Built on Facts

Yesterday some of my fellow students and I had this homework assignment which, long story short, amounted to doing some changes of variables. One part of the problem in particular was not very transparent until we realized we were missing a factor of a Jacobian.

“I’m just going to write ‘The Jacobian enters in a natural way’ and present the conclusion as an accomplished fact.”, one of my friends said. Obviously it didn’t enter in anything approaching like a natural way, but if there’s one thing hard science books and papers like to do, it’s talk about hard stuff like it was easy. In that spirit, here’s some patented homework tricks I’ve seen. (This is not serious. Don’t try this at home or you will probably fail!)

1. Bluster. Given a proof to do, start with the given and work forward a few lines. Then work backward a few lines from the conclusion you’re supposed to prove. In the middle, write the word “trivially”.

2. Be green, recycle. Have to do an integral equation in a math methods class? Realize it’s the same as the scattering problem you’re doing in quantum mechanics class and reuse the answer. Actually you can really use this trick, it’s good to use the same knowledge across disciplines.

3. Shotgun approach. Write down everything you can think of that’s even vaguely related from the book. Something’s got to be right!

4. The Librarian. Make it a library science Ph.D. instead of a physical science Ph.D. by scouring every reference from Wikipedia to Spectrochimica Acta B in hopes that someone else will have already done your problem and written the answer for you.

5. The Socialite. Make friends with all the older grad students and hope they remember how to do your problem.

Any others you’ve seen?

Of course if you’re really in school, you’re there to learn and the best thing to do is buckle down and learn it. After all, the whole point of science is to solve problems that no one has done before, so not only does school give you the tools, it gives you actual practice in solving difficult problems that happen to have been done before. Good luck, and don’t be a slacker!

Comments

#1 Thony C.
September 16, 2008

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.
#2 Dave
September 16, 2008

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
#3 Dunc
September 16, 2008

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…
#4 Jon
September 16, 2008

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
#5 Carl Brannen
September 16, 2008

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.
#6 2-D Man
September 16, 2008

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.
#7 Eric Lund
September 16, 2008

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.
#8 Eric Lund
September 16, 2008

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.
#9 MartinB
September 16, 2008

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.
#10 DA
September 16, 2008

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…
#11 Peter
September 16, 2008

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!
#12 Paul Johnson
September 16, 2008

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
#13 CCPhysicist
September 16, 2008

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.
#14 Scotty B
September 18, 2008

My HS Chem teacher once said that if you were having trouble/didn’t know the answer, just put: “It’s all relative”
#15 Anonick
September 18, 2008

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.
#16 Starhawk Laughingsun
October 13, 2008

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