Solutions to Selected Exercises from 245C, Notes 3: Distributions

I haven’t posted anything in a while. Partly because I’ve been busy with family matters, but mainly because I’ve actually made some friends this quarter and so instead of typing up solutions by myself, I just talk about the exercises with them. The work is more engaging that way, but that method has the draw back of de-motivating me. I feel less of a need to write solutions up when I already went over them with an actual audience. But things have calmed down a bit, and now I’m less busy than I was, so I now plan to update more regularly.

Quick aside. Does anyone know how to allow WordPress to understand user-defined Latex commands? [Edit: Professor Tao informed me how]

My hang up is everything looks better fixed-width, but WordPress cuts off some of the equations when I have a fixed-width theme. I don’t know if that problem was particular to the theme I chose, or whatever, but because of it, I’ve been forced into this less nice flexible-width theme.

[Edit: I have finally fixed the known errors in this post. I actually made the corrections at least a month ago, but out of sheer laziness, did not repost until just now.]

Solutions Notice for Notes 13

I have Notes 13 up and nearly completed. There’s one small fragment of Exercise 2 that needs to be done, and two parts to number 4 that need to be done.

I found out that doing all the exercises a very time consuming task, and this is a significant lowering of the bar, but I’ll proably have to resign to just giving partial solutions or outlines for most exercises.

245B, Notes 13: Compactification and Metrisation

Here are some partial solutions to the problems formulated in Notes 13 that can be found here.

Marjoe

I just saw a documentary called Marjoe that’s available in full on youtube. It’s about a man that used to be (and actually still was at the time of filming) a Pentecostal minister. Our unfortunately name hero/sort-of-villian became a minister at the age of 4. His parents paraded him around as a novelty act until he got sick of it as a teenager. He went back to preaching as an adult, because, well, if you had a get rich quick scheme you’ve spent a lifetime perfecting, wouldn’t you go out and do it? I was almost tempted to write, “this time, purely as a cynic looking for some quick cash,” but he plainly admits that he never believed what he was preaching. He seems more upset that his parents didn’t give him any cut of the cash than ruining his childhood. They did teach him how to make a living.

The movie’s not an attack on Pentecostalism. Marjoe even gives them an honest endorsement as the Christian curch he’d belong to if he had to choose one. They never mention in the movie any doctronial isssues on which the Pentecost church differs from other churches. Sure there’s the shaking on the floor, the healing through prayer, and other shows, but the club handshakes don’t tell you a club’s beliefs and values.

I like Marjoe, it’s hard not to like him. He’s smart, charaismatic, and has a certain power. I must admit that I have bias towards people like that because I’m the polar opposite. Those people are strange to me. I don’t understand how they tick, from where they get that power. So I’m always interested when something takes a closer look at that type of person.

This movie is a behind the curtain look of a rouse and its con man. He explains some fake miracles to his camera crew, but that’s only a fraction of what he does. The con isn’t his parlor tricks but him. He has passion and energy. He speaks with conviction and power. He’s a skilled entertainer, and even when he’s not singing his voice has a musical quality to it. When you watch him preach there is no crack in the performance. There is no keyhole through which we see that jaded cynic that must be half-laughing half-crying at the power his performance has over his audience.

This isn’t harmless fun. He even recognizes the bad he’s doing. I’ve read accounts of James Randi doing cold-readings (for those of you that haven’t taken an interest in the battle between skepticism and psuedo-science/paranormal-activity, a cold-reading is the name of the parlor trick off of which John Edwards has based his entire), and he puts on a good show. But at the end, he always reveals that it was just that, a show. And at no points did he ever collect money from the people he was tricking. I don’t know if this was intenttional but the symbolism smacks you in the face. There is a scene where Marjoe’s audience line up and puts money in a waste bin. He realizes what he’s doing is wrong, he doens’t feel guilty enough to not take his victims’ money,  but the desire to end his sham is the impetus for the creation of the movie.

There isn’t really too much straight criticism found in the movie. The strongest piece would be a zoom-in on an elaborate broche pinned to a woman that asks the people in the pews to donate money to the cash-straped church, while reassuring them that the church doesn’t spend foolishly. Even when Marjoe’s father is presented, all Marjoe says is that the only thing they can really talk about is his father’s back-yard.

Probably the best scene is one towards the end that features Marjoe, his girl friend, and a dog. At this point he’s stated how he’s tired of his double-life, the lies, and he wants a new life with the girl he loves. It’s a huanting scene because he’s at full-force in it. It shows the incredible talent and personality that’s essentialy been wasted on a single trick. He’s not giving up just a rouse, but what’s been his life. It’s an increidbly interesting movie if only because it is the atonement of a fascianting person.

But I have to admit, if there is one child prohet I’m going to follow, it would be this one. Sorry Marjoe.

Introductory Remarks

This is the first in what I hope to be many posts. The immediate goal of this blog is to collect and post solutions to the various exercises that Professor Tao has posted in his various course notes. Ideally, this blog would have been created in early January when his latest course (Math 245B) began. Right now, his Math 245B exercises are a way to work out the kinks to posting and maintaining a blog, so that when Professor Tao starts his 245C course (in two to three weeks) this blog will be ready for the onslaught of exercises he has in store.

There is a huge backlog of problems. I plan on initially just having thirteen essentially blank posts (one for each of his notes), with each post just consisting of the exercise numbers, and I’ll fill the space next to each of those numbers with the corresponding proof as I get around to typing one up or posting a submitted answer. This way my posts are ordered the same way as Professor Tao’s.

I’ll post the problem lists soon, and I will fill in what I can when I have time, but as I said before, I do hope to receive help. If this blog is a sort of answering of a challenge from Professor Tao’s blog, then this blog is at a serious disadvantage in thus duel. As previously stated, there is a tremendous backlog of problems, intrinsically it takes less time read a problem than it is to answer it, and I am much more of a mere mortal than Professor Tao.

So here we go.