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Famous Unsolved Math Problems as Homework

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Re: Famous Unsolved Math Problems as Homework

#61

Post by tokenrove »

ghshephard wrote: post #11
relet wrote: post #5

Earlier quoted context omitted.

The important part of this was: * Students are forced to depart from the “answer-getting” mentality of mathematics. * Students are forced to redefine success in learning as making sense and increasing depth of understanding. * Students are able to work in a context in which failure is completely normal. If your class tends toward revolt, they have been way too far strayed from the first point, and that may be the pro…

Undergraduates (at least for the first few years) have to be in the "Answer Getting" mentality. I'm fine with curve balls being thrown at graduate students, and maybe, just maybe, fourth year students, depending on the course - but can you imagine what a freshman/sophmore student would do if faced with this situation?

One of the things people often fail to learn in university is that, once they leave, they will be judged on what they have learned, not on their grades. I think that the sooner an undergrad learns that getting an answer wrong on a homework assignment isn't the end of the world, the better. For their own stress levels, too.

The focus on grades and "the right answer" instead of learning and thinking is probably why it can be so frustrating for both parties when someone fresh out of university comes to a (programming) job interview.

I've noticed a lot of attempts on freelancing sites to pay a contractor to complete homework and school assignments. I can't imagine a worse form of self-sabotage, and it seems like students have profoundly the wrong message about education.

Re: Famous Unsolved Math Problems as Homework

#62

Post by sophacles »

ghshephard wrote: post #11
relet wrote: post #5

Earlier quoted context omitted.

The important part of this was: * Students are forced to depart from the “answer-getting” mentality of mathematics. * Students are forced to redefine success in learning as making sense and increasing depth of understanding. * Students are able to work in a context in which failure is completely normal. If your class tends toward revolt, they have been way too far strayed from the first point, and that may be the pro…

Undergraduates (at least for the first few years) have to be in the "Answer Getting" mentality. I'm fine with curve balls being thrown at graduate students, and maybe, just maybe, fourth year students, depending on the course - but can you imagine what a freshman/sophmore student would do if faced with this situation?

I very strongly disagree. This applies to programming and engineering as well as math you know... There is way too much "there is a right answer" focus on undergrad. An aspect of working with newly graduated people I really dislike is that they always ask "am I doing it right?" or "What's the right way" and not even faintly grasping the idea when I tell them "I don't know, that's why we're doing it - if there was a known good solution, we'd just buy it and move on".

Thing is - it's not these kids' fault, once they do grok the notion of "not yet solved", they are great. It's that they spend the last 16 years being punished for getting something wrong, in a context where there is only a right answer or wrong answer, and that fact is known - even in subjective topics.

Re: Famous Unsolved Math Problems as Homework

#63

Post by 0xffff2 »

mturmon wrote: post #53

One of my favorite C.S. professors, in a first-year grad class, gave out 3 of these problems as homework, including the first one, without indicating whether it was easy or hard. The problem was posed as a while loop, and the question was, does the loop terminate for arbitrary n>0, so it seemed very tractable: given: n > 0. while n != 1: if n is odd: n = 3n + 1 else: n = n/2 It was a tease. I tried a couple of differ…

This is a pretty good example of how far computing hardware has come. I was able to eliminated 2 to 50k in 81ms in completely unoptimized C# just now. Makes me wonder who has taken this approach the farthest these days.

Re: Famous Unsolved Math Problems as Homework

#64

Post by yeldarb »

mturmon wrote: post #53

One of my favorite C.S. professors, in a first-year grad class, gave out 3 of these problems as homework, including the first one, without indicating whether it was easy or hard. The problem was posed as a while loop, and the question was, does the loop terminate for arbitrary n>0, so it seemed very tractable: given: n > 0. while n != 1: if n is odd: n = 3n + 1 else: n = n/2 It was a tease. I tried a couple of differ…

Now I'm curious, is it guaranteed to terminate? Is there a name for this problem?

It needs to land on a power of 2 at some point.

Re: Famous Unsolved Math Problems as Homework

#65

Post by [deleted] »

cschmidt wrote: post #33
chris_wot wrote: post #20

Earlier quoted context omitted.

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 vi…

[deleted]

Re: Famous Unsolved Math Problems as Homework

#66

Post by _asummers »

yeldarb wrote: post #64
mturmon wrote: post #53

One of my favorite C.S. professors, in a first-year grad class, gave out 3 of these problems as homework, including the first one, without indicating whether it was easy or hard. The problem was posed as a while loop, and the question was, does the loop terminate for arbitrary n>0, so it seemed very tractable: given: n > 0. while n != 1: if n is odd: n = 3n + 1 else: n = n/2 It was a tease. I tried a couple of differ…

Now I'm curious, is it guaranteed to terminate? Is there a name for this problem? It needs to land on a power of 2 at some point.

It's the Collatz Conjecture. [0]

[0] https://en.wikipedia.org/wiki/Collatz_conjecture

Re: Famous Unsolved Math Problems as Homework

#67

Post by ggchappell »

yeldarb wrote: post #64
mturmon wrote: post #53

One of my favorite C.S. professors, in a first-year grad class, gave out 3 of these problems as homework, including the first one, without indicating whether it was easy or hard. The problem was posed as a while loop, and the question was, does the loop terminate for arbitrary n>0, so it seemed very tractable: given: n > 0. while n != 1: if n is odd: n = 3n + 1 else: n = n/2 It was a tease. I tried a couple of differ…

Now I'm curious, is it guaranteed to terminate? Is there a name for this problem? It needs to land on a power of 2 at some point.

> Now I'm curious, is it guaranteed to terminate?

No one knows.

> Is there a name for this problem?

The statement that it always terminates is the Collatz Conjecture. It's the first problem in the posted article.

Re: Famous Unsolved Math Problems as Homework

#68

Post by ghshephard »

Kalium wrote: post #60
ghshephard wrote: post #46

Earlier quoted context omitted.

I was traumatized by my undergraduate calculus courses. And that was without the profs (who were all excellent) slipping in any "Unsolved Research problems." This entire thread has been like Trauma Trigger [ http://en.wikipedia.org/wiki/Trauma_trigger ] I just want to make sure the undergraduate instructors reading this thread realize that doing this on the sly in a standard problem set would be a very, very bad idea…

With that in mind, what do you think is the acceptable way to get students out of the answer-getting mentality?

I think what the professor did was exactly correct, have them experience something new mathematically, but give them the heads up that they weren't (likely) to be solving it, as it's a new pattern they hadn't recognized before.

Re: Famous Unsolved Math Problems as Homework

#69

Post by ggchappell »

0xffff2 wrote: post #63
mturmon wrote: post #53

One of my favorite C.S. professors, in a first-year grad class, gave out 3 of these problems as homework, including the first one, without indicating whether it was easy or hard. The problem was posed as a while loop, and the question was, does the loop terminate for arbitrary n>0, so it seemed very tractable: given: n > 0. while n != 1: if n is odd: n = 3n + 1 else: n = n/2 It was a tease. I tried a couple of differ…

This is a pretty good example of how far computing hardware has come. I was able to eliminated 2 to 50k in 81ms in completely unoptimized C# just now. Makes me wonder who has taken this approach the farthest these days.

> ... who has taken this approach the farthest these days.

Tomás Oliveira e Silva of the Universidade de Aveiro, in Portugal, apparently. According to a page on his personal website [http://sweet.ua.pt/tos/3x+1.html] he has verified it up to 5 x 2^60.

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