MyMaths MyLife

Pure mathematics is more like art. Pure mathematicians work on building a foundation for a theory. One nice feature about pure mathematics is that it is free from argument. When a mathematician makes a discovery there is no opposition, as in science. And his theory stands the test of time, unlike science where one law is shown to be wrong in special cases. But once a foundation is build (like complex analysis) applied mathematicians take its result and use it to solve important problems.

Pure math is much more difficult. Classes in applied math consist of memorizing the steps to solve problems. However, classes in pure math involve proofs, which implies a good understanding of the subject matter is required. In pure math you need to justify everything you do. Which can sometimes make a simple argument long and complicated. It is easier for someone in pure math to learn applied math rather than someone in applied math to learn pure math.

Determinants and matrices, they look alike. Their similarities caught many unaware and results in "excitements" and much interests.

Both contain numbers within. But ......

- determinants are bounded by two straights lines whereas matrices are by square braces

- determinant resulted in a single numerical value, whereas matrices are sets of numbers grouped within the braces

- determinant can be extracted from matrix, but not the other way round

- there are inverse matrix but not inverse determinant

- a scalar multiplier affects only a single row or single column of a determinant, but affects all the numbers within a matrix