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Famous Unsolved Math Problems as Homework

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Re: Famous Unsolved Math Problems as Homework

#51

Post by superuser2 »

ColinWright wrote: post #19
ghshephard wrote: post #11

Earlier quoted context omitted.

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 disagree - in my experience the "answer getting" mentality is the largest barrier to doing "proper" math that there is. The students are unwilling to just try stuff to see what happens, because they think there's one way to do it, and one answer to find. They think they need to find the right process, apply it without making any stupid errors, get the answer, and move on. That's a huge problem when you've trying to…

>They think they need to find the right process, apply it without making any stupid errors, get the answer, and move on.

Perhaps because they've been conditioned for 12 years to believe that this is what "math" is.

Re: Famous Unsolved Math Problems as Homework

#52

Post by ghshephard »

ColinWright wrote: post #50
ghshephard wrote: post #34

Earlier quoted context omitted.

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 allotte…

This sounds more like secondary school than university. Certainly for first year undergrad there are worksheets and a significant workload, but it sounds like you're describing what I think of as straight school-type work.

Maybe I was just a lazy student in high school, but I don't ever recall stressing over math homework. I'm struggling now to remember if I even had math homework -presumably I did, but it didn't lay down any memories.

But SFU (a not so bad University in Canada), - Calculus 151 in Images theater, and Calculus 152. I recall the workload in those two courses very, very distinctly. Both first year courses. In hindsight, I think they served the purpose of filtering out students who weren't prepared to work hard...

Re: Famous Unsolved Math Problems as Homework

#53

Post by mturmon »

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 different ways to prove it, but of course nothing worked. Then I tried to find a counter-example. The numbers get pretty big, in some cases, because applying

  n = 3n + 1
several times in a row will blow "n" up, despite the intervening n = n/2. This was before arbitrary-precision arithmetic was a thing, so the only tool I knew that could do this was the Unix "dc". I think I was able to get up to n=10K or 50K on our campus VAX.

That was about 30 years ago. I still remember it fondly.

Re: Famous Unsolved Math Problems as Homework

#54

Post by andrewstuart2 »

geon wrote: 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

> A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis.

I love fun stories like that. And I love that it shows this guy is crazy brilliant yet humble enough to shrug off that success and just assume he had to figure out something else for his thesis. At least that's my interpretation.

    faithInHumanity++;

Re: Famous Unsolved Math Problems as Homework

#55

Post by SAI_Peregrinus »

noja wrote: post #48
darkxanthos wrote: post #26

Earlier quoted context omitted.

You can to a degree. I've done it a bunch for my math classes. :) EDIT: Also wolfram alpha

So how does it look? Lots of parentheses? Are the special characters replaced with something?

Write it in TeX, then search for that.

Re: Famous Unsolved Math Problems as Homework

#56

Post by Nadya »

superuser2 wrote: post #51
ColinWright wrote: post #19

Earlier quoted context omitted.

I disagree - in my experience the "answer getting" mentality is the largest barrier to doing "proper" math that there is. The students are unwilling to just try stuff to see what happens, because they think there's one way to do it, and one answer to find. They think they need to find the right process, apply it without making any stupid errors, get the answer, and move on. That's a huge problem when you've trying to…

>They think they need to find the right process, apply it without making any stupid errors, get the answer, and move on. Perhaps because they've been conditioned for 12 years to believe that this is what "math" is.

It also doesn't help that they hide details and sometimes straight up lie to students during those first 12 years. To avoid "confusing" them.

Students aren't usually taught subtraction is adding a negative number. Students aren't usually taught division is multiplying by a fraction. Students aren't usually taught that there are ways of counting outside of the decimal 'base 10' way of counting, or the advantages of counting in Octal, or how to count in Binary on your hands.

Math teachers love to say "2+2 does not always equal 4" but never explain that's only true in Base2-4 where the representation of "4" doesn't exist and it is represented as 100, 11, or 10.

So not only are we taught "there's always an answer". We're not taught other concepts and sometimes information is left out entirely until you reach a college level of mathematics - at which point all these lies, unexplained concepts, and "answer-seeking mentality" become a problem.

Re: Famous Unsolved Math Problems as Homework

#57

Post by abecedarius »

onion2k wrote: post #17
geon wrote: 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…

There's something to that, but for an approach to be worth trying you don't have to expect it to work: just that you'll learn something about the problem.

Re: Famous Unsolved Math Problems as Homework

#58

Post by ctdonath »

riffraff wrote: post #30
onion2k wrote: post #17

Earlier quoted context omitted.

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

They're not hard. They're things we'd expect a solid CS student grok in one year.

He just happened to be the first to grok them. Question is how he came to face those problems without any apparent precedent.

Re: Famous Unsolved Math Problems as Homework

#59

Post by DanBC »

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?

They get furious.

https://news.ycombinator.com/item?id=8972744

(I don't know why you were so heavily downvoted. I upvoted you.)

Re: Famous Unsolved Math Problems as Homework

#60

Post by Kalium »

ghshephard wrote: post #46
paulpauper wrote: post #41

Earlier quoted context omitted.

let it go, man. You keep belaboring the point

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?
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