There are many summer internships in the DC/MD/VA area for undergraduate mathematics majors. A good place to start searching is here.
Many UMW mathematics majors have obtained summer internships and eventual permanent employment at the Naval Surface Warfare Center at nearby Dahlgren, VA. Information about their summer employment opportunities can be found here.
There are also many mathematics-specific summer research programs sponsored by the National Science Foundation at colleges and universities across America.
Internship Opportunities at Geico – contact Courtney Kowalchick by e-mail CKowalchick@geico.com or by phone 540-286-4489
Opportunities at Science Education Programs at Oak Ridge National Laboratory can be found here.
The Summer Math Institute (SMI) at Cornell aims to prepare undergraduates for the challenges of graduate school in the mathematical sciences. More information may be found on the SMI web page: http://www.math.cornell.edu/~smi/