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First read https://artofproblemsolving.com/news/articles/avoid-the-calc...

By one of my early mathematics tutors in San Diego math circle

Then buy something like: Mathematical Proofs: A Transition to Advanced Mathematics (3rd Edition) (Featured Titles for Transition to Advanced Mathematics) https://www.amazon.com/dp/0321797094/ref=cm_sw_r_cp_api_i_K4...

Also art of problem solving vols 1-2 are now classics for that age.

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