1 00:00:00,365 --> 00:00:01,740 PROFESSOR: So I usually start out 2 00:00:01,740 --> 00:00:05,670 by handing out a sheet of usually three to five questions 3 00:00:05,670 --> 00:00:07,140 that I give to everybody. 4 00:00:07,140 --> 00:00:08,820 These are questions that I'm eventually 5 00:00:08,820 --> 00:00:12,076 going to answer in the course of the lecture, 6 00:00:12,076 --> 00:00:13,950 but I give the questions out at the beginning 7 00:00:13,950 --> 00:00:17,120 because I want people to have something to think about 8 00:00:17,120 --> 00:00:19,380 while I'm talking, especially when-- it's not 9 00:00:19,380 --> 00:00:21,697 uncommon for people to go off into a daze, 10 00:00:21,697 --> 00:00:24,030 and it's good for them to have something to think about. 11 00:00:24,030 --> 00:00:26,280 And also, ideally, they answer the question themselves 12 00:00:26,280 --> 00:00:28,620 before I get to the answer. 13 00:00:28,620 --> 00:00:30,120 Then we proceed to-- 14 00:00:30,120 --> 00:00:31,260 depending on the day-- 15 00:00:31,260 --> 00:00:33,210 in a day when we're doing lectures, 16 00:00:33,210 --> 00:00:35,897 I'll proceed to present material, ask questions, 17 00:00:35,897 --> 00:00:37,980 and then, when I get to an appropriate breakpoint, 18 00:00:37,980 --> 00:00:39,900 try to give people a chance to solve the problems that I've 19 00:00:39,900 --> 00:00:42,390 handed out, and occasionally have people come up 20 00:00:42,390 --> 00:00:45,234 to the boards, and give their solutions on the board. 21 00:00:45,234 --> 00:00:46,650 Sometimes I'll bring in materials. 22 00:00:46,650 --> 00:00:48,233 Like if we're doing polytopes, I might 23 00:00:48,233 --> 00:00:51,930 bring in an icosahedron, or a dodecahedron, 24 00:00:51,930 --> 00:00:55,050 or some more sophisticated shapes. 25 00:00:55,050 --> 00:01:01,830 Or we might be working with tiles or various other pieces 26 00:01:01,830 --> 00:01:05,550 we might be using to investigate combinatorial problems. 27 00:01:05,550 --> 00:01:07,200 And then on some of the days-- of least 28 00:01:07,200 --> 00:01:10,410 two or three days of the course are devoted to nothing 29 00:01:10,410 --> 00:01:12,709 more than problem solving, so I don't do any talking 30 00:01:12,709 --> 00:01:15,000 during those days at all other than to answer questions 31 00:01:15,000 --> 00:01:15,972 that people may have. 32 00:01:15,972 --> 00:01:17,430 And people work either individually 33 00:01:17,430 --> 00:01:19,600 or in groups on solving problems. 34 00:01:19,600 --> 00:01:21,660 And then the last day of the course, we actually 35 00:01:21,660 --> 00:01:26,640 had a contest, where the students had an opportunity 36 00:01:26,640 --> 00:01:29,160 to pit their brains against some of the more challenging 37 00:01:29,160 --> 00:01:30,400 problems that are out there. 38 00:01:30,400 --> 00:01:32,733 And actually I should mention, a lot of the students who 39 00:01:32,733 --> 00:01:35,080 take the course are very interested in mathematics, 40 00:01:35,080 --> 00:01:37,140 and one of their motivations for doing the course 41 00:01:37,140 --> 00:01:39,690 is to better prepare themselves for some of the math 42 00:01:39,690 --> 00:01:41,880 contests that are out there-- contests like the AMC, 43 00:01:41,880 --> 00:01:45,600 the AIME, and the US Math Olympiad. 44 00:01:45,600 --> 00:01:49,110 And I think a lot of kids find the combinatorics questions 45 00:01:49,110 --> 00:01:51,520 on those tests to be some of the most challenging, 46 00:01:51,520 --> 00:01:53,122 whereas my attitude is always when 47 00:01:53,122 --> 00:01:55,080 I look at those tests, about half the problems, 48 00:01:55,080 --> 00:01:56,380 I have no idea how I would solve them. 49 00:01:56,380 --> 00:01:58,320 But when I look at the combinatorics problems, 50 00:01:58,320 --> 00:01:59,850 they're gimmes. 51 00:01:59,850 --> 00:02:02,297 And my hope is that by the end of the course, 52 00:02:02,297 --> 00:02:04,380 the kids who take the course think the same thing, 53 00:02:04,380 --> 00:02:06,960 but the nice thing about the existence of these contests 54 00:02:06,960 --> 00:02:09,990 is it gives me a wonderful source of problems 55 00:02:09,990 --> 00:02:12,529 to throw at the kids.