If you ask a drunkard what number is larger, 1/3 or 2/7, he might not be able to tell you. But if you rephrase the question: What is better, 2 bottles of vodka for 6 people, or 2 bottles of vodka for 7 people, he will tell you right away. - Gelfand
The legendary Soviet/Russian mathematician I.M.Gelfand ran a series of lectures for many decades back in the Soviet times. Later when he immigrated to the United States of America he started a correspondence program for eager math students.
A number of books were written led by Gelfand catering to the middle and high school math student. Some of the books were perhaps written when he was in his country of birth in Russian and only later translated to English. A few were written probably in his last decade. I am listing the books as I know it to the best of my knowledge. It would be lovely to acquire more books by him. I will add one more book to the list even though it does not have the name of Gelfand associated, since it was recommended by the original Gelfand schools as a text for Geometry (it is an exceptional book!)
All books are very concise. Some have fewer than 100 pages even. These books are very cheap and I believe some are sold by Dover too. Originally they were published by Birkhäuser a former Swiss publisher. The problem sets are excellent for the set of students the books are targeting. The theory is crisp and to the point. Problem solving is the focus, rightly so.
Book list is below. The first four were the order in which students were taught back in the Soviet times at Gelfand school (actually there were two variations of the first book but I am listing the one which is available today).
The Method of Coordinates by Gelfand, Glagoleva, and Kirillov
Lines and Curves by Gutenmacher, and Vasilyev
Algebra by Gelfand, and Shen
Trigonometry by Gelfand, and Saul
Functions and Graphs by Gelfand, Glagolevam, and Shenol
Sequences, Combinations, Limits by Gelfand, Gerver, Kirillov, Konstantinov, and Kushnirenko
Lectures on Linear Algebra by Gelfand
I would have hoped he wrote a book on Calculus for the school student but unfortunately what I read was that it was in the works but never made it. He did write a book on Calculus of Variations but that would perhaps be out of scope for the school student. In the list above the first four are the core curriculum and the last three are for the preparation for Calculus I would say.
I wanted to work through Algebra by Gelfand and Shen, first published in September 1993. It is a 150 page book covering 72 topics related to school level algebra. The book presents 342 problems some with solutions, and others without. I have curated a list of problems from this book for teaching students which I do as a hobby.
My solutions aims to provide correct approaches to all the 342 problems listed in Algebra. Each solution is carefully checked, either by hand (particularly for proofs) or programmatically using Scheme (a dialect of Lisp). LLMs have helped me in typing it out in LaTeX. All errors are my own, please report any issue on GitHub.
The solutions are here in this repository. It is still work in progress.
Both the PDF file as well as the .tex file are provided for use.