Ask HN: Recommend a maths book for a teenager? • Hacker News Board

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

#121

Post by jacobolus » Fri, Jul 03, 2020, 10:27 PM UTC

mhh__ wrote: post #19

Visual Complex Analysis. Partly because it's a brilliant book and partly because Complex Analysis is often really really badly taught. If you haven't read it, it teaches complex analysis in terms of transformations and pictures rather than solely algebra. It's very clever; Also touches on some concepts in physics and vector calculus. If you like the style 3Blue1Brown uses, he cites VCA as an inspiration for that styl…

If you like pictures, another couple nice books are Nathan Carter’s Visual Group Theory and Marty Weissman’s Illustrated Theory of Numbers, both of which should be accessible to motivated high school students.

http://web.bentley.edu/empl/c/ncarter/vgt/

http://illustratedtheoryofnumbers.com

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

#122

Post by soVeryTired » Fri, Jul 03, 2020, 10:28 PM UTC

I stumbled on Q.E.D by Feynman at a young age - it had a deep influence on me. I also read parts of "the mathematical experience" by Davis and Hersch, and "Godel, Escher, Bach" by Douglas Hofstadter.

It's not really maths, but Spacetime Physics: Introduction to Special Relativity would have been great for me at that age.

The Princeton Companion is a cool book, but it'd be better suited to a graduate in mathematics.

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

#123

Post by lanstin » Fri, Jul 03, 2020, 10:28 PM UTC

Metamathematics by Kleene. Fairly accessible math, mostly new and developed from the start it takes one into compatibility theory and formalization of maths in a way that makes Godel easy to understand and just full of cool ideas that are very relevant to today’s world of computers and the limits to certainty.

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

#124

Post by jacobolus » Fri, Jul 03, 2020, 10:31 PM UTC

enriquto wrote: post #117

jacobolus wrote: post #90

Earlier quoted context omitted.

This would be better for a 10–14 year old in middle school or early high school.

Hmmm. There's no way my 10 year old daughter would read beyond the first page of that thing. For 15-16 it's great.

This is more about level of preparation / past experience than age per se. The OP describes a “bright, self-motivated child in their late teens who is into maths” and is a few years ahead of their peers. The mentioned book might seem a bit easy or elementary for this particular kid. The two Berkeley Math Circle books might be better. https://mathcircle.berkeley.edu/books

You are right that a book aimed at well prepared Russian 12-year-olds in an extracurricular math circle might be fine for 16-year-old average American students.

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

#125

Post by galkk » Fri, Jul 03, 2020, 10:31 PM UTC

There's a good gift, a bad gift, and a book though

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

#126

Post by gen220 » Fri, Jul 03, 2020, 10:36 PM UTC

If they like calculus and can stand proofs, I’d recommend a Course of Pure Mathematics by Hardy. It totally blew my mind when I was that age, to see how everything was “connected” by proofs, starting with real numbers. Despite being proof heavy, I found the writing style singularly legible and comprehensible.

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

#127

Post by lanstin » Fri, Jul 03, 2020, 10:36 PM UTC

sgillen wrote: post #27

If they have been exposed to diff eq at all I can recommend Strogatz Nonlinear Dynamics and Chaos. It's a very interesting subject, and the text is one of the most approachable I've come across for any subject.

Chaos by James Gleick is also a good intro to some chaos maths and a great bio read, with the stories of Feigenbaum wrestling with the new ideas.