The study of algebra is commonly referred to as arithmetic. This is a branch of mathematics which is a broad science.
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There are no types of algebra which are their algebra. If you study and master them, they become yours.
algebra
algebra come from the study of general property of numbers perticularly the realnumbers
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One can study linear algebra and its applications at many educational institutions. One can also study it online at websites such as study mode. And if one chooses to study this subject at home there are books available online and in bookstores.