Last semester, a number of emails like this circulated:
Subject: Math Requirements
Dear James Stankewicz,
My name is Firstname Lastname and I am a graduate student at the University of Prestigious Institution studying for my ph d in math. I am taking a class and we are studying Field and Galois Theory and one of the requirements is to contact a graduate student from any other university and do an e-mail consultation with them regarding a problem pertaining to what we study. I would like to know if you would be able to help me fulfill this requirement. To do so, all you need do is answer the given problem to the best of your ability and then rate the difficulty of the problem for a Gradute Level Algebra Class on a scale from 1 – 10, 1 being the least difficult, and 10 being the most difficult. It would be more feasible if you could type your answer using the Latex software and e-mail it over as a pdf file, but it is not required. The problems go as follows:
1. Let S be the group of all permutations of F5. (Take note that no element of S is actually a field automorphism of F5, except the identity
permutation, since F5 has no nontrivial field automorphisms.) Let A be the
subgroup of even permutations. Let N be the subgroup of permutations of the form x|–> ax+b for a in F5^x, b in F5. Let D be the subgroup of
permutations of the form x|–> +/-x+b for b in F5. Let C be the subgroup of
permutations of the form x|–>x+b for b in F5.
(a) Show that N is the normalizer of C in S.
(b) Write down the cardinalities of the five groups S, A, N, D, and C, and determine all inclusion relations among them.
(c) Show that the only subgroups of S containing C are S, A, N, D, and C.
2. Let k be a field, let f(X) in k[X] be an irreducible quintic polynomial with five distinct roots, let K be the splitting field of f(X), and let G=Gal(K/k). Thus G can be identified with a subgroup of S5 via its action
on the roots of f(X).
(a) By making a suitable identification of the roots of f(X) with the
elements of F5, show that G is isomorphic to one of S, A, N, D, or C.
(b) Let k=Q, let p be a prime, and let f(X)=X^5 – p. Which group is G? What
is the fixed field of the subgroup C of G?
The letters S, A, N, D and C stand for “symmetric”, “alternating”, “normalizer”, “dihedral”, and “cyclic” , respectively
I got one of these from someone at a random university last month. Weird. Even if its legit I wouldn’t bother (but I doubt its legit, Firstname isn’t a first year and so probably isn’t taking a course on Field and Galois Theory..)
It was at this point that I contacted Firstname Lastname via his/her math department email and said that he/she ought to contact yahoo to get this email account closed down.
The name of the person has been protected because giving a name would only embarass the victim. If you see an email like this sent around, please make sure to contact the person whose name was used to get a response. No one deserves to have their name dragged through the mud like that!
Well, let’s see… If this isn’t an attempt to get someone to do their homework (and it’s pretty clear that it isn’t), then it’s ordinary spam. If so, then the most sensible way of dealing with it is marking it as spam and forgetting about it. I think this email has nothing to do with academic honesty, dishonesty or anything else academic. Replying to this email with moralistic ‘do your own homework’ is giving the spammers exactly what they need: a confirmation that the email address is alive. In other words, this is a mathematical version of ‘I am the lawyer of an Arab prince, he died in a crash and left millions, please help me get a hold of the money, and you’ll be given your share of the wealth’ type of email.
Ah, but you can check easily enough and see that said Nigerian prince does not exist. And in any case, if said Nigerian prince did exist, you’d never meet him.
In this case it’s a real person whose reputation could be harmed by the email scammer.
This is why I’m advocating not replying with “Do your own homework” but contacting the actual person whose name is being used so he/she can put a stop to it.
Irene, I believe that Jim is referring to the dishonesty of using some real grad student’s name and institution.
For what it’s worth, googling a couple of phrases finds where this homework assignment comes from: math.hunter.cuny.edu/cpetsche/AlgebraHW8.pdf So besides the grad student whose name was used, maybe it might also be worth letting the teacher of this course know that (presumably) one of their students was responsible for this? (Of course, you may well have done this already.)
(Of course, that’s taking the email at face value as phishing for homework, rather than a more general phishing for live email addresses, which as you point out is not clear.)
I had the same thing happen to me back in March. Someone out of the blue emailed me asking for help solving some basic algebra questions, e.g., to show some low-degree poly. in Q[x] is irreducible. I asked for background and the person claimed to be a Ph.D. student in math at Berkeley and signed with a first name and last name. I checked with a student in the dept. there that nobody by the name this emailer was using existed on the whole campus (not really a surprise). I never wrote back.
I’m not sure what to make of this. This is a very specific meassge, and thus not suited to spam just anyone to look for active email accounts or any other reason. Spammers want the highest probability of response, and surely an algebra question is not the way to go about it!
On the other hand, the mathematics community on the internet are a fairly helpful bunch. If it were an attempt to get their homework done, there are other ways that will probably work. There are pleny of forums the question could be posted to, or they could go to irc.efnet.org #math, where surely someone will take the time to help them understand it.
Although, for a busy student I suppose it only took a few minutes to type up and send to a few dozen email addresses taken from math department websites. Might be worth the effort.
There is an upside to things. If this is what spammers must resort to, then they are in trouble. On the other hand mathmatics is a subject one learns by actively doing math. Anyone I have met in my time that copied assignments from others rather than doing them on their own has done poorly come exam time. So with any luck this guy will not do well, and thus not meet the requirements to stay at prestigious school.
Just as a note: Someone recently posted a comment making a specific accusation about who sent out the emails.
Don’t do that.
Being that RigTriv is a blog, any accusations made here cannot possibly be substantiated in a meaningful way. That confines such accusations to the realm of pure rumor and we’re not doing that here. I made this post to make people aware a) that this sort of cheating occurs even at this level and b) that such cheating can be harmful to more than a school’s honor code or the cheater him/herself.