I'm looking for recommendations for a maths book for a bright, self-motivated child in their late teens who is into maths (mainly analysis) at upper high-school / early undergrad level.
It would be a birthday gift, so ideally something that is more than a plain textbook, but which also has depth, and maybe broadens their view of maths beyond analysis. I'm thinking something along the lines of The Princeton Companion to Mathematics, Spivak's Calculus, or Moor & Mertens The Nature of Computation.
What would you have appreciated having been given at that age?