Wikipedia:Reference desk/Archives/Mathematics/2011 January 8

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January 8

Pretty stupid question about statistics

What are the WP articles for broken line graph, frequency polygon, frequency curve, cumulative frequency polygon and cumulative frequency curve? (I bet WP uses fancy names for the titles. :P ) Kayau Voting IS evil HI AGAIN 13:37, 8 January 2011 (UTC)

Chart should lead to most of that. Dmcq (talk) 13:50, 8 January 2011 (UTC)

Thanks, I found the broken line graph and made an RDR. Unfortunately, I could not find the others. Kayau Voting IS evil HI AGAIN 13:54, 8 January 2011 (UTC)

List of graphical methods gives a few more. Also just doing a search by putting the terms in the search box should help. For instance putting 'cumulative frequency curve' in the serach the first return was cumulative frequency analysis. It's probably a good idea to add a few redirects between where a name has graph chart or plot in its name, I'll have a look at that. Dmcq (talk) 14:00, 8 January 2011 (UTC)

Thanks! I did know about the cumulative frequency analysis article, although I didn't understand a word of it. :P By the way, class boundary, class limit, and class width are also redlinks, you may want to redirect them to something useful. Kayau Voting IS evil HI AGAIN 14:07, 8 January 2011 (UTC)

There seems to be very little about bunching data into classes other than via classifiers. It isn't used much in actual statistics nowadays, just in displaying the data in histograms. In fact the only thing I could find was an article I mainly wrote myself called assumed mean. The closest to that nowadays would be quantization error. I notice the histogram article switches between calling them categories, classes and bins. Dmcq (talk) 21:40, 8 January 2011 (UTC)

cumulative distribution function is much better for cumulative frequency curve. hate to say this but Wolfram Mathworld seems to have articles for most of what you said. Dmcq (talk) 21:48, 8 January 2011 (UTC)

I know this is probably a very stupid thing to ask, but both the CF analysis page and the cumulative distribution function page seem to be about probability (that's what the cats say...) However, the CF polygon/curve I have in mind is, like that described in Wolfram Mathworld, a chart that presents continuous data in a way similar to a histogram. Are they actually the same thing? Kayau Voting IS evil HI AGAIN 00:51, 9 January 2011 (UTC)

Cryptography

At my bank, online access to one's bank account is made secure through the use of a small cryptography device.

It works as follows:

the bank website provides a random number, the *challenge*. You put your debet card into the cryptography device and enter the challenge and the secret code of the debet card. If the secret code is correct, the device replies with another number, which you type into the bank website to login.

I always thought this was a nifty way of verifying the user has his debet card and knows its secret code, without actually sending the secret code over the internet.

Today I learned, much to my surprise, that the cryptography device is non-deterministic: it gives different replies for the same inputs. I am baffled. What is going on here? 83.134.178.145 (talk) 14:39, 8 January 2011 (UTC)

Could it have a clock and use the date/time as another input ? This would mean the results would "expire" if the website doesn't get the code within whatever time frame they allow. Why do this ? Let's say someone has a key-logging program on your computer, and gets the code you typed in. If they try to use it fraudulently some time later, hopefully the code would have expired by then. StuRat (talk) 15:41, 8 January 2011 (UTC)

he can't use it sometime later anyway, because the bank website will give a different challenge number next time, which ensures a different input to the device at every login. Furthermore, the device is only as big as a common cell phone and has worked for years without battery replacement - in fact it doesn't even have an opening to replace the battery, presumably to prevent tampering. I suppose it could contain a very low-power clock, but in that case what would be the point of the challenge number? The device maps (challenge number,secret code)->password number, and the bank website provides a new challenge number at every login. The challenge number and password number are both up to 8 digits long. 83.134.178.145 (talk) 16:16, 8 January 2011 (UTC)

"he can't use it sometime later anyway, because the bank website will give a different challenge number next time" -> Well, if the person with the key-logging program is an untrustworthy room-mate, and uses your own computer, and you have failed to log off, he could gain access that way, if the web site hasn't yet timed out. The time-out period for the website might be longer (say half an hour), than the time-out to enter the validation code (say 2 minutes). StuRat (talk) 22:49, 8 January 2011 (UTC)

Banks I've used with a similar system (but no challenge number, just a non-deterministic map from secret code -> password number) gave results that did expire after a few minutes. Sometimes if I dallied in copying the number I would get rejected. Eric. 82.139.80.114 (talk) 18:10, 8 January 2011 (UTC)

And since the device took no input other than my card and PIN, it would have to have had an internal clock to have that behavior. Eric. 82.139.80.114 (talk) 18:11, 8 January 2011 (UTC)

Many cryptography algorithms allow for random numbers. Take a VERY simplistic example. You give me a number. I will give you a number such that if I add it to the number you gave me and mod 11, it will produce a result of 5. So, if you give me 7, I can give you any number n such that (7+n)%11 = 5. In a real algorithm, the restrictions are more complex, but they allow for multiple answers. -- kainaw™ 18:16, 8 January 2011 (UTC)

The output expired after a few minutes, which meant that the number was produced by a system that knew what time it was. Since the input (card and PIN) were constant, that meant the device had an internal clock. Eric. 82.139.80.114 (talk) 01:44, 9 January 2011 (UTC)

Group theory: what is precise definition of A: B en A.B ?

Hello,

I have been confused about this for quite some time. In many articles I see the following notation for groups

$PSU(3,5).2$ and $C_{5}:C_{2}$

I am aware of the notion of (external and internal) semidirect, and highly suspect that there is a relation. I remember from my own undergraduate course in group theory that $G=A.B$ should mean that G has a normal subgroup isomorphic to$A$ with the quotient isomorphic to$B$. It also said that $G=A:B$ should mean that there is a normal subgroup isomorphic to A, another isomorphic to B, trivially intersecting and generating the entire group.

So my questions are:

1) Is this the correct standard notation? (I often see it being used in articles without any name, explanation or reference).

2) Is this sufficient information to determine the entire group? It seems not, because both the cyclic group of order 10 and the dihedral group of order 10 could then be written as $C_{5}:C_{2}$ . But then why is this notation used like that?

Many thanks in advance! — Preceding unsigned comment added by Evilbu (talk • contribs)

Could you be more specific about which articles you're seeing this in? My understanding is A:B denotes the set of (left or right depending on the author) cosets of B in a group A, with [A:B] or something similar meaning the index of B in A when B is a subgroup. I think the dot notation is sometimes used for the subgroup (of a permutation group) that fixes a letter. Group theory is still young enough that different notations are often used by different authors.--RDBury (talk) 23:04, 8 January 2011 (UTC)

I find it hard to give examples that are publicly available. It seems these authors used the Atlas or GAP. This is an example from the online Atlas were both notations are used when giving maximal subgroups : Atlas: Maximal subgroups of M24. The first interpretation you give (of A:B) looks like what I was taught). But apart from the notation, my second question remains as well: does this make completely clear to readers in what isomorphism class this group is? — Preceding unsigned comment added by Evilbu (talk • contribs)

It looks like this is notation I'm not familiar with but from the examples it appears to be telling how the permutation group breaks down into orbits. If you know that the group is a maximal subgroup of a specific permutation group then such information would indeed determine the isomorphism class. If no one here knows then I'd suggest looking at the paper version of the Atlas and some of the references there. Sorry not to be more help.--RDBury (talk) 17:10, 9 January 2011 (UTC)