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## The Algebra Tree

Algebra can seem like a confusing subject. It is filled with various symbols such as x, y and z and terms to remember such as variable, coefficient, term and polynomial. However, rather than getting bogged down in the “trees” of algebra, I think it’s helpful to look at the forest. What is the place of Algebra in all of Mathematics?

Having taught math for a number of years, I have found a good model for the relationship between the different math subjects is a tree, with the most central part being algebra. That’s why I call it the algebraic tree. Let me continue to explain.

First we have the roots of this tree and of mathematics itself, which is arithmetic. We learn arithmetic in elementary school because it is fundamental to future math learning. Addition, subtraction, multiplication and division are central processes.

The basis of this tree of mathematics is algebra. Algebra feeds on Arithmetic and goes beyond it. For example, an important process in algebra is solving equations. However, this could not be done without knowledge of arithmetic, especially addition, subtraction, multiplication and division. Another algebraic process is the simplification of algebraic expressions. This again requires the use of basic arithmetic.

Where then do the other disciplines of mathematics fit into the tree of algebra? I would call them branches. For example, there is geometry. In geometry, you deal with a lot of geometric figures such as circles, triangles, and squares. However, to successfully solve related problems, you usually need to use algebra. For example, to find the area of a circle, you must solve an equation using a process learned in algebra.

Another branch would be trigonometry. Trigonometry focuses a lot on relationships in triangles. It uses special concepts such as sine, cosine and tangent. However, you could not use such concepts properly without using your knowledge of algebra.

A third branch would be statistics. Statistics deals with data analysis tools that can be used in practice, such as in business and psychology. However, to use these tools, you will need to use algebra. For example, a tool for comparing two sets of data to see if they are related is called correlation. Two things you expect to see correlated are people’s height and weight. The bigger they are, normally the more they weigh. You can calculate a number called the correlation coefficient which provides an indication of the strength of this relationship. However, the process of performing this calculation requires algebra.

So in summary, if you have problems with Maths and especially with Algebra, remember this tree of Maths… the Tree of Algebra.

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