Pleez..help me in Maths...?

Question

these r few ques regarding B.A. Ist yr Maths...
1) wht do u mean by-'a is congruent to b modulo H' ? Also what is Modulo....
2) what r Arbitary Set ..??
3) what do abelian & non-abelian group means.?.
4) how to insert symbols in the ques. while asking a ques here?

these ques. r mainly 4m "Groups & Cosets"
also sugest me some publications -4 good books to prepare 4 Ist yr. Maths bcoz websites r not working.

Answer 1

"a congruent to b mod H" just means they both have the same remainder when divided by H. e.g. 12 and 27 mod 5: each of them when divided by 5 leaves remainder 2.

The word "arbitrary" means you just make it up or pick it -- it isn't derived by any rule.

abelian means commutative: i.e. when the operation which is part of the definition of the group is performed on two members, order doesn't matter. e.g. the set of integers under addition is abelian because
m + n = n + m, but the set of integers under subtraction (actually I don't think that's even a group!!) isn't abelian because
m - n is not equal to n - m.

I don't know. Exactly what symbols do you mean? Use words if you can't get the symbol on the keyboard.

Answer 2

'Modulo' is a fancy way of saying 'remainder after division'. If you divide 15 by 7 you get 2 with a remainder of 1 (the remainder is always an integer. It only gets divided by the divisor if you're making a decimal fraction) In this case we'd say 15(mod 2) = 1. Or 17(mod 3) = 2. What if there's no remainder? Well 15(mod 3) = 0. We also say, for example, that 7 is 'congruent' to 45 modulo 14 to mean the same thing (7 = 45(mod 14)) Why bother? Because (as you'll find out) 'modular arithmetic' can help you do a lot of things much easier and it allows you to prove a lot of other interesting things about the integers. There's also a 'mod' button on the Windoze calculator (in scientific mode) that does modular calculations for you. Find it and play with it ☺

An 'arbitrary set' is just what it says. A set of arbitrary 'things' that all have some arbitrary characteristic in common. For example, 'the set of all integers greater than 0 and less than 5' would be {1,2,3,4}. Or you might have 'the set of all long sleeved blouses in my closet'.

'Abelian' means that some binary operation (an operation which requires 2 inputs) is commutative. Let's call # some sort of 'operation' on 2 things. If a and b are things that # can operate upon, then # is Abelian if a#b = b#a. 'Huh?' you say? If a and b are numbers, then a+b = b+a and a*b = b*a. That's nothing special. But it *is* special. What if a meant 'putting on shoes' and b meant 'putting on socks' and # meant 'followed by'? Now a#b is not the same thing as b#a. If you've studied matrices, you already know that if A and B are matrices of the same size then AB =/= BA in general.

Inserting symbols is done by using the extended IBM character set. For example, hold down the 'alt' key and type 251 on the numeric keypad (with the 'num lock' set to on). You should get √. Or π is alt 227. You can find lists of these on various websites such as http://telecom.tbi.net/asc-ibm.html


Doug



Doug

Answer 3

em.....i dont think those r math question.....