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Famous Unsolved Math Problems as Homework

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21–30 of 99 posts

Re: Famous Unsolved Math Problems as Homework

#21

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?

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

Re: Famous Unsolved Math Problems as Homework

#23
These are great problems the first two seem to have obvious modes of proof at first sight ...

What I particularly like is that the Erdos-Strauss problem is one that's accessible to a junior schooler - once you know fractions you can investigate. I could see it forming part of a project like the graph theory investigations posted formerly, http://jdh.hamkins.org/math-for-eight-year-olds/.

Re: Famous Unsolved Math Problems as Homework

#24
post #8

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,…

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

I think so long as they say it must be independent work and give a time limit then it's fair.

Re: Famous Unsolved Math Problems as Homework

#27
post #4

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,…

Seriously? You think students would revolt after being given an interesting problem to think about for 15 minutes?

I'm guessing you've never taught math to undergraduates. Unless they are math majors, for the most part they really don't like being given harder-than-average questions, let alone open problems.

Re: Famous Unsolved Math Problems as Homework

#28

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.

Re: Famous Unsolved Math Problems as Homework

#30
post #17
post #6

As a student in 1939, the mathematician George Dantzig once arrived late to a lecture. He mistook the unsolved problems on the blackboard for homework, and solved two of them. http://en.wikipedia.org/wiki/George_Dantzig

I imagine being told that a problem is unsolved changes the way you approach it. You'll assume that 'obvious' things have been tried before. Without that psychological barrier you can try out ideas that are obvious to you that might not have occurred to anyone yet. Telling someone that a problem is unsolved implies they won't be able to solve it unless they're better than all the people who've approached it before in…

relevant:

> When asked, "How could you possibly have done the first interactive graphics program, the first non-procedural programming language, the first object oriented software system, all in one year?" Ivan [0] replied: "Well, I didn't know it was hard."

[0] http://en.wikipedia.org/wiki/Ivan_Sutherland

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