### Tuesday, May 31, 2005

## 17:09

So, I visited my family over the weekend. Our idea was to camp out in tents in the back yard and then go on day trips. These plans were changed somewhat due to uncooperative weather, but we still had fun. Friday night we watched National Treasure and The Day After Tomorrow, and yesterday we played Frisbee golf.

### Wednesday, May 25, 2005

## 8:25

I need to do something about my cell phone today. Like replace the battery or replace the phone. My two-year contract is about to run out anyhow.

Did I mention that the vision test for getting the driver's license confirmed what I already suspected? My vision isn't that great, but my right eye is worse. I couldn't read some of the numbers with the right eye. Apparantly I have 20/40 on the left and 20/50 on the right.

Did I mention that the vision test for getting the driver's license confirmed what I already suspected? My vision isn't that great, but my right eye is worse. I couldn't read some of the numbers with the right eye. Apparantly I have 20/40 on the left and 20/50 on the right.

### Tuesday, May 24, 2005

## 15:50

Yesterday was my birthday, a fact which I didn't remember until the day before yesterday. And what did I do on my birthday? Mostly I tried to renew my driver's licence, a feat which I didn't fully accomplish until today. They needed proof that I was no longer living in California, and I had to take the written test. As near as I can tell the main difference between Idaho and California is that Idaho has an Open Range law.

Not having heard from anyone yesterday, I figured they were generally busy. Last night at around 21:30 I was bored and decided to walk over to campus and check my email. On my way there, Greg's younger brother Mike called me with an algebra question. It turned out to be too complicated to handle over the phone, so he met me on campus and we worked it out up in my office. Somewhere along the line I mentioned that it was my birthday, so after we finished he bought me a milkshake at Space Burger.

After that I was sitting at home drinking my milkshake and reading Mostly Harmless, when I got a call from Kyle. He said he's heard that it was my birthday and I wasn't doing anything. I said that news travelled fast, and he said not that fast, he just happened to be at Greg's house, along with Abe and Josh. So they came and picked me up and we went back to Greg's to play Star Wars: Galactic Battlegrounds while half-watching Pirates of the Caribbean. And as it turned out, they got a cake on their way to pick me up, which was very nice of them. So I had a very good birthday. I got to do algebra problems and everything!

Not having heard from anyone yesterday, I figured they were generally busy. Last night at around 21:30 I was bored and decided to walk over to campus and check my email. On my way there, Greg's younger brother Mike called me with an algebra question. It turned out to be too complicated to handle over the phone, so he met me on campus and we worked it out up in my office. Somewhere along the line I mentioned that it was my birthday, so after we finished he bought me a milkshake at Space Burger.

After that I was sitting at home drinking my milkshake and reading Mostly Harmless, when I got a call from Kyle. He said he's heard that it was my birthday and I wasn't doing anything. I said that news travelled fast, and he said not that fast, he just happened to be at Greg's house, along with Abe and Josh. So they came and picked me up and we went back to Greg's to play Star Wars: Galactic Battlegrounds while half-watching Pirates of the Caribbean. And as it turned out, they got a cake on their way to pick me up, which was very nice of them. So I had a very good birthday. I got to do algebra problems and everything!

### Wednesday, May 18, 2005

## 9:54

Bible study this morning at 7:30. Romans 2. External conformity to the law versus internal holiness.

Okay, here's a thought about the star formations. Say the total number of stars is N, and say F(N) yields the number of combinations on N stars. You start out with the top row, which has X stars in it. Then you have N-X stars to play with beneath that. There will be F(N-X) such combinations, as long as X < (1/2)N. But of course it's more complicated if some of the combinations are not allowed because the top row isn't long enough to accomodate them.

Okay, here's a thought about the star formations. Say the total number of stars is N, and say F(N) yields the number of combinations on N stars. You start out with the top row, which has X stars in it. Then you have N-X stars to play with beneath that. There will be F(N-X) such combinations, as long as X < (1/2)N. But of course it's more complicated if some of the combinations are not allowed because the top row isn't long enough to accomodate them.

