Cool videos.

In the second one, another approach is to notice that .

That's slick... I'll have to remember that if I shoot that clip again. May have to talk you into doing some of these

Richard, your presentation skills are really amazing. Especially I like your kind of hip-hop move to the web-cam, if you don't knoe theorem XYZ check out ABC! Stick to that. It is really cool. I also like that you started out by using a standard approach which does not lead you anywhere without quite an effort and then following the proper solution you always motivate the intermediate steps on how you could have thought of that particular step. Simply great!

I remember that problem from 6th grade. I didn't know the quadratic formula, so I ended up guessing 64. (I learned how to do the problem at the dinner banquet.) Viewing the video know, I think I could have understood that in 6th grade.

These videos are really awesome! You could make the classes better, in my opinion, by making some for them. For example, going over material/problems you don't have time to cover in the class, presenting solutions to some of the midterm/final problems and so forth.

Hm, it would be pretty cool to set up a camera/whiteboard somewhere at MIT to record videos and put them on the wiki or something. With all the former USAMO/MOP/etc people in the Boston area I'm sure we could get a wide variety of topics and lecturing styles. That would be cool...not sure how feasible it would be though. Heh, I could always turn my dorm into a recording studio Not sure how my roommate would like that (not sure who my roommate is yet...).

I like the videos! They really display the way that people should approach problems: testing values to find a pattern then applying techniques to solve the generalization.

I really enjoy this type of approach. I find that I can break down most amc and aime problems into sort of an algorithm where for each topic there is a set of techniques that I can try. One hard part about this is that you do not always know that the idea is going to work. But that is the fun of problem solving.

I find that it really helps me to try and make my own techniques (like you did with finding a pattern and doing things to reduce computation).

Ex. there are a significant number of problems that I have encountered that used the sine area formula. Of all the geometry techniques that I have forced myself to organize, that is one that I missed. (I was pretty light on looking at your solutions in AoPS 2. ) However, as I encountered problems on the forums, like

If is in with , then find .

For new problem solvers, it would be helpful to really emphasize some way of organizing your thoughts into generalizations like this. Furthermore, challenging them to make their own generalizations would help people to understand better. I suppose the question: how could I have done this myself? is a good starter.

Of course as problems progress in difficulty, this method does not seem like it can work because there are so many problem that seem obscure and intimidating. As I started out with this idea, I did not think that this could work on olympiad problems. But your class proved me wrong; even solving olympiad geometry problems is subject to a set few of techniques.

P.S. You did a nice job of explaining so everybody can understand. This reminds me that I need to learn how to explain problems better. I felt that my school teacher, while unable to teach me anything, really knew how to explain problems so that anybody could understand. Instead of learning math in that class, I tried to learn her method of explaining things so that everybody could understand. Often when I try to explain things to people at my school, they just get confused. I usually skip lots of steps. Ex. for that binomial theorem problem, I would be like "by the binomial theorem...| and write:

.

In my mind, applying the binomial theorem is trivial because it is just a theorem where you plug in numbers. But I see that is not reeally going to help people because they may become intimidated and not concentrate on the important part of the solution; the logic and motivation.

(looking forward to woot!)

I HAD THAT PROBLEM! I had absolutely NO idea how to work it, though. It's really amazing how much I've improved since back in the day.

Something is wrong with my computer. I can't seem to see anything, but I can hear what you are saying.