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I'm a student in university studying math first year. I would like to know what are the best books that shape and build the right math and abstract thinking skills . I don't mind if they are general books. And i prefer an easy read rather than a hard one. Thank you.

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  • $\begingroup$ This. $\endgroup$ – Git Gud Oct 10 '13 at 22:42
  • $\begingroup$ Here is a list of mathematics books organized by subject: ocf.berkeley.edu/~abhishek/chicmath.htm. $\endgroup$ – Andrew Elkouri Oct 10 '13 at 22:44
  • $\begingroup$ I at least tried to add the soft-question tag. Can anyone think of more? $\endgroup$ – Stefan Smith Oct 10 '13 at 22:44
  • $\begingroup$ @StefanSmith big-list, self-learning $\endgroup$ – Git Gud Oct 10 '13 at 22:45
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I would recommend to start with some mathematical logic and set theory. They could train your rigorous reasoning well enough to deal with any math theory. For logic, First Order Mathematical Logic by Angelo Margaris is an excellent (and cheap!) introductory book to begin with. For set theory, Elements of Set Theory by Herbert B. Enderton is also good enough for introduction (It treats both naive set theory as well as axiomatic way). Later if you are interested in these subjects, there are lots of good books and papers that you can explore.

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  • $\begingroup$ Why the downvote? These areas of study are certainly accessible at an elementary level and could give a good start to someone looking to get a taste of math. $\endgroup$ – frogeyedpeas Oct 11 '13 at 0:13
  • $\begingroup$ I upvoted this answer to compensate for an apparent downvote. I see nothing wrong with this answer, unless all the books stink, which I doubt. One could argue that one should learn some logic and set theory before learning different kinds of abstract math. $\endgroup$ – Stefan Smith Oct 11 '13 at 2:10
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Personally, I'm not enthusiastic about "learn how to think books". Instead, I believe that one learns how to do by doing. That is, find a topic that interests you and study it and learn it.

When, in the course of doing this, you find you need some background, then learn that background material sufficient so you can move forward in your main topic.

(But, I should add, I'm a physicist and not a mathematician, and maybe this is an important distinction here.)

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  • $\begingroup$ I agree that one learns how to do mathematics by doing problems. $\endgroup$ – Stefan Smith Oct 12 '13 at 2:32
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Spivak's Calculus. Do the exercises, they are great. Especially if you're currently taking calculus (even without proofs).

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