Talk:Discrete Mathematics/Number theory

I'm thinking that the idea of groups (that is, sets-with-operations) should be well introduced before this section. That way, division can be described as, for a set S, $$f:S\times (S-\{0\})\to S$$. By suddenly assuming that operations (which, yes, are really just functions with two arguments) are known and defined, we're doing much, much more hand-waving than is healthy.

Yes, it's an intuitive idea, but one of the big parts of discrete math is formally defining things that we've learned to take for granted.

Grendelkhan


 * I do strongly think that it's important to introduce groups afterward. I mean how can one introduce something like the group Z3 under addition modulo 3 without having to explain the "modulo 3" part?


 * If there's too much handwaving, we can surely put our hands down and clean up the text. Do you think that we should define things about division in Z more formally? Dysprosia 06:20, 7 Feb 2004 (UTC)


 * Finite groups may require a bit of handwaving (thought the group consisting of {1, -1} and multiplication is pretty intuitive), but infinite groups like (Z,+) and (Q*,*) can be introduced right after sets and functions.


 * I notice that there's already an in-depth treatment of groups in Abstract_algebra/Groups; maybe a quick introduction geared to the material at hand? Something like "A group is a set along with an operation. An operation is a function of two arguments. An in-depth treatment of groups is over at Abstract_algebra/Groups, but these are the essentials for right now." Cosets, *morphisms, order---these things don't need to get described until formal group theory.


 * It'll also depend on how much group theory's going to come up in chapters between here and its formal introduction. If you don't define the basics here, you might end up doing it piecemeal over the following bunch of chapters, all hodge-podgey. Grendelkhan 17:05, 9 Feb 2004 (UTC)


 * Wouldn't it be somewhat useful to not introduce groups in this book, but give link to that Groups book entirely? After all, that is the best thing about a web book like this, linking. huopa 14 Jul 2004

Isn't it GCF (greatest common factor), not GCD? At least, that's the way I was always taught. - SamE 04:35, 25 Jun 2004 (UTC)


 * It does have different names. Let's just stick with the notation that's there? Dysprosia 05:26, 25 Jun 2004 (UTC)

I'm surprised this isn't its own text. Is there some reason for it to be part of Discrete Math? MikeBorkowski 12:00, 1 May 2005 (UTC)

No discussion of primes is complete without mention of the primorials--Billymac00 14:59, 12 July 2007 (UTC)