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Algebra: The Beginnings

As mentioned in a previous post, our math abilities are a by-product of our language skills. Indeed, mathematics can be thought of as another language, limited in its subject matter but powerful in developing its own sentences (equations). Maths has its own set of words (symbols), its own dialects (scientists use a different set of symbols and equations than do engineers), and its own syntax and grammar. Algebra is the mathematical version of syntax and grammar, which is why it is such and important subject. It underpins all that is mathematics.

You are already familiar with many of the symbols (words) used in maths:

+ means “plus” or “positive” depending on context

− means “subtract” or “negative” depending on context

× means “multiplied by” or “times”

÷ means “divided by”

= means “equals”

So you already can read math sentences (equations) like 2 + 3 = 5 and you already know that there are rules (syntax) to be followed when writing an equation. For example, 2 3 + 5 = uses the same symbols, but it doesn’t make sense.

Other equations are 3 = 3, 4 = 4, or 2 = 1. Just as in language, maths sentences can be true or false. But let’s start with an obviously true sentence: 3 = 3. Now if I add 1 to both sides of the “=” sign, I get:

3 + 1 = 3 + 1 or 4 = 4, another true equation. Now let’s divide both sides by 2:

4 ÷2 = 4 ÷2 or 2 = 2, Another true equation. I can do this all day, but let’s just do one more:

2 – 2 = 2 – 2 or 0 = 0. In each step, notice that I had to do the same thing on both sides. If there is only one algebra rule you can remember, it’s this one: you can create a new true equation from a true equation by doing the same arithmetic on both sides of the equation. We will see some caveats (cautions) later regarding this, but this is the most important rule in algebra.

Tomorrow, I will introduce the idea of equations with unknown numbers.

My logo

Let me explain a bit about my logo. The foreground words are self-explanatory except for the 𝜋 symbol used in place of the “T”. 𝜋 is the Greek letter pi. Greek symbols are used extensively in maths and 𝜋 is the most common one used. You will see it used many times in subsequent posts.  The background equations not only have math equations, but symbols representing all sorts of math applications: astronomy, biology, chemistry, genetics, nuclear physics, electronics, … . I think this is a very appropriate logo for me. What do you think?

Why can we do maths?

Ever wonder why humans can do math? What was the evolutionary pressure that gave us the ability to do calculus? It turns out that our math abilities are a by-product of our language abilities. A good book that explains this is “The Maths Gene” by Keith Devlan. Check it out!

Introducing the DavidTheMathsTutor Blog

Hi all, Well after a bit of learning how to set up a blog site and addressing the security concerns and a lot of trial and error, I’ve finally set up the blog site. I’m sure some tweeking will occur in the early days, and I’m open to comments to improve the site. I will post my first official math related post soon. Hopefully, the facebook page will be automatically updated.