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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?

#161

Post by ivansavz »

giantg2 wrote: post #6

This isn't bad. I'm surprised it's expensive now. https://www.amazon.com/No-bullshit-guide-math-physics/dp/099...

I forgot to mention, there is an extended PDF preview of the book you can see here: https://minireference.com/static/excerpts/noBSguide_v5_previ...

Also some parts of the best parts of the book are available in full as standalone free tutorials: SymPy = https://minireference.com/static/tutorials/sympy_tutorial.pd... ; mechanics tutorial = https://minireference.com/static/tutorials/mech_in_7_pages.p... ; concept maps = https://minireference.com/static/tutorials/conceptmap.pdf

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

#162

Post by ivansavz »

giantg2 wrote: post #154
ivansavz wrote: post #78

Earlier quoted context omitted.

Thx for plug. Indeed it would be a good book for any highschooler interested in more advanced topics. > I'm surprised it's expensive now. Yeah amazon pricing is weird. My intent is for the book to be sold ~$30, but if I tell this price to amazon they start selling it for $20 after discounting, and then readers buy it less because they think it is not a complete book, but just some sort of summary notes. Nowadays I se…

I could have sworn that it was between $15 and $20 when I got it a few years ago.

It's very possible if you purchased it when I had set the price to ~$30 and amazon was discounting it to ~$20.

BTW, I've released several "point" updates and the book is now at v5.3. Please reach out by email if you're interested in having the PDF (I have a free-PDF-with-proof-of-purchase-of-print-version policy, including all updates).

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

#164

Post by abhgh »

jacobolus wrote: post #121
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

I recently gifted Illustrated Theory of Numbers to a friend, and it is indeed beautifully illustrated.

I would also recommend "Prime Numbers and the Riemann Hypothesis" for its illustrations and exposition [1].

[1] https://www.amazon.com/gp/product/1107499437

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

#165

Post by rsaarelm »

Sanjoy Mahajan's The Art of Insight in Science and Engineering (available online, https://mitpress.mit.edu/books/art-insight-science-and-engin...). Takes a very pragmatic look to doing mathematics, while not pulling many punches on how advanced the mathematics gets. Would have appreciated this a lot, math books are usually split into dry theory where you have to already know math to be able to properly read them and books that are simplified to death for people who are forced to study math and don't want to.

Tim Gowers' Mathematics: A Very Short Introduction is a popular book on doing mathematics. Not a textbook that teaches you mathematics, so wouldn't give this as the only book, but popular "what's the field like" books could be very interesting to a high schooler.

Also, not suitable for the only book, Penrose's The Road to Reality. It gets very advanced and probably can't be fully tackled without additional mathematical education, but it tries to be an honest exposition of the math needed for modern physics from the ground up without explicitly resorting to external knowledge. I would have loved a "this will teach you all of the math if you can get through it" book like this even if I never did manage to get through it.

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

#166

Post by jldugger »

> 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

> What would you have appreciated having been given at that age?

Deep math is cool and all, but right now I'm working through a used copy of the Freedman, Pisani and Purves Statistics textbook https://amzn.to/2YVvU6o It's chock full of actual examples from real research and statistics, complete with citations. I just worked through some problem sets today, analyzing some twin studies establishing the link between smoking and cancer. Other topics I can recall: robbery trials, discrimination lawsuits, and coronary bypass surgery.

That said, it's an actual textbook, and expects the learning to come from engaging in problem sets. And it's far less technical than the Stats for Engineers course I barely passed. If you're looking for something less textbooky, Super Crunchers (https://amzn.to/3eTz5RL) is sort of a layman's book on the subject of prediction and statistics.

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

#167

Post by ian-g »

If you want them to look beyond Analysis, would an intro to discrete math maybe be what you're looking at?

Discrete Math With Ducks[0] (and the professor that taught from it) is the reason I focused on the discrete side of things. It doesn't take itself too seriously, and it introduces a range of topics in the area. Plus the mindset is different from analysis. It's an interesting shift

[0] https://www.maa.org/press/maa-reviews/discrete-mathematics-w...

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

#168

Post by pjungwir »

jameshart wrote: post #128

Have they worked through everything Martin Gardner ever wrote?

I second this! Gardner would be something more recreational and fun than a lot else out there. The Colossal Book of Mathematics is a good way to get a lot in one place. The Night is Large is also great but less math-focused.

I don't see any recommendations for Smullyan yet. The Lady or the Tiger is the classic I think, but I really loved Forever Undecided.

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

#169

Post by nikisweeting »

Gödel's Proof and GEB blew my mind in high school, gave me the motivation to actually attend my math classes, because it finally showed me there was more interesting stuff at the end of the math tunnel. Of course I only understood a fraction of it then (still do), but it was eye-opening.
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