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What Is Algebra?

What is algebra? What does it have to do with variables? And where did it come from? Keep on reading to learn the secret to understanding algebra!

By
Jason Marshall, PhD,
April 5, 2013
Episode #148

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What Is Algebra?

People often think that “algebra” sounds like a big and scary thing, but I think that’s mostly just because they don’t understand what it actually is. Which is a real shame because algebra is incredibly useful in the real world. Plus, it turns out that the big ideas behind it all are actually fairly straight-forward. So today we’re going to combat this universal fear and misunderstanding of an otherwise beautiful subject by diving in and answering the big question: What is algebra?

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The Problem with Algebra

The problem with algebra is that it isn’t a simple tangible object…like a spoon. If it was, it’d be easy to explain. After all, few people who manage to eat lunch with a spoon will have trouble explaining how it works afterwards. But, unfortunately, that’s just not what algebra is. So, what is it then? Well, instead of being a thing like a spoon, algebra is more analogous to being something like a style or a method of using a spoon...

I’m thinking of a sensible two-fingered (plus a thumb) grip versus a crazy five-fingered silverware stranglehold. Sure, both styles will get the job done, but one technique is definitely more elegant and efficient than the other.

The same is true with “style” in math. One type of method—sometimes algebraic—is usually most appropriate for solving a particular type of problem. But styles are much harder to recognize, point at, and label than things—which is why recognizing and labeling algebra can be tricky. So then what’s the best way to think of algebra?

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