Many opportunities for undergraduate research exist at UB and elsewhere. Undergraduates who may be interested in pursuing graduate study in mathematics should take advantage of one or more of these opportunities. Updated information can be found at the American Mathematical Society.
A senior honors thesis is typically completed over two semesters, usually but not always in one's senior year. The student works on a project with a faculty mentor. Typically one registers for MTH499-Independent Study in the fall and then MTH 497-Honors Thesis in Mathematics in the spring. Satisfactory completion of an honors thesis is required to graduate with departmental honors.
The National Science Foundation sponsors many different summer research programs for undergraduates. These usually include travel and housing money plus a modest stipend. See the current list of NSF REU programs.
These are specially designed programs for mathematics. Many of the available study-abroad programs also offer excellent opportunities to study mathematics.