In my country the education system is very expensive, so I’m considering starting an organization to teach lower-income students for free. In particular, to motivate them into the science fields. So, I’m asking for general recommendations on good mathematics books. Books that are useful for both children and adults, and at the same time are helpful and powerful for them to improve their skills in mathematics. Any suggestions? Thank you very much.
I'd put my money on:
These books appeal to people in all subject areas. I myself taught a bit on math through literature at the secondary level, and I gleaned three short stories from the corresponding section in World.
For inspiration, Innumeracy by John Allen Paulos, which shows why people are so ready to say they're bad at math. He's a mathematics professor, so he's seen it.
Mathematical Snapshots by Hugo Steinhaus is festooned with examples of connections within and outside of mathematics. I could easily get 25 conference presentations from this book alone.
I guess it's clear that I am not one for the traditional curriculum, preferring books with a student-oriented (rather than math-oriented) focus. I loved Calculus: A Liberal Art by W. M. Priestley, and liberally used it when teaching AB and BC Calculus.
If you're looking for specific textbooks, I can vouch for Contemporary Pre-Calculus through Applications and Contemporary Calculus through Applications, both developed by the North Carolina School of Science and Mathematics faculty. I've taught using both of them and they are phenomenal, although the Calculus one might be hard to find.
My favorite series of high school books is from the University of Chicago School Mathematics Project. I was only able to use two of them: Functions, Statistics, and Trigonometry, and Precalculus and Discrete Mathematics, found in their entire series for grades 6–12.
Ever since they came up with the acronym, I've contended that although the STE parts belong together, the M isn't like STE. M should exist between the humanities and the sciences, and the closer you get to the humanities the better. Have a look at A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form to see why.
Some of these books exist in inexpensive Dover editions. They're worth investigating.
I'm only allowed 8 links, and have probably written more than I know already.
It seems that your main concern is cost. I therefore suggest you look for sources of free textbooks. If you're looking for books for undergraduate students, then you might want to take a look at the books from OpenStax.
From its Wikipedia entry:
OpenStax (formerly OpenStax College) is a nonprofit ed-tech initiative based at Rice University. Since 2012, OpenStax has created peer-reviewed, openly licensed textbooks, which are available in free digital formats and for a low cost in print.
They have free textbooks on Math, Science, Social Sciences, Humanities, and AP. For math, they currently have textbooks on Prealgebra, Elementary Algebra, Intermediate Algebra, College Algebra, Algebra and Trigonometry, Precalculus, Calculus (Volumes 1, 2, and 3), Introductory Statistics, and Introductory Business Statistics.
Overall: I recommend two tracks: (1) books that are motivational and (2) books that are helpful. For all of them, I would emphasize books that are more common/popular as it will be more likely to get a native language translation. Also, for the charitable bang for the buck, emphasize books that have cheap editions (more likely in the popular ones as there will be current paperback prints).
You don't mention it, but: I think bigger challenges than the content will be (1) funding and (2) outreach. I feel like your question is already super broad (but lacking in detail on your situation, like WHAT country or age target or ability target, which would allow us to help you better), so won't address them. But these are probably bigger challenges than the books. I do see something like a national (perhaps participative) exam with prizes as a useful idea. I'm not sure how to restrict it to low income awardees though.
Motivational books: Feynman "what do you care what other people think" and "surely you are joking". Microbe Hunters. Men of Mathematics. All of the Heinlein juveniles, especially Starman Jones, Have Spaceship Will Travel, and Citizen of the Galaxy (as they emphasize education and a bit of Horatio Alger). All of these should be available in Arabic.
Useful books: Schaum's Outlines, especially the older ones for First Year College Math, Calculus, etc. Practical man's Guide to Trig, Calc, etc. Also Calculus made Easy. These may all be English only.