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I am just finishing grade 12 pre-calculus at my school and have strong interest in math. The problem is, it seems some important elements of higher level math are not in my schools curriculum that are sometimes taught in pre-calculus.

My school offers Calculus and uses Stewarts text. I am planning to take it but what I can't decide is whether or not I should be self studying logic / set theory / proofs before studying calculus at a post secondary level to be able to handle rigorous texts in post secondary like Spivak.

If I was to just go ahead and take the Calculus that my school offers would I be adequately prepared for first year post secondary calculus / linear algebra courses or would most of the proofs / set theory be taught in first year p.s. courses?

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  • $\begingroup$ You certainly should, as a matter of interest, do some mathematics that is more proof-oriented, rather than computation-oriented. I would not recommend going through "logic/ set theory/proofs" as a subject, but others might not agree. School calculus courses, specially those not subject to an external exam, can differ considerably even if they use the same text. Mastery of large parts of Stewart would be very useful for university. $\endgroup$ – André Nicolas Feb 24 '14 at 21:25
  • $\begingroup$ Formal set theory and logic won't make much sense until you have more background in calculus and algebra. You will probably get all the set theory you will need in the introductory chapters of your textbooks. In 1st year, you will probably be introduced to few standard proofs, e.g. the so-called delta-epsilon proofs in calculus, some proof by induction in algebra. Then you will be ready to systematically learn other methods of proof. If you are chomping at the bit, you might play around with some proof software I have developed (free download at dcproof.com ) $\endgroup$ – Dan Christensen Feb 25 '14 at 6:40
  • $\begingroup$ I think the book "Introductory Mathematics: Algebra and Analysis" by Geoff Smith is everything you're looking for. You can read the preface and some reviews at Amazon: amazon.com/… $\endgroup$ – etothepitimesi Mar 25 '14 at 4:19
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I highly recommend these $3$ introductory books, in this order. They cover basic undergrad level math that you will definitely encounter in many undergraduate/graduate courses.

Mathematical Proofs: A Transition to Advanced Mathematics

The Higher Arithmetic: An Introduction to the Theory of Numbers

Discrete Mathematics and Its Applications

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You'll probably end up taking an intro to proofs class if you major in math. I studied a lot of the stuff before hand, so I thought it was easy, but then I got to higher math, and I was screwed, because I didn't know how to adjust to not knowing anything. I really struggled/continue to struggle with more heavy theoretical math.

It just depends on you, though. I didn't really know anything about proofs either going into it, and yes, you will be at a disadvantage, but it's possible to learn. Just don't expect it to be as easy as it is now, because I promise, it gets a lot harder later.

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