The Maths Thread

[andmark]

Originally Posted by vcs

Basically the remainder of dividing one integer by another. For example 8 modulo 3 is 2.

Ah, thanks.

[blahblahblah]

Originally Posted by andmark

Ah, thanks.

definition of congruent:


A number `a` is said to be congruent to `b` modulo `m` if `m` divides (a-b)

its written as a ≡ b mod m

so we can say that when we write a≡b mod m ,, `b` is the remainder that is obtained when` a` is divided by `m`.

now let us take a few examples:

9≡1mod2

13≡1mod4

but now u get this doubt, when 13 is divided by 4 , remainder is why only 1 ? why cant we say the remainder is -3 ????

infact this doubt is correct. we can even write

13≡-3mod4

so we can write in various ways as we wish to..

[Uppercut]

The only time I've ever come across the modulo function is in computer programming. Is it much use anywhere else?

[Redbacks]

Originally Posted by Uppercut

The only time I've ever come across the modulo function is in computer programming. Is it much use anywhere else?

You could say time. with a 24 hour clock being mod 24 a general thing that people would use without thinking about it say when doing something in 30 hours.

I guess it would still require computer programming of some sort but Cryptology also makes extensive use of the mod function for coding. The RSA algorithm used in banking a prime example.

[vcs]

Originally Posted by Redbacks

You could say time. with a 24 hour clock being mod 24 a general thing that people would use without thinking about it say when doing something in 30 hours.

I guess it would still require computer programming of some sort but Cryptology also makes extensive use of the mod function for coding. The RSA algorithm used in banking a prime example.

Yeah, there is an entire branch of mathematics based on modulo arithmetic - rings, fields and groups all use modulo arithmetic if I'm not mistaken.

[Spark]

big segment of algebra - i.e. group theory - is based on modular arithmetic (quotient groups and what not)

a big section of ring theory is as well. number theory too.

[Neil Pickup]

Originally Posted by Redbacks

You could say time. with a 24 hour clock being mod 24 a general thing that people would use without thinking about it say when doing something in 30 hours.

I guess it would still require computer programming of some sort but Cryptology also makes extensive use of the mod function for coding. The RSA algorithm used in banking a prime example.

I appreciated that, even if nobody else did.

[vcs]

Yes cryptography, and error-correcting codes (used in storage, data transmission networks) are all based on modulo arithmetic.

[Spark]

i might be wrong as it's been a while but i think error-correction/detection in cpu's work on churning stuff through polynomial rings? that's modular arithmetic.

[vcs]

Originally Posted by Spark

i might be wrong as it's been a while but i think error-correction/detection in cpu's work on churning stuff through polynomial rings? that's modular arithmetic.

Yep..

[cover drive man]

Question:

What's the difference between an irrational number and a constant?

[silentstriker]

Irrational number = you can't express that number as a fraction (like log 2).
A math Constant = a number that arises 'naturally' in math (like pi). A physical constant = a number that is somehow a fundamental part of nature (e.g, the gravitational constant).

[silentstriker]

There is overalp - pi is both irrational and a constant. It is also a transcendental number....

Hell, you can even say that pi is also a physical constant.

[cover drive man]

Couldn't you say that all constants are irrational?

[cover drive man]

And vice versa?