Vaguely Suspicious Homework Strategies

Your friend's comment about the "naturally entering Jacobian" reminds me of something that happened during one of my analysis lectures when I was a maths undergraduate. Our analysis professor took pleasure in writing the theorems to be proved on the board and then proving them from scratch without notes, preparation, books or any other aids other than his own brain and his innate mathematical talent. A task made all the more difficult by the fact that he was a finite group theory specialist who didn't really like or at his own admission understand analysis. The process actually made his lectures really fascinating, as he would analyse the problem out loud sketching possible approaches to the proof depending on the theorem in question suggesting possible lemmas that he might need on the way etc. Also when his proposed strategy went wrong he would then analyse why and what he needed to change in order to find the correct proof. One day in a particularly long and difficult proof he arrived at an expression that was literally three metres long. This expression had the required end product as its first three elements minus a simple one. Not wishing to start all over again and having run out of time the professor simple put a set of brackets around the remaining two and three quarter metres of the expression and wrote equals one i.e. (...)=1, smiled sweetly and left the lecture hall.

I was once working with a group of friends on an undergrad thermodynamics problem. Whatever problem we were working on was of the form "Given X, prove that X=Y", with X and Y being equations. We began expanding X, and eventually got to a dead end. One of my friends finished the question like this:

X=Big horrible expansion
Clearly,
X=The book's given answer

Man, #1 sounds kinda like my second year Maths lecturer - except that when challenged, he's expand the "trivially" into three boards worth of algebra and then berate the questioner for having to ask.

I dropped out in second year...

Anyone ever "mistakenly" do a similar problem to the one that was assigned--one you actually know how to do--and see if the professor/grader gives you a pass?

Hehehe :)

When I started physics grad school I already had an MS in math and mostly could whip out the problems fairly quickly. But too many people used #5 on me, so I got into the bad habit of not doing the work until the night before it was due. Then I could honestly tell them that I hadn't started on it yet.

There's also the 'Q' factor, which is similar to the Bluster. Start with what you're given work a few lines into it, take (what you're supposed to get)/(what you've actually got) and then say, 'based on a factor of Q = (the mentioned ratio) the identity is proven.
I remember #3 being used some of my classmates when we were doing electrodynamics (I'm an undergrad, btw.). David J. Griffiths has such a ubiquitous textbook on the subject that I've heard that one can just punch 'Griffiths x.xx' into Google and a worked solution for that specific problem will be in the first ten hits every time.

Technique #1 will fail if your professor is the older guy in this famous Sydney Harris cartoon.

I've heard rumors of complete solution sets to Jackson (grad level E&M, for those not in the know) problem sets circulated among certain grad students (a combination of #4 and #5), but I've never seen one.

Oops, mangled link in my comment #7 above:

http://socsci2.ucsd.edu/~aronatas/project/cartoon.math.miracle.3.12.htm

I refer, of course, to the "Then a miracle occurs" cartoon.

Jon at #4
Yes, I did this in my final theoretical physics exam - was asked for the radiation charateristic of a linearly accelerated electron and explained that of an electron on a circular path. Neither me nor the professor noted that I was on the wrong track - I realised this afterwards.

And considering cheating, when my PhD advisor had to teach the introductory maths lecture, he started the very first lecture by writing lots of "-" onto the black board and then he said: "I'll surely forget a few minus signs during my calculations. If I do, just take one of these..."

I doubt this would work on a homework, though.

Undergrad Thermo. 3am. The answer was in the back, so we knew what we had to get to. We must have gone wrong somewhere, because the smattering of variables and logs that we had could, in no conceivable fashion, equal the correct answer.

In an attempt to make the TA smile and perhaps prod him to enlighten me by pointing out where I went wrong, I pulled a #1 (because I was too tired to try anymore), but instead wrote "The Magical Thermo Fairy reduces this mess to:".

The TA must not have found it amusing and didn't feel the need to help, because he just put a big "X" over it. :-( Now I will never understand thermo...

ON my grad level E&M exam which was a 72 hour "take-home" the maths were so horrendus that I basically ended up taking it as far as I could in the time allowed (six questions in about 60 hours of possible working time). I then wrote a multipage document for each question which covered just about everything I knew about techniques I could have used, what sort of intermediate stages I should have got and how it should have worked out. I also had about a half page on possible numerical solution techniques applicable to each question. On the morning it was due, the rest of the class (three other guys) whined about not enough time, too many questions, intractable integrals (ie not recognizable in any reference book) etc. They asked for and got another 72 hours to work on it! At that point I had slept less than 8 hours in the three days and felt I had spent enough of my life on it. I handed in what I had done. I got a b+ on the course - I am pretty sure the none of the others managed to actually complete the questions correctly and they did not try and prove they at least understood the material.

So ther's another strategy for you - at least show you do understand the theory, techniques and what was supposed to happen!

The best is getting credit after getting stuck in the last step and writing:

"Obviously it follows that this ought to be true.

QED?"

Totally got credit for incomplete calc proofs

There is a more powerful variant of #1: Proof by Emphatic Assertion.

#4 reminds me of the grad student who thought that he could find the answer to his PhD problem in a journal somewhere. The concept that it was an original problem that no one, not even his adviser, had solved proved to be quite a revelation to him. Method #4 and lots of memorization had worked pretty well for him in the past.

My HS Chem teacher once said that if you were having trouble/didn't know the answer, just put: "It's all relative"

This is not really a "trick", and I'm sure everyone does this:

I had this ridiculously long problem in a Classical Mech assignment, which involved lots and lots of numbers. Even the question was impossible to make sense of. What I did was, I did as much as I could about the question, taking every possible path leading out of the question to... anywhere. I calculated everything I could related to the question premise, and joined together some of the stuff at the end.

Still haven't got my grade on that. ;)

The funny thing is I actually used number 1: Bluster on a abstract algebra test in college only instead of trivially i wrote "now obviously". Ironically, I got full credit for the answer :)