Hi, I'm picking the last part of the question to answer you.

Everyone knows how important the prime numbers are in Computer
Science. And also everyone should know that there is no algorithm to
compute / identify if a number is prime or not: you just have to
divide the number consecutively by others until you conclude that
there are no divisors and thus the number is prime.

The difference between knowing your math and do this in a brute force
approach is the difference between being able to calculate if a number
is prime or not (specially for very large numbers).

For instance, is a number is not divisible by 2, it will not be
divisible by 4, or by 6 or by any other pair. So if you conclude that
the number is not divisible by 3, you can skip the pairs in the
division check. And the same thing applies to multiples of 3, 5, and
so on.

This is just using concrete maths. You can find examples in almost any
area of maths, for example, in graph theory. The shortest path
algorithm that routes our data packets in the Internet is a purely
mathematical algorithm which happens to be usable in computer networks
(thanks, E. Dijkstra!).

Best regards,

Nuno

2009/12/10 Rammohan Vadlamani <[email protected]>:
> Hi all,
>          I have been practising java programming for the past one year and
> have learnt pretty much of it. But I want to program really big stuff. Can
> any one tell me how should I proceed. I have also heard that algorithms and
> mathematics play a big role in programming. Can any one let me know the
> significance of algorithms and maths in the field of computer programming.
>
> Rammohan
>
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