## Experience with Math camps?

With summer fast arriving (yeah, I know we have to get through winter and spring first) kid's thoughts turn to summer Math camp. "Yeah, right", you say. Well, for those of us who really enjoyed Math in high school, Math camp was a lot of fun.

This post is not intended to be a list of Math camps. I may create one later but you can Google and find a bunch. The list from the American Mathematical Society (AMS) is a good starting place for your research if you're looking for camps for high school kids.

In the late '70s I attended the Ross Program at the Ohio State University. It was the toughest summer I ever had and the most rewarding one at the same time. I was pretty good at Math in school but this camp really worked me. While I can't say that I was mature enough at the time to fully appreciate what I was learning I will say that the camp opened my eyes to how cool Math is at a much deeper level than ever before. The camp left me with a deeper appreciation for the beauty and rigor of mathematical thinking.

This particular camp was grueling. Every single class day (5 days a week) we had a lecture given by the late Professor Arnold Ross on Number Theory and we had these brutal problem sets to do by the next day. The problem sets had maybe a dozen problems on them. Some were explorations. Others were proofs. The proofs were called "PODASIPs", which stood for "prove or disprove and salvage if possible." So, the things we were trying to prove weren't always true, or maybe they were true if some condition were tweaked. Needless to say, these problems were really hard and all of us students got to know one another really well because we needed to work together.

I have heard numerous stories of people's lives being changed for the better because they did this particular program for a summer. I'm sure it's true for other programs as well. This blog wouldn't exist and my passion for Math probably wouldn't burn as brightly as it does were it not for early experiences I had in my life that ignited and fueled that passion.

I'd be very interested to know what experiences readers have had with Math camps. If you have a comment that would make for a good post I'll be happy to publish it as a guest post, giving you full credit.

Joshua ZuckerFebruary 25th, 2008 - 22:05

I’m also an alum of the Ross program (from the mid 1980s) and it’s certainly the one I remember from my school-age math experiences. It had a big impact on the way I think about math, particularly in its emphasis on numerical experimentation, conjecture, and then (my name for PODASIPs) prove, or disprove and improve, your conjecture.

I still have a Tshirt from that camp with a proof of quadratic reciprocity on it.

SolFebruary 25th, 2008 - 22:13

Josh,

Nice to meet another Ross alum. I also have one of those yellow quadratic reciprocity t-shirts! And, I still have all of the problem sets from my summer. You’re fortunate to be old enough, like me, to have Professor Ross himself teach your classes.

MickeyFebruary 27th, 2008 - 17:33

Hey –

I found this site via some google searches while looking for fun and interesting problems for jr. high and high school kids. I love the site.

I attended Young Scholars Program at the University of Chicago for 5 years from summer after 6th through after 10th. It wasn’t a camp, so most of the kids were locals. Definitely an enjoyable experience, probably not as challenging and hardcore as Ross, but definitely left me with a great joy in mathematics as well as a knowledge of topics that I had never considered before.

SolFebruary 28th, 2008 - 17:51

Mickey,

I’m glad you like the site. University of Chicago is certainly a quite prestigious school in general and in Math specifically so I imagine the caliber of training was quite high. Developing a great joy in Math is a great achievement. Congratulations!

Joshua ZuckerFebruary 28th, 2008 - 18:03

My main memory of Ross is when we proved there are no integers between 0 and 1. Before Ross, it would never have occurred to me that there was anything to prove. And the proof was beautiful (we assumed well-ordering principle, instead of the usual induction, which leads to a stylish proof of this fact).

Is there a particular problem that you remember well?

SolFebruary 28th, 2008 - 22:07

Joshua,

I remember the proof of there being no integers between 0 and 1, the well ordering principle (WOP) , and the indirect proof: Assume there is an integer between 0 and 1, consider the set of all integers between 0 and 1, by the WOP there is a least element in this set. Call it L. Then, 0 < L < 1. Multiply everything in the inequality by L. Then, 0 < L^2 < L. L^2 is an integer because multiplication is closed under integers. So, L^2 is an integer and L^2 is less than L. But, we said that L was the smallest integer between 0 and 1. So, we’ve hit a contradiction. There is a problem that I enjoyed, but I’d have to look at my notes to remember it. It had something to do with inversion of a number theory formula and combinatorics. I remember being overjoyed at the cleverness and utility of that inversion.

sam shahMarch 2nd, 2008 - 15:21

Your post inspired me to do some reminiscing about my math camp experience in high school. I started typing it here, but it became too long, so I put it on my blog:

http://samjshah.wordpress.com/2008/03/02/recollections-of-theorems-past/

Thanks for making me remember the good times! And keep on blogging (love it!).

-Sam Shah

SolMarch 5th, 2008 - 17:28

Sam,

Your outstanding post puts mine to shame! It’s a great story I encourage everyone to read.

GAILDecember 21st, 2008 - 14:53

My question.

is in cheaper to have 2 people for 2 1/2 hours at 8.00an hour and 3 people for 5 1/2 at 8.00 an hour for 184 days.

or

3 people for 5 1/2 hours at 8.00 an hour for 184 days.

if there is a savings how much would it be.