For something that's a little more fun to read and covers fundamental topics. (Foundations for higher mathematics) I'd recommend Gödel, Escher, Bach by Douglas Hofsteader. It changed the way I approach problems to this day.
Ask HN: Recommend a maths book for a teenager?
31–40 of 194 posts
Re: Ask HN: Recommend a maths book for a teenager?
#32Abstract Algebra by Pinter and Introduction to Topology by Mendelson are two fantastic books, published by Dover, that are too elementary to be used as university textbooks on those subjects but as a result are great for a more casual reader. They are well motivated and rarely omit details. They would serve as a great introduction to undergraduate math.
Re: Ask HN: Recommend a maths book for a teenager?
#33"Proofs from the book" is very neat.
Re: Ask HN: Recommend a maths book for a teenager?
#34For analysis you absolutely MUST read Principles of Mathematical Analysis by Walter Rudin. Covers everything and is literally a gold standard text in modern analysis. "Baby Rudin" is essentially the analysis bible that all subsequent texts worked off of.
Re: Ask HN: Recommend a maths book for a teenager?
#35I'm going to go a completely different direction from other recommendations and say Concrete Mathematics by Knuth and Patashnik. They will definitely be able to use skills from analysis and calculus here, but there are so many additional tools in this book that it's very much a worthwhile digression. The marginal notes are great, as well!
I own this book, and it's a favorite of mine.
https://www.amazon.com/Concrete-Mathematics-Foundation-Compu...
Re: Ask HN: Recommend a maths book for a teenager?
#36For broadening their view:
- Proofs and Refutations by Imre Lakatos (https://en.wikipedia.org/wiki/Proofs_and_Refutations) (makes you think about what a proof really is)
- The World of Mathematics: not a lot of math proper, doesn’t have much depth, but lots of examples of applied math, interwoven with mentions of the history of mathematics (https://www.amazon.com/World-Mathematics-Four-Set/dp/0486432...)
Re: Ask HN: Recommend a maths book for a teenager?
#37During 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 introduction, hopefully they would be as well :)
Re: Ask HN: Recommend a maths book for a teenager?
#38I'm going to guess that for the OP, their reader is already past this level, but sharing anyway for the benefit of others, as I think it's a great book for roughly around that age:
https://www.amazon.com/Prof-McSquareds-Calculus-Primer-Inter...
Re: Ask HN: Recommend a maths book for a teenager?
#39I'm going to go a completely different direction from other recommendations and say Concrete Mathematics by Knuth and Patashnik. They will definitely be able to use skills from analysis and calculus here, but there are so many additional tools in this book that it's very much a worthwhile digression. The marginal notes are great, as well! I own this book, and it's a favorite of mine. https://www.amazon.com/Concrete-M…
Great pick. Note: you can get it for $20 less AND support a local used book store if you buy it from alibris. https://www.alibris.com/Concrete-Mathematics-A-Foundation-fo...
Re: Ask HN: Recommend a maths book for a teenager?
#40I suggest "What Is Mathematics?" by Richard Courant and Herbert Robbins. https://en.wikipedia.org/wiki/What_Is_Mathematics%3F
My high school math professor recommended this to me 40 years ago.
I got it, then put it on a shelf for 20 years. When I picked it back up, it somehow had become delightful! Perfect subway reading.