Who Is Fourier? A Mathematical Adventure

I would second the recommendation for Who is Fourier? A Mathematical Adventure. It's an unusual and engaging introduction to waves, Fourier coefficients, and transforms. The slope is gentle but not dumbed down. https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n... (https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2nd/dp/0964350432#:~:text=In%20Who%20is%20Fourier%3F,exponentiation%2C%20differentiation%2C%20and%20integration).

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.

My recommendation below is not the equivalent of a Feynman's series for math, but one that is pegged much lower, for someone interested in basic remedial math. It is called "Who is Fourier: A Mathematical Adventure". I was tremendously surprised by this unusual gem of a book. It covers the range from basic arithmetic to logarithms, trigonometry, calculus to fourier series. https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n... (https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2nd/dp/0964350432)