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Ask HN: Recommend a maths book for a teenager?

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Re: Ask HN: Recommend a maths book for a teenager?

#65

Post by impendia »

I'd consider something by John Stillwell. For example, Numbers and Geometry, which investigates the connections between number theory and plane geometry -- two subjects which your child has probably seen, but not seen related.

Stillwell is a magnificent writer -- he loves to go on digressions, and to talk about the history of the subject. My impression is that his books are a bit rambling for traditional use as textbooks, but perfect for self-motivated reading for exactly the same reason. He makes the subject fun.

(Disclaimer: I haven't read this book in any sort of depth, but I have read another of Stillwell's books cover to cover.)

Concerning your other recommendations: The Princeton Companion to Mathematics is magnificent, but in practice it's something he'd be more likely proudly own and display on his bookshelf than to read; it's quite dense. Spivak's Calculus, from what I've heard, is magnificent. Probably best in the context of a freshman honors class, but I can imagine that someone disciplined could love it for self-study. Don't know Moor and Mertens.

Re: Ask HN: Recommend a maths book for a teenager?

#66

Post by mci »

The Cauchy–Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities is a graded problem book that will teach them the principles and practice of mathematical proofs like no other book. Here is its MAA review: [0]. A pirate PDF is a Google search away. Take a look and see if you like it.

[0] https://www.maa.org/press/maa-reviews/the-cauchy-schwarz-mas...

Re: Ask HN: Recommend a maths book for a teenager?

#67

Post by mhh__ »

Koshkin wrote: post #55
tobinfricke wrote: post #44

The Road to Reality by Roger Penrose. https://www.nytimes.com/2005/02/27/books/review/the-road-to-...

This book is totally inappropriate for learning mathematics, especially for a teenager. A well-prepared layman, maybe, but not a teenager who just wants a good introduction to the subject.

It's an inspired book, but it's not a textbook.

It's purpose to me at least was as a guide to the mathematics that was too difficult for me to understand straight away but could be considered the end goal to a given study i.e. As Symplectic Geometry is Analytical Mechanics.

Re: Ask HN: Recommend a maths book for a teenager?

#70

Post by msla »

javajosh wrote: post #48
MperorM wrote: post #37

During the first year of my undergrad someone introduced me to Gödel, Escher, Bach. I thought it was mind blowing at the time and still find it to be an incredible introduction to formal systems, thinking mathematically and understanding the concept of proofs. All these concepts are central to higher level mathematics, and are not covered in high school (at least not the Danish one). I'm was very thankful for that in…

I have to disagree with you here, and strongly. I don't think Gödel, Escher, Bach is a good book. Hofstaeder is clearly very smart, curious, and open-minded, and I love all those things, but the book itself is just so pretentious and sort of pointless. It's precisely the wrong kind of book you want to give a bright teenager, because it will only encourage them to get a head-start inserting their head up their own ars…

> I don't think Gödel, Escher, Bach is a good book. Hofstaeder is clearly very smart, curious, and open-minded, and I love all those things, but the book itself is just so pretentious and sort of pointless.

I'm curious: Do you feel this way because it isn't a math textbook?

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