16 May Algebra Basics
Algebra is one of the most basic and broad mathematical concepts. It can be defined as the study of mathematical symbols and the laws of manipulating those symbols. Fun fact: a mathematician who studies algebra is called an Algebraist. The word Algebra itself is of Arabic origin and it means ‘‘reunion of broken parts’’. Surprisingly enough many people find Algebra challenging. Let us take a closer look at exactly what Algebra is.
Algebra can be divided into two main groups. These are Elementary and Abstract (sometimes called Modern) Algebra. Elementary Algebra is distinguished by the use of letters to represent unknown or varying values in a given mathematical equation or expression. This provides an easy reference to that unknown value. It also makes the equation or expression both simpler and easier to manipulate. A practical example would be the force of gravity. Since it changes from place to place and also changes with altitude,it becomes impossible to assign a particular figure to its value. This is where algebra comes in handy. It will assign the letter ‘g’ to the value of gravitational force at any point.Abstract algebra is an advanced form of mathematical study. It focuses on algebraic structures such as groups and lattices etc. it is primarily studied by professional mathematicians.
Having understood the concept behind Algebra, tackling algebraic problems becomes easy. Taking note that the letters are representing the required unknown value. It is also important to remember that the algebraic terms are also prone to the laws of arithmetic operations. For example if the letter moves from one side of the equal sign to the other, its sign (+/-) must change accordingly. Formulating algebraic equations to solve real life mathematical problems should also be easy. Just assign the unknown value an algebraic term like ‘x’ and consolidate with the values that you do know. For example, if I know I had fifty dollars but I don’t know how much I spent, I would say I spent ‘x’ dollars. After counting what I have left, say $12, I now know that x + 12 = 50. Using arithmetic laws, I can easily figure out that x = 38.
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