teaching:topics:algebra:first
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teaching:topics:algebra:first [2021/09/25 23:08] simon |
teaching:topics:algebra:first [2024/05/21 07:42] simon |
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| \(\quad x^2-4;\ \ x-2;\ \ \frac{x^2-4}{x-2};\ \ 2y-3.\) | \(\quad x^2-4;\ \ x-2;\ \ \frac{x^2-4}{x-2};\ \ 2y-3.\) | ||
| - | <wrap #equation />An **equation** uses an \(=,\) it is a statement that two //[[#expression]]s// have the same numerical value. It is often a description of a 'fact' we know about the unknown quantities we are trying to find. In all of this each letter always represents the same quantity, we use different letters when we want to talk about different quantities. Uppercase and lowercase letters are distinct. This all starts out very much like arithmetic, but with some numbers we do not know yet. But we are mathematicians, so we have abstracted and generalised and made it very much more powerful than simple arithmetic. A simple but not trivial arithmetic-like example: | + | <wrap #equation />An **equation** uses an \(=,\) it is a statement that two //[[#expression]]s// have the same numerical value. It is often a description of a 'fact' we know about some unknown quantities we are trying to find. Sometimes it is more like a question, we want to know if or when it is true or false. With more than one letter an equation describes a relationship between those quantities. We can use equations to define new properties we find useful to have a name for, so we can talk about them. We can use them to state rules we have found about things. "Things" here might mean mathematical concepts as abstract as "numbers" or "triangles" or it might mean quantities we have seen in the would around us. In all of this each letter always represents the same quantity, we use different letters when we want to talk about different quantities. Uppercase and lowercase letters are distinct. This all starts out very much like arithmetic, but with some numbers we do not know yet. But we are mathematicians, so we have abstracted and generalised and made it very much more powerful than simple arithmetic. A simple but not trivial arithmetic-like example: |
| \[\large 2a - 3(b+c) = a-2c.\] | \[\large 2a - 3(b+c) = a-2c.\] | ||
teaching/topics/algebra/first.txt ยท Last modified: 2024/05/21 08:07 by simon
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