Concrete Mathematics

> I haven't read any of Knuth's stuff because doesn't having 7 volumes kinda imply it can't possibly be well edited? That's a very bad assumption in this case. The contents of TAOCP are very well edited, just massive in scope and it's one man putting it all together. However, those aren't his only books. Concrete Mathematics is a completed text that expands on, in particular, the math in Chapter 1 of TAOCP. Literate Programming is a collection of papers on topics in programming, and is the first of eight such books. If you want interesting but mildly impractical, check out his Computers & Typesetting [0] which includes two books which are actually literate programs. [0] https://www-cs-faculty.stanford.edu/~knuth/abcde.html

I would recommend highly "What is Mathematics" by Richard Courant and Herbert Robbins. This is very accessible book for high schoolers who are keen and interested in mathematics, and will expose the reader to a broad array of topics and pique the interest and awaken the imagination and instill the beauty of mathematics. This in turn can drive the reader to find out more and fall in love with the subject. I would second this by "Concrete Mathematics" by Graham, Knuth and Patashnik. This is actual university course book with very formal proofs and theory, but the subject matter is still largely accessible to serious high school students and demonstrates beautiful reasoning examples throughout. It is also very practical book, after covering techniques in this book, one can often times calculate exact sums of infinite series quicker than estimating their bounds. If your high school student decides to study math at university level, the techniques and skills taught in this book will prove invaluable in broad areas of study.

Concrete Mathematics is a great book, really good content and techniques about computing things, and a lot of depth and useful history and side information.

Concrete Mathematics by Ronald Graham, Donald Knuth, and Oren Patashnik https://en.wikipedia.org/wiki/Concrete_Mathematics Also Knuth's TAOCP series are very formal and dense, in a good way.