences for undergraduates (REUs) in the Mathematical Sciences. The main goal of these programs is to introduce students (usually those who will be either juniors or seniors during the next academic year) to research topics in Mathematics; they last anywhere between four and eight weeks during the summer.
It is still possible to apply for financial support (which typically includes travel and local expenses, as well as a stipend) to participate in these programs during Summer 2016. The selection process is highly competitive, and in most cases consists of an application form, and two or three letters of recommendation from faculty who are familiar with the applicants' abilities.
If you have successfully taken or are currently taking advanced (300 level) Mathematics/Statistics classes (and especially if you are seriously thinking about pursuing graduate studies in the future), do browse the lists of current REUs maintained by the NSF and AMS and consider applying to those that may be of interest to you. Note that there will be a lot of intersection among the three lists. If you decide to apply, please don't hesitate to contact any of your professors in the Department of Mathematics & Statistics with any questions that you might have. We will be happy to assist you in any way we can.
LUROP, Loyola's center for experiential learning, is a great resource for Loyola students that can help you find a research program that is right for you. RamblerLink also lists math and stats jobs and internship summer opportunities.
For your convenience, below we give a selection from the ever-changing lists above (updated January 23rd, 2017), funded by NSF or other agencies/institutions: