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Famous Unsolved Math Problems as Homework

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Re: Famous Unsolved Math Problems as Homework

#31

Post by iamcurious »

ghshephard wrote: post #10
iamcurious wrote: post #7

Earlier quoted context omitted.

I have done that occasionally. They complain, but only in jest.

You've handed out a math assignment that was an open unsolved problem and not told your students what you had done prior to them leaving for the day?

You've handed out a math assignment that was an open unsolved problem

Yes.

and not told your students what you had done prior to them leaving for the day?

No. As the comment I responded to says: I

reveal the full truth after they have been working for fifteen minutes or so.

Re: Famous Unsolved Math Problems as Homework

#32

Post by iamcurious »

chris_wot wrote: post #21
ghshephard wrote: post #10

Earlier quoted context omitted.

You've handed out a math assignment that was an open unsolved problem and not told your students what you had done prior to them leaving for the day?

Yeah, their "jesting" involved the lecturer, vaseline, a flagpole and lots and lots of string beans.

It strikes me that you expect students to behave that way for challenging them. Maybe it is a matter of cultural differences? In my university, at the most they would complain to the administration. And even then the problem would have to be tied to their grade so they could make the case of unfairness.

Re: Famous Unsolved Math Problems as Homework

#33

Post by cschmidt »

chris_wot wrote: post #20
cschmidt wrote: post #13

In grad school, I had a graph theory professor who assigned a research problem he was stuck on as homework. He didn't tell us that until later, after I had a wasted a lot of time trying to solve it. It wasn't very cool.

What, you call that a waste of time?

I did feel like it has been a waste of time. He just mixed it in with a bunch of textbook problems. It wasn't a particularly elegant or insightful, just something technical he wanted the answer to. I don't think anyone in the class got it right, as we didn't really have the tools to make progress on it. It was a first year grad class.

It was one of the only times I had a really bad professor in grad school. He was visiting for six months, and you could really tell he didn't want to be teaching. He used an out of print book (Graph Theory With Applications by Bondy and Murty), which meant I had to go to the library to even read it. He lectured at a level that was beyond us, and he literally wouldn't tell us where his office was, so he wouldn't have to answer questions. Maybe with a different teacher I would have been less annoyed about the research problem.

Re: Famous Unsolved Math Problems as Homework

#34

Post by ghshephard »

toothbrush wrote: post #28
ghshephard wrote: post #3

The most important part of this was, "When I use these problems for in-class work, I will typically pose the problem to the students without telling them it is unsolved, and then reveal the full truth after they have been working for fifteen minutes or so." Any professor who handed out that assignment to an undergraduate class without fair warning, would likely face a full scale revolt, possible threats of violence,…

I can imagine the students now. All of them like, "omigod we're being forced to learn something by investigating things and being creative omigodomigod it has no known answer gasp". Yeah, that'd be embarrassing.

It's more like, "Student has a standard 15 credit semester, means 15 hours of classroom lecture + 45-60 hours of study/assignments outside of class. Student is micro-scheduling the number of minutes they have to answer each of the standard 20 Calculus questions (God, it was always 20 question) which they have to have in to the TAs before next lecture. 60 questions/week, every week, and you have about 12 hours allotted, which works out to no more than 12 minutes per question. Any questions you go over that 12 minutes, you need to steal from other questions and somehow solve more quickly, and remember, this is all new material for the student. If you blow your budget on math, it either comes out of other classes, or sleep.

That's the context in which being thrown a heretofore unsolved problem in calculus is not particularly amusing for an undergraduate.

Re: Famous Unsolved Math Problems as Homework

#35

Post by pjc50 »

ghshephard wrote: post #12
pjc50 wrote: post #8

Earlier quoted context omitted.

Cambridge used to do this routinely. Your university may vary.

What year of student? Freshmen/Sophmore?

There were a few unsolved conjectures presented on the board on occasions. What was more common, as a first year maths student, was to be presented with homework that had 10 questions on of which one would be marked "hard" and one "very hard". Some of the "very hard" questions would be unsolved research problems.

Some interviewers would present unsolved problems in interviews as well, if a candidate was happily eating their way through the regular material.

Cambridge is a little unusual in that the only mark that people cite is the one on the final year exam. I believe US universities operate by continuous accumulation of marks? And that ongoing disputes over marking are more common because of this?

It's also already working with a highly selected group of people from the far tail of the ability distribution, and looking for a way to identify the exceptional among the merely very high ability.

Re: Famous Unsolved Math Problems as Homework

#37

Post by chris_wot »

iamcurious wrote: post #32
chris_wot wrote: post #21

Earlier quoted context omitted.

Yeah, their "jesting" involved the lecturer, vaseline, a flagpole and lots and lots of string beans.

It strikes me that you expect students to behave that way for challenging them. Maybe it is a matter of cultural differences? In my university, at the most they would complain to the administration. And even then the problem would have to be tied to their grade so they could make the case of unfairness.

Your imagination immediately jumped to only bad possibilities.

Re: Famous Unsolved Math Problems as Homework

#39

Post by ghshephard »

iamcurious wrote: post #32
chris_wot wrote: post #21

Earlier quoted context omitted.

Yeah, their "jesting" involved the lecturer, vaseline, a flagpole and lots and lots of string beans.

It strikes me that you expect students to behave that way for challenging them. Maybe it is a matter of cultural differences? In my university, at the most they would complain to the administration. And even then the problem would have to be tied to their grade so they could make the case of unfairness.

My university had a pretty liberal withdrawal policy if you did so prior to mid-terms. Instructors who weren't competent, or who acted like jackasses, didn't get complaints - the students just dropped the class and focussed their energy on instructors who were both competent, and not inclined to sabotage them.

Re: Famous Unsolved Math Problems as Homework

#40

Post by ghshephard »

pjc50 wrote: post #35
ghshephard wrote: post #12

Earlier quoted context omitted.

What year of student? Freshmen/Sophmore?

There were a few unsolved conjectures presented on the board on occasions. What was more common, as a first year maths student, was to be presented with homework that had 10 questions on of which one would be marked "hard" and one "very hard". Some of the "very hard" questions would be unsolved research problems. Some interviewers would present unsolved problems in interviews as well, if a candidate was happily eatin…

What you are describing is entirely fair. The student has been fairly warned that they might not be able to solve the problem in the 8-10 minutes that their incredibly packed schedule allocates to it. They aren't being blindsided by an unsolved research problem masquerading as a standard question on a problem set. Fair game.
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