There are no types of algebra which are their algebra. If you study and master them, they become yours.
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It isn't; the algebra 1 and 2 that you get taught in middle or high school is elementary algebra. When (if you want to) you get into more advanced algebra, you can learn linear algebra (matrix algebra) and abstract algebra (which involves sets, operations on sets, groups, and many more concepts), and probably several more types of algebra I've never heard of.
3 types of relations in algebra are to graph, table, and map the x,y ordered pairs. just learned this! C:
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Today, we study many types of math. When you ascend to different grade levels, you are taught more types of math. Examples are: Algebra Calculus Geometry etc.
Algebra is important because it is the stepping-stone for other types of math, such as logarithms, geometry, and physics. If someone had not invented algebra, much of what we know today would not be known.