Spending a semester in another country can be a great way to increase your understanding. There are some especially attractive options for mathematics majors at HMC because of our long-standing interactions with programs in places such as Budapest, Hungary, England, and Australia.
There's lots of information about these and other programs available on the HMC Study Abroad site, including sample study-abroad major plans that outline how you can arrange your schedule to make it possible to go abroad in the fall or spring semester of your junior year.
As always, please be sure to consult your advisor about your plans as early as possible. You should also keep in mind that taking mathematics classes abroad will require preapproval from the department's Curriculum Committee to ensure that they meet the requirements of courses in our program. Other departments may have similar restrictions on what sorts of classes can apply toward your degree, so be sure to check with them, as well!