I wasn't the best student in high school but I always saw the mathematics as an interesting subject, now I have to choose a degree and I'm really considering pure mathematics.
I have something like 6 months of free time, so maybe it'll be a good idea to prepare for the course. Any book recommendations?
I would like to improve mathematical thinking for my future studies and general math books (Calculus and Algebra books will be great too)
Thanks.
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This does not necessarily answer your question, but just to get you inspired and to get a feel of what pure math is about: Fermat's last theorem by Simon Singh is a great read. It is probably because of that book that I went on to study math.
If you need to look for books to study you can also look at the course description of the first year courses at the university you wish to enroll at. There it is probably stated which books these courses will use. If not, try e-mailing the professors with that question. I am sure they will appreciate your enthousiasm!
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I personally would recommend Spivak's Calculus book. I am not sure what texts you will be using for your first year classes, but for me this book was really enjoyable and helped bridge the gap between high school math and university math. It has detailed proofs, and will introduce you to more sophisticated ways to prove theorems than whatever you would have studied in high school. For me first year calculus using this book really put me on firm ground to jump into other areas of math.
If you would also like a nice introduction to algebra (group theory in this case), I also enjoyed Armstrong's Groups and Symmetry book. It will give you a small taste of what more advanced mathematics will be all about, and will be very different from the comforts of calculus.
I recommend What is Mathematics? by Richard Courant and Herbert Robbins, and Set Theory and Metric Spaces by Irving Kaplansky.
Take your time with Courant's book first. Kaplansky's book is more advanced; for now you can use it as a secondary source.