Hold when x and y are any numbers at all. In particular the laws of arithmetic (commutative, associative and distributive) hold. Because the letters are simply stand-ins for numbers, arithmetic is carried out exactly as it is with numbers. In algebra we are doing arithmetic with just one new feature − we use letters to represent numbers. How this notation evolved will be discussed in the History section. The development of mathematics was significantly restricted before the 17th century by the lack of efficient algebraic language and symbolism. Thus algebra enables us to write down general statements clearly and concisely. All of these can be captured by the algebraic statement 3 x + 2 x = 5 x, for any number x. We could replace the number 6 in this statement by any other number we like and so we could write down infinitely many such statements. We know from arithmetic that 3 × 6 + 2 × 6 = 5 × 6. You can see how compact the formula is compared with the verbal description. The simple algebraic statement E = mc 2 states that some matter is converted into energy (such as happens in a nuclear reaction), then the amount of energy produced is equal to the mass of the matter multiplied by the square of the speed of light. The letter c represents the speed of light, a constant, which is about 300 000 000 metres per second. This remarkable formula gives the relationship between energy, represented by the letter E, and mass, represented by letter m. Our modern algebraic notation greatly simplifies this task.Ī well-known formula, due to Einstein, states that E = mc 2.
As these patterns and relationships became more complicated, their verbal descriptions became harder and harder to understand. Before the introduction and development of algebra, these patterns and relationships had to be expressed in words. Many parts of mathematics are initiated by finding patterns and relating to different quantities. It provides the written language in which mathematical ideas are described. Algebra is a fascinating and essential part of mathematics.
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