I start UChicago in the fall and would like to test into their Honors Analysis sequence (the test being in late September). I’m about midway through Spivak and I really enjoy it. I hope to finish the book in the next few weeks but I'm conflicted about what to go on to next. I would like to do Lang’s Linear Algebra (and hopefully start Herstein’s Topics in Algebra if I have time) but I’m not sure if Lang’s book on multivariable calculus would be better preparation for the test. I’ve heard Spivak’s Calculus on Manifolds is good as well. With these considerations in mind, what is likely to be the best/wisest course of action (if you have experience with Chicago’s Honors Analysis, all the better).
Also, I hope this question doesn't get flagged. There are many students in similar situations (making hard decisions about what areas to study after calculus) for whom this question would likely serve well and provide guidance.