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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.

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closed as too broad by Tommi Brander, Chris Cunningham, Brendan W. Sullivan, user52817, Xander Henderson Apr 3 '18 at 20:07

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ On what age range are you going to focus? Pre-school, primary (elementary), secondary (high school), or tertiary (college)? $\endgroup$ – Joel Reyes Noche Apr 1 '18 at 6:32
  • $\begingroup$ Isn't the Jordanian curriculum good enough? Should they obtain a official degree from the state? What about other subjects? $\endgroup$ – Paracosmiste Apr 1 '18 at 16:49
  • $\begingroup$ @JoelReyesNoche , Actually , I'm going to focus on Primary and Secondary .. , Any Suggestions for students in these range ? , Thanks $\endgroup$ – Mohammed Rizqallah Apr 1 '18 at 20:34
  • $\begingroup$ @inéquation , Unfortunately , it's not good enough , yes should I get it and I did ... Sorry ? Other subjects ? What do you mean ? $\endgroup$ – Mohammed Rizqallah Apr 1 '18 at 20:39
  • $\begingroup$ @MohammedRizqallah My advice is to search other curricula and find the one that suits you. It's better to use another curriculum designed by specialists and tested by millions of students than to design a curriculum from scratch. Also avoid using books about mathematics in general. By other subjects I meant physics, chemistry, poetry.... $\endgroup$ – Paracosmiste Apr 2 '18 at 9:40
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I'd put my money on:

Mathematics and the Imagination by Edward Kasner and James Newman The four-volume set The World of Mathematics that Newman edited.

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.

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  • $\begingroup$ I'm only allowed 8 links --- ??? This is news to me. Also, I've made several stack exchange posts with over 50 links, even one with over 80 links. $\endgroup$ – Dave L Renfro Apr 1 '18 at 0:36
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    $\begingroup$ @DaveLRenfro Users below a certain reputation threshold (I don't know what, I think it's fairly low) are pretty limited with including links and in-line pictures $\endgroup$ – pjs36 Apr 1 '18 at 3:37
  • $\begingroup$ Thanks Lee , It's really helpful , btw , I'm not sure if we can pay any books because this organization depends on " Donations " of people , but I'll search on these book in Libraries for get them free, I'm interested to get more advises of you Note : About that my reputation because I'v shared this question on " math.exchange " I'm new and I didn't know that rule " i can't ask this question there " Thanks for understanding . $\endgroup$ – Mohammed Rizqallah Apr 1 '18 at 21:08
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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.

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    $\begingroup$ it's really useful , Thanks a lot $\endgroup$ – Mohammed Rizqallah Apr 1 '18 at 20:44
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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.

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  • $\begingroup$ Thanks sir , Actually I think i can't spend the time with students on these books " Motivation books " , I was mean in motivation about " math topics are useful and I can make it fun for student " useful + fun " at the same time , You can understand my mean if you visit " Brilliant.org " , take a look at " Number Theory and basic math " Wiki , almost I want to teach the students from this website , but I'm trying to contact with Brilliant for take the acceptance , " Useful books " are good for that i think , However Thanks for helping $\endgroup$ – Mohammed Rizqallah Apr 1 '18 at 20:50

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