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I'm an adult who tries to learn math from the ground up in his free time.

I've decided to start with arithmetic, but I don't know where to go next. I'm a type of person who learns by reading. I want to understand math, not to memorize it.

What topics (starting from arithmetic and on) to study? In what sequence? Please recommend textbooks.

I know some very very basic things, such as addition, subtraction, and how to find square roots. My foundation in math is very poor. I can say, safely, that till yesterday, I didn't know what ones, tens, and hundreds are, what place value is, what points and coordinates are and a lot more.

Mahmood Muhammad Nageeb
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  • Your arithmetic has to be solid. Things like tables and knowing how to do long division and fraction operations are a must. Then I would look for a pre algebra book (ebay, amazon etc) and begin with that. Also, Khanacademy is a good place to learn from in addition to your textbook. – imranfat Oct 11 '16 at 15:54

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Two possibly useful old books that I've come across in a nearby library are:

Aaron Bakst (1900-1962), Arithmetic for Adults. A Review of Elementary Mathematics, F. S. Crofts and Company, 1944, viii + 319 pages. one amazon.com review

Burdette Ross Buckingham (1876-1962), Elementary Arithmetic. Its Meaning and Practice, Ginn and Company, 1947, viii + 744 pages.

Interestingly, both seem to be freely available (legally also) on the internet. If you don't like lengthy on-screen reading, you can print out the pages (might have to do it one page at a time) or try to obtain a copy using interlibrary loan at your public library.

Regarding your question about what to study after arithmetic for high school mathematics, the subjects would be (elementary) algebra (typically a two year sequence), geometry, trigonometry, and precalculus (often includes trigonometry). Rather than worry about textbooks to use after arithmetic at this time, I would recommend that you focus on the task at hand -- arithmetic. In general, you'll find that the more you know, the more your previous plans wind up being changed because you begin to develop a better understanding for what approaches you like and you're better able to pick out books that function best for you (at these later times). I learned a lot of math on my own (most of high school math and all of the 3-4 semester college calculus sequence, and much of elementary linear algebra) simply by picking books from libraries and bookstores that I liked and that were books I felt I could learn from. The more I learned, the more I found that my own choices tended to be better for me than what others might have suggested, which often tended to be little more than what textbook they learned from rather than a reasoned choice from the thousands of available textbooks.

Dave L. Renfro
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