Second undergraduate versus masters with qualifying year
If possible, avoid the 2nd undergrad. To see if possible, pick an online copy of a typical textbook, level advanced undergraduate/graduate, and browse it for fun, and do some of the early exercises. Examples: Artin: Algebra; Munkres: Topology; Spivak: Calculus on Manifolds (or more advanced; Guillemin &amp; Pollack;: Differential Topology); or better yet, browse whatever the curriculum of your chosen university indicated for this fall semester as text books. It doesn't have to appear easy, as you are supposed to learn it; and learning math is hard, no matter what your future classmates will falsely claim: most of them struggle too. But it shouldn't terrify you either.