> 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?
Common Sense Mathematics by Ethan D. Bolker and Maura B. Mast
My friend was assigned this book for a quantitative reasoning class in college and I was so impressed by how approachable it was. It's got sections on things like climate change and Red Sox ticket prices.
Excerpt from preface:
"""
One of the most important questions we ask ourselves as teachers is "what do we want our students to remember about this course ten years from now?"
Our answer is sobering. From a ten year perspective most thoughts about the syllabus -- "what should be covered" -- seem irrelevant. What matters more is our wish to change the way we approach the world.
"""