Talk:Advanced modular arithmetic theory

Intro

This article in its current form is dog crap, and needs to be re-written. It is meant to be provide an advanced expostion of modular arithmetic that goes beyond the scope of the more basic article modular arithmetic. (User:Linas forgot to sign)

Agreed--this has almost nothing "advanced" in it. Most of this ought to be/is in the basic article. I would vote that instead of having this article, we link to more advanced articles from the basic article.

• Theorems about primality tests
• Structure of the multiplicative group of integers modulo n
• Lagrange's theorem about polynomials mod primes (at most deg(p) roots)
• Quadratic residue
• Quadratic reciprocity
• Primitive roots

--Superninja 06:39, 10 Mar 2005 (UTC)

Most of the stuff in this article is indeed in the basic article. The stuff which is not, is on purpose. I, and other people, think that the extra stuff in here does not fit well with what is already in modular arithmetic (it is poorly written, and jumps a bit in the level of knowledge required).

But all of this is debatable. I would be very happy to discuss this with you.

I agree with you that this article is worthless. If it stays longer that way, I could even submit it for deletion or redirect it.

If you have time, could you please improve on this article? (I don't have the necessary background). Linas who contributed the material in here (second half) seems to not care much about it, except for doing the cut & paste thing (if you check the history). Oleg Alexandrov 16:06, 10 Mar 2005 (UTC)

Oleg, you made a promise on this, which you now seem to be backing out of. The agreement as I understood it was that almost all of the content would be cut out of the modular arithmetic article, including all the stuff about rings, music, art, chinese remainder theorem, etc. and moved to this article. I thought the whole point of these edits was to direct people like Superninja to edit this article, and not the modular arithmetic article, which would be kept spare and simple. So what happened to this promise?

The problems we discussed about modular arithmetic was its idiosyncratic, non-standard point-of-view-ish treatment of the topic, which would be cured by editing everything out of it, and directing readers to this article the longer, more complex, "in-depth" article on the topic.

Yet above, you are calling this article "worthless" and a candidate for deletion ... can you make up your mind? And if you do delete this, could you maybe copy my edits back into the modular arithmetic article? Otherwise, what was the whole point of this strange game? linas 05:08, 21 Mar 2005 (UTC)

My language was too strong. Sorry.

I did not see our agreement that way. I imagined that after you copy the stuff over here, you will rewrite it into a totally new article relying on modular arithmetic (without repeating it), and from a higher math perspective. I thought you will not stop with a cut & paste. Let us now see if Superninja plans to do anything about this. Oleg Alexandrov 05:19, 21 Mar 2005 (UTC)

Well, wouldn't it be easier to put the sections on number theory, group theory and algorithms back into the modular arithmetic article? Ring theory is an advanced topic, and yet you didn't cut that section out. Why? Why not preface the ring theory by first introducing Euclid's algorithm? This would make the modular arithmetic article easier to read, easier to understand, easier to grasp. Ditto for number theory, that should also come before ring theory. You felt it necessary to chop out Eucilid's algorithm and yet you kept the section on rings. Why? Surely Euclid's algorithm is far more deserving of inclusion in modular arithmetic, than a link to rings and ideals? Why keep modular arithmetic opaque and lop-sided and ugly-looking in this way? Why not make it smooth and even and balanced? linas 15:22, 21 Mar 2005 (UTC)

I can answer all these questions. But one should start by asking if you really want to get into this, you mentioned earlier you don't have time for this. Oleg Alexandrov 15:46, 21 Mar 2005 (UTC)

Question

Linas wrote in the article:

The first encyclopedia entry on modular arithmetic was written by Euclid, in Book 7 of Euclid's Elements.

Now, was it encyclopedia what Euclid wrote? The Euclid's Elements page says it was a mathematical treatise, aka, an Abramowitz and Stegun before its time. Oleg Alexandrov 22:11, 5 Feb 2005 (UTC)

Yes well, encyclopedia is an 18th century Enlightnment concept, so, by definition, anything written before that time cannot technically be called an encyclopedia. On the other hand, the Elements, along with Aristotle's works and Pliny's History, come close to what in modern times would be called an "encyclopedia". So I think the usage is entirely approriate. A&S is an excellent reference work, but its neither encylopeadic nor is it a treatise. linas 00:17, 6 Feb 2005 (UTC)

Now we are getting into fine points about what an encyclopedia is, and whether Euclid wrote about modular arithmetic or ordinary arithmetic. Thus, never mind. Could you check the talk page of Fixed point theorems in infinite-dimensional spaces? I have a question there about the paragaph you inserted. Thanks. Oleg Alexandrov 02:16, 6 Feb 2005 (UTC)

Recommendation

Redirect and merge this page with Modular arithmetic. Then in that article when concepts that are meant for more advanced students, put in links like the one I just did for modular arithmetic and have then link to specific concepts. This would be easily done via a list of them in the main article.

Some stuff in this article is of rather bad quality. By merging back this and the other planned things, we would get a huge article ranging from the fine details implementation of modulo function in computing to very abstract algebra. That would be quite a mess I think. Oleg Alexandrov 5 July 2005 15:56 (UTC)