Motivation In my Number Theory Class…

[Lucretius]

I'm sure that for many of you this class is old news; but I just started elementary number theory this summer and, as much as I love the challenge of the course, and doing these proofs; I feel like an amateur boxing Mike Tyson here. These things are chewing me up and spitting me out. Granted I can do some of the proofs, but a lot of them (granted my classmates are struggling too) are just plain impossible (nearly so) for me to figure out, and when I see the actual proof it almost discourages me even more because the proof is so obvious after having seen it.

I was wondering how you were able to stay motivated for hours, days, working on a proof that in the end you were never able to solve… perhaps it is just me, but I get discouraged plugging away hour after hour on a problem only to find it has some simple solution that wasn't one of the hundreds of different ways I tried to approach it. I took both logic courses offered at my college to prepare for proofs, and I have taken a proofs class before, which was the only college math course I managed to ace, so I was hoping this would be about the same, but it's not! How do you all stay motivated?!

Thanks!

 

[The|M|onster]

I'm hoping to become a number theorist one day myself. I agree that it can be pretty discouraging sometimes, but this is one of the oldest fields of pure mathematics and I also think it is one of the most beautiful. I find that if I struggle with a problem for an extended period of time it is best that I leave it be for a while. I'll take a walk in the park or go for a run. I usually always carry a pocket notepad and a pencil with me in case something hits me. Sometimes it does, sometimes it doesn't.

The most important thing I try to remember is that there is never one solution. Sure, some proofs might be more elegant than others, but I am more proud of original thought than finding the simplest solution.

Also, go to your professor's office hours every time they are offered. I find that I learn more in office hours than I do in class because I can actually have someone look at my proofs.

Don't give up!

 

[Lucretius]

How long should I go at these proofs before I realize they're a lost cause? I worked on this fibonacci sequence one for several hours over the course of a few days, and in the end, someone else just ended up doing the problem on the board.

I'll have to rearrange office hours with my professor, as my two summer courses have conflicting office hours… (9 AM has office hours at 10, 10 AM has office hours at 9!). He did say this class would be probably THE hardest one we would take as an undergrad in mathematics (I hope my physics major doesn't have such a difficult one as well! though perhaps I'm a little masochistic and want the challenge) but, I feel like I can do this if I set my mind to it. I've always liked the notion of a proof, and getting them right is great; it's just I don't get them right as often as I'd like!

 

[Feldoh]

If you can't figure a problem out just stop working on it for a bit. I find that a lot of the time the solution will just pop into your head when you don't even mean to be thinking about the problem. Take a break, there's no point in trying to solve something that isn't going to come to you immediately, time is a precious commodity.

 

[ralphhumacho]

How long should I go at these proofs before I realize they're a lost cause? I worked on this fibonacci sequence one for several hours over the course of a few days, and in the end, someone else just ended up doing the problem on the board.

I'll have to rearrange office hours with my professor, as my two summer courses have conflicting office hours… (9 AM has office hours at 10, 10 AM has office hours at 9!). He did say this class would be probably THE hardest one we would take as an undergrad in mathematics (I hope my physics major doesn't have such a difficult one as well! though perhaps I'm a little masochistic and want the challenge) but, I feel like I can do this if I set my mind to it. I've always liked the notion of a proof, and getting them right is great; it's just I don't get them right as often as I'd like!

Personally (this may not work for you), I work on 3-5 problems at a time, spending 15 minutes on each one and repeating the process until I'm done (or until I get tired, which is usually around the 3 hour mark).

Don't fret about not getting the right answer. Proofs are (caution: cliche) all about the journey.

The only advice I can really give is: A) know all definitions and statements of theorems inside out B) keep trying - don't peek at the answer book!