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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?

#11

Post by rramadass »

Some of the books that you mention seem a bit too hard for a teen, so you have to be careful not to demotivate them by expecting too much of them; instead i suggest a simpler approach before tackling the big ones;

* Functions and Graphs by Gelfand et al. - A small but great book to develop intuition.

* Who is Fourier? A Mathematical Adventure - A great "manga type" book to build important concepts from first principles

* Concepts of Modern Mathematics by Ian Stewart - A nice overview in simple language.

* Mathematics: Its Content, Methods and Meaning by Kolmogorov et al. - A broad but concise presentation of a lot of mathematics.

* Methods of Mathematics Applied to Calculus, Probability, and Statistics by Richard Hamming - A very good applied maths book. All of Hamming's books are recommended.

There are of course plenty more but the above should be good for understanding.

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

#12

Post by alimw »

I think the Princeton Companion would be a nice gift because it's something they can dip into as they desire. With a more linear book you may appear to confer an obligation to wade through it from beginning to end. (I also really like the Companion and although I've never splashed out on a copy for myself I wish someone else would :) )

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

#14

Post by bobmaxup »

Jan Gullberg - Mathematics: From the Birth of Numbers

https://www.amazon.com/gp/product/039304002X

Amazon.com Review What does mathematics mean? Is it numbers or arithmetic, proofs or equations? Jan Gullberg starts his massive historical overview with some insight into why human beings find it necessary to "reckon," or count, and what math means to us. From there to the last chapter, on differential equations, is a very long, but surprisingly engrossing journey. Mathematics covers how symbolic logic fits into cultures around the world, and gives fascinating biographical tidbits on mathematicians from Archimedes to Wiles. It's a big book, copiously illustrated with goofy little line drawings and cartoon reprints. But the real appeal (at least for math buffs) lies in the scads of problems--with solutions--illustrating the concepts. It really invites readers to sit down with a cup of tea, pencil and paper, and (ahem) a calculator and start solving. Remember the first time you "got it" in math class? With Mathematics you can recapture that bliss, and maybe learn something new, too. Everyone from schoolkids to professors (and maybe even die-hard mathphobes) can find something useful, informative, or entertaining here. --Therese Littleton

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

#15

Post by logicslave »

The classic text on analysis is Principles of Mathematical Analysis by Rudin. Its very difficult and leaves it to the reader to understand the terse proofs. It starts from the beignning, with no math background assumed about the reader. The terse proofs are written in such a way to force the reader to gain deep mathematical intuition. Some of the proofs are elegant and beautiful. I would absolutely recommend it. You can see a pdf here:

https://notendur.hi.is/vae11/%C3%9Eekking/principles_of_math...

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

#16

Post by bordercases »

logicslave wrote: post #15

The classic text on analysis is Principles of Mathematical Analysis by Rudin. Its very difficult and leaves it to the reader to understand the terse proofs. It starts from the beignning, with no math background assumed about the reader. The terse proofs are written in such a way to force the reader to gain deep mathematical intuition. Some of the proofs are elegant and beautiful. I would absolutely recommend it. You…

> It starts from the beignning, with no math background assumed about the reader.

It assumes that you have enough mathematical maturity to deal with proofs left to the reader.

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

#19

Post by mhh__ »

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 style.

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