This might be a silly recommendation, but "Higher Algebra" by Hall and Knight was brilliant for me when I was around 15 or so.
Ask HN: Recommend a maths book for a teenager?
181–190 of 194 posts
Re: Ask HN: Recommend a maths book for a teenager?
#182This is a beautiful book, especially if he or she is into magic: Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks by Persi Diaconis, Ron Graham
Re: Ask HN: Recommend a maths book for a teenager?
#183Linear Algebra Done Right
Re: Ask HN: Recommend a maths book for a teenager?
#184Have 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 .
I thought of a few others that are "fun":
- The Annotated Turing by Charles Petzold
- Quantum Computing since Democritus by Scott Aaronson
- Euclidean and Non-Euclidean Geometries by Marvin Jay Greenberg (a textbook, but an easy one to read on your own)
- Gödel's Proof by Nagel and Newman (best if he can read it with a partner and talk through the steps)
- Prime Obsession by John Derbyshire
Some of those have already been mentioned, but consider this another vote for them. :-)
Re: Ask HN: Recommend a maths book for a teenager?
#185A little off-topic (and perhaps more useful for younger students) but you could do worse than introduce them to the achievements of Gauss (though they are probably somewhat familiar), who as a teenager had discovered and rediscovered several important theorems - his foundational Disquisitiones Arithmeticae was written at 21. https://www.storyofmathematics.com/19th_gauss.html This book is aimed at a young audience, th…
The books by Tent are mathematically at a 4th or 5th grade level. They’re sort of like Jean Lee Latham’s bio of Nathaniel Bowditch (you learn a fictionalized life story but you can’t really grok the person’s contribution). Of course, most mathematicians lead far more boring lives than Bowditch did in his youth, so the kind of kid who is reading Harry Potter by 4th or 5th grade is going to find them very dry.
Re: Ask HN: Recommend a maths book for a teenager?
#186There are many books on that front, particularly the ones related to recreational math or intro higher math (see https://mathvault.ca/books for instance). Spivak's Calculus as an intro would be an interesting start, though Stewart's Calculus is dense but more accessible.
Re: Ask HN: Recommend a maths book for a teenager?
#187I enjoyed "our mathematical universe" by max tegmark. It's not the books intention to teach mathematics, but rather explain how the author sees a link between mathematics and the universe.
It will be some new mathematical concepts for him, but I reckon he will be able to Google what does are.. I also find it extra motivating to learn a new mathematical tool when I know what type of problem it can solve!
Re: Ask HN: Recommend a maths book for a teenager?
#188Since you mention analysis, I recommend Yet Another Introduction to Analysis and Metric Spaces by Victor Bryant. They should be at the right level and a lot of fun.
Another analysis suggestion is Creative Mathematics by H.S. Wall. It is a book that walks a high school level student through creating the proofs themselves. The topic covered is a stripped down version of analysis, calculus, and later even differential geometry. It's really brilliant. Going slow and having fun when you're a teen would be much more productive than going fast and burning out.
The Spivak book is a good suggestion and might be a little difficult depending on their actual background. The books by Gelfand mentioned by someone else (there's actually a series of them that cover algebra, functions, coordinates, trigonometry, etc.) would help provide the needed background.
The book Conceptual Mathematics is claimed to be aimed at high school students. Maybe give it a whirl and see what happens. If they know calculus, then Advanced Calculus: A Differential Forms Approach by Harold Edwards is a gem. The first three chapters should be readable, as they give heuristic discussions of the topic.
Re: Ask HN: Recommend a maths book for a teenager?
#189"The Symmetries of Things" [1] by John H. Conway, Heidi Burgiel, and Chaim Goodman-Strauss.
A fantastic and beautifully illustrated expository work describing symmetry groups such as the 17 wallpaper groups in the plane (think Escher), and other tiling groups in for example the hyperbolic plane. Love the use of orbifold notation as opposed to crystallographic notation.
[1] https://www.amazon.com/Symmetries-Things-John-H-Conway/dp/15...
Re: Ask HN: Recommend a maths book for a teenager?
#190Concrete Mathematics by Knuth and Patashnik (already mentioned for u/pmiller2) if the kid likes numbers. That's perhaps the guiding thread of the book -- it's about the beautiful (yet usually very elementary and natural) things you can do with numbers. Geometry Revisited by Coxeter and Greitzer and/or Episodes in Nineteenth and Twentieth Century Euclidean Geometry by Honsberger if the kid is into plane geometry. It's…
Another great book that's worth a read is "Things to make and do in the 4th dimension" by Matt Parker.
It is a really interesting book as it covers multiple topics from mathematics and being that you are a young reader you might benefit from that exposure to topic.
From there on you can fine the topics that interest and dive deeper and learn the nitty gritty!
Thats how I personally found my passion in topology.