; (iii) the third or fourth year of a program of undergraduate education at a four-year degree-granting institution of higher education, is certified by the institution of higher education to be pursuing a major in a subject described in clause (i)(II); (iv) the third or fourth year of a program of undergraduate education at an institution of higher education (as defined in section 101(a)), if such institution of higher education demonstrates, to the satisfaction of the Secretary, that— (I) such institution of higher education offers a single liberal arts curriculum leading to a baccalaureate degree, under which students are not permitted by the institution to declare a major in a particular subject area, and the student— (aa) studies, in such years, a subject described in clause (i)(II) that is at least equal to the requirements for an academic major at an institution of higher education that offers a baccalaureate degree in such subject, as certified by an appropriate official from such institution; or (bb) is required, as part of the student's degree program, to undertake a course of study in a subject described in clause (i)(II) which consists of at least— (AA) 4 years of study in mathematics; and (BB) 3 years of study in the sciences, with a laboratory component in each of those years; and (II) such institution offered such curriculum prior to February 8, 2006; (v) the fifth year of a program of undergraduate education that requires 5 full years of coursework, as certified by the appropriate official of the degree-granting institution of higher education, for which a baccalaureate degree is awarded by a degree-granting institution of higher education, is certified by such institution of higher education to be pursuing a major in a subject described in clause (i)(II)