Summer Self-Study?? Hi, I'm high school senior from Vancouver, Canada and I'm entering U of Chicago this fall! I've searched through the forum like literally hundred times and still unsure of what to do for this summer. So, to introduce myself, I took AP Calc BC in gr.10 but never pushed myself further into studying higher level mathematics. Because my school only offers up to IB Math 12 HL, I took the course in gr.11 which include basically AP Calc BC + vectors + matrices + statistics + etc and I self studied IB Further maths which is (Advanced) Geometry + Set, relations, and Groups + Series and Differential Equations + Number Theory + Graph Theory + (Advanced) Statistics&Probability. I'm fairly good at math I'd say; I made CMO and USAMO in grade 12 and without any intense training. And I'm also a fast learner. But it's been a while since I studied math seriously and I haven't also been properly introduced to formal proofs. I studied bits of multivariable calc and linear algebra but im not quite skilled at these areas. I really want to make into Honors Analysis at UoC this fall so I've searched around the forum to choose which to read but I just wanted to hear you guys' opinions. So here's the plan How to Prove It: A Structured Approach - Daniel Velleman (Currently Reading) Naive Set Theory - Paul Halmos Mathematical Analysis I/II - Vladimir A. Zorich Linear Algebra Done Right - Sheldon Axler I know it's a tight schedule and I will most likely not be able to finish all those anyways. But, I wanted to know if there are other alternatives or extra books that I should read to be prepared for Honors Analysis. I know of Spivak, Apostol, Courant. Only reason I chose Vladimir Zorich was because it seemed very comprehensive and ordered (but I don't exactly know its level). IMO, Spivak lacks content (not to say it's easy, I know it's the bible of rigorous single-variable calculus) and Apostol is somewhat dry and also seems sort of messy (+ it contains LA and DE as well as probability, areas which I'd like to study from other books) and Courant is supposed to be physically intuitive and has more to do with applications. but I don't think it would be that much of a jump from what I already know. Correct me if I'm wrong. Please comment on books by Zorich if anyone knows since it seems it's quite new and not many people know about it. Or else, recommend me other combination of books (or other books on Linear Algebra) that I should study off from. If you would still recommend Spivak, please recommend me a multivariable counter part to it! Thank you all in advance.