I've been tutoring 'Artemis' for over a year and a half now*. This fall he picked up the book Introduction to Number Theory, by Mathew Crawford, from Art of Problem Solving, and we've spent most of our sessions since then working out of that. I like not having to worry about what we're going to explore, and he seems to like the problems we encounter each week. He and I work through each problem together. Sometimes I hold back more, and get him to do one on his own, and sometimes I do more (with him correcting my mistakes). We skipped most of the first 3 chapters, because he knew most of that.
Number Theory includes so many cool ideas. I especially like playing with modular arithmetic, and seeing the power it can have. I've never taken a number theory course myself, so I'm consolidating my thinking, and enjoying the stretching.
Here's a problem from the book (modified a bit):
[Please don't give complete solutions in the comments. But I'd love to know if you've played with it, and what approach you took.]
Enjoy!
_____
*Search on Artemis to find all the posts.
Number Theory includes so many cool ideas. I especially like playing with modular arithmetic, and seeing the power it can have. I've never taken a number theory course myself, so I'm consolidating my thinking, and enjoying the stretching.
Here's a problem from the book (modified a bit):
I've got one part solved, and am still thinking about another part...Consider n! and the sum 1+2+...+n.
When is the sum a factor of the factorial?(problem 6.31)
[Please don't give complete solutions in the comments. But I'd love to know if you've played with it, and what approach you took.]
Enjoy!
_____
*Search on Artemis to find all the posts.
0 Komentar untuk "Tutoring & Number Theory"