Spivak is an excellent choice but may be too advanced depending on his level. I would also strongly recommend any of the books in the Art of Problem Solving series: https://artofproblemsolving.com/store/list/aops-curriculum I've got a PhD in bioengineering but I'm currently going through Introduction to Counting and Probability and I'm really enjoying it. Some others (not AOPS series): Nelsen - Proofs Without Words Polya - How to Solve it Strogatz - Nonlinear Dynamics and Chaos
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