### Sunday, May 15, 2005

## 16:41

So, it's been a while since I've posted. This is because I was catching up in my classes, and then taking finals. That's about all I did for the past however long, so there really wasn't much to post anyway. I'm going to be doing qualifying exams in August probably, so I have to get ready for them. Written in Algebra and oral over everything.

So, let's see...highlights. Starting on about Tuesday of last week, finals week, I had a sore throat which gradually got worse. This was nice timing for the two hour presentation I had to give in Representation Theory in Friday. Fortunately I was still able to talk at that time.

Friday afternoon I was planning to head back home for my cousin's high school graduation, but I missed the bus. I thought it left at 16:15, but it actually left at 16:10. So I got there a couple minutes early and was actually about three minutes late. I wasn't feeling great, so it was probably just as well.

Friday night I ended up watching the last two episodes of Enterprise. They were good, but it was disappointing that they couldn't play the series out for a few more seasons.

Saturday night, we had a party for all the local college graduates from the church. Afterwards we went to Greg's house and watched Episode II, but I slept through most of it. Then I went home and slept for about 12 hours straight. I didn't make it to church and I didn't play Ultimate Frisbee, but I feel a little bit better. I still can't talk well.

Next Thursday a bunch of us are going to go watch Episode III. Should be fun. Not sure when I'm going to see Hitchhiker's.

Meanwhile, I need a summer job.

Okay, enough about life; let's talk about math. Part of the stuff my presentation was on had a connection with combinatorics. Without getting into what these shapes are for in Representation Theory, consider shapes formed by connected squares with the following requirements:

-) The rows are all left-justified.

-) Each row is as long or longer than the one below it.

Examples (using *'s instead of squares):

***

**

**

*

*

****

***

***

*

Now, you can gradually build all the possibilities by starting with a single * and considering all the possible ways you can add one more at each level. Thus:

1:

*

2:

**

*

*

3:

***

**

*

*

*

*

4:

****

***

*

**

**

**

*

*

*

*

*

*

And so on. (With 5, there are 10 possibilities.)

The question is, can you come up with some kind of formula for the sequence that give the number of possible shapes for each number of stars? The first few numbers, based on the above examples, would be: 1, 2, 3, 5.... I think there is a way to generate the numbers recursively, but I don't know it yet.

So, let's see...highlights. Starting on about Tuesday of last week, finals week, I had a sore throat which gradually got worse. This was nice timing for the two hour presentation I had to give in Representation Theory in Friday. Fortunately I was still able to talk at that time.

Friday afternoon I was planning to head back home for my cousin's high school graduation, but I missed the bus. I thought it left at 16:15, but it actually left at 16:10. So I got there a couple minutes early and was actually about three minutes late. I wasn't feeling great, so it was probably just as well.

Friday night I ended up watching the last two episodes of Enterprise. They were good, but it was disappointing that they couldn't play the series out for a few more seasons.

Saturday night, we had a party for all the local college graduates from the church. Afterwards we went to Greg's house and watched Episode II, but I slept through most of it. Then I went home and slept for about 12 hours straight. I didn't make it to church and I didn't play Ultimate Frisbee, but I feel a little bit better. I still can't talk well.

Next Thursday a bunch of us are going to go watch Episode III. Should be fun. Not sure when I'm going to see Hitchhiker's.

Meanwhile, I need a summer job.

Okay, enough about life; let's talk about math. Part of the stuff my presentation was on had a connection with combinatorics. Without getting into what these shapes are for in Representation Theory, consider shapes formed by connected squares with the following requirements:

-) The rows are all left-justified.

-) Each row is as long or longer than the one below it.

Examples (using *'s instead of squares):

***

**

**

*

*

****

***

***

*

Now, you can gradually build all the possibilities by starting with a single * and considering all the possible ways you can add one more at each level. Thus:

1:

*

2:

**

*

*

3:

***

**

*

*

*

*

4:

****

***

*

**

**

**

*

*

*

*

*

*

And so on. (With 5, there are 10 possibilities.)

The question is, can you come up with some kind of formula for the sequence that give the number of possible shapes for each number of stars? The first few numbers, based on the above examples, would be: 1, 2, 3, 5.... I think there is a way to generate the numbers recursively, but I don't know it yet.