Thursday, March 31, 2005
14:49
Nothing noteworthy has been happening. Just a lot of homework.
Monday, March 28, 2005
14:17
I visited my family over the weekend. It was nice to make it there in time for the Good Friday communion service. I spent most of the afternoon on Saturday working on Representation Theory. Then I had to leave early on Sunday to go work on it some more, so I missed playing Risk with my sister and cousins.
Friday, March 25, 2005
15:26
I'm visiting my family this weekend. I get off work in 4 minutes, and the bus leaves in 44 minutes.
Thursday, March 24, 2005
10:21
I woke up at exactly 8:00 this morning. Not a great start since my class starts at 8:00. I made it there by about 8:30, though. Only missed the proof of one lemma, which I can read in the book anyway.
Tuesday, March 22, 2005
22:20
So I got a call from my mom earlier and found out that my sister and cousins might be coming down with my uncle this evening. Later I got a call from my sister saying they weren't coming. I was doing homework in the quiet section of the library, so I turned off my phone after that. Later I went to work. After I got off work, I turned on my phone and there were three messages letting me know that: a) They were coming after all. b) They accidentally hit redial and recorded random noise on my voice mail. c) They were playing pool in the Student Union Building and I could join them after I got off work. So I did. That was fun. I didn't know my sister was that good at pool. They are driving home now.
There's a flier in the computer lab here advertising two math guest lectures on April 1st. One of them starts half an hour before I get off work, but I can make it to the second one. I'm very happy about this, because it's about Collatz' Conjecture. That's right, the open question in number theory that I've been mildly obsessed with since I was twelve. I'm almost excited about this.
Time to finish up Representation Theory homework.
There's a flier in the computer lab here advertising two math guest lectures on April 1st. One of them starts half an hour before I get off work, but I can make it to the second one. I'm very happy about this, because it's about Collatz' Conjecture. That's right, the open question in number theory that I've been mildly obsessed with since I was twelve. I'm almost excited about this.
Time to finish up Representation Theory homework.
Monday, March 21, 2005
16:23
My roommate got in at 5:00 this morning. He had to go to class at 8:00. It's kind of weird having him back again after living alone for two weeks.
Sunday, March 20, 2005
21:31
Okay, I'm an idiot. The positive integers do not form a group under multiplication. Duh, there's no inverses! They do, however, form a semigroup with an identity, also called a monoid. It's even abelian, but I'm not sure if an abelian monoid has a special name.
Friday, March 18, 2005
17:39
Okay, I haven't made a mathematical post in a while, and I want to explore an idea I just had. The positive integers form a group under multiplication. Call it G. G is infinitely generated, and the most natural basis set for G would be P, the set of prime numbers. Come to think of it, that's the only possible basis set. Any given prime would have to be in it, since a prime can't be written as a product of other integers, and once you've got all the primes, putting any other integer into the set would violate the uniqueness criterion. Okay, so we've got G which is generated by P. Let's consider endomorphisms of G. If f: G -> G is an endomorphism, then f is completely determined by where it sends elements of P. Here's the thought I had earlier: Suppose f(2) = 3, f(3) = 2, f(p) = p for p in P\{2,3}. I thought this might shed some light on the Collatz problem since it deals so much with 2's and 3's. Anyway, let's look at a table:
1 - 1
2 - 3
3 - 2
4 - 9
5 - 5
6 - 6
7 - 7
8 - 27
9 - 4
10 - 15
11 - 11
12 - 18
13 - 13
14 - 21
15 - 10
16 - 81
17 - 17
18 - 12
19 - 19
20 - 45
21 - 14
22 - 33
23 - 23
24 - 54
25 - 25
Okay, I can see one thing already. f(x) = y <=> f(y) = x. So f is its own inverse. Interesting. You could also set up something more complicated, I suppose. Like, put all the primes into pairs and swap them. Okay, I've run out of ideas for the moment. Brainstorm finished.
1 - 1
2 - 3
3 - 2
4 - 9
5 - 5
6 - 6
7 - 7
8 - 27
9 - 4
10 - 15
11 - 11
12 - 18
13 - 13
14 - 21
15 - 10
16 - 81
17 - 17
18 - 12
19 - 19
20 - 45
21 - 14
22 - 33
23 - 23
24 - 54
25 - 25
Okay, I can see one thing already. f(x) = y <=> f(y) = x. So f is its own inverse. Interesting. You could also set up something more complicated, I suppose. Like, put all the primes into pairs and swap them. Okay, I've run out of ideas for the moment. Brainstorm finished.
Thursday, March 17, 2005
16:29
When I logged in yesterday, all my messages were back. *shrugs* Maybe I'll keep that address.
Tuesday, March 15, 2005
16:12
I am not happy about Hotmail. For no apparant reason, they deactivated my account. I was able to reactivate it, but all the messages were deleted. The screen informing me of this said that it happened because the account was innactive for over thirty days. This is not true. I checked my email there last week. Those saved messages were a large part of why I was keeping that as my primary address. I'm switching to gmail.
15:19
So, Sunday night Abe, Kyle, Greg and myself played LOTR Risk. We tried a four person free-for-all, dealing all the territories randomly. I was dealt most of Gondor, which pretty much sealed my fate, because Gondor is like Russia: No one will let you keep it. If we had played the game all the way out, Kyle would have conquered the board before the ring got destroyed.
Yesterday we went on a hike and saw snow. That's right, snow. The white stuff that we don't have down here in the lowlands any more.
Last night we had a get together at Dan and Sarah's instead of the usual Monday night Bible studies, since so many students are out of town. That was a lot of fun. There are still several of us who haven't left.
Today we are probably going to watch The Incredibles. Isn't Spring Break great? Still lots of homework to do, though. But I'm making progress.
Yesterday we went on a hike and saw snow. That's right, snow. The white stuff that we don't have down here in the lowlands any more.
Last night we had a get together at Dan and Sarah's instead of the usual Monday night Bible studies, since so many students are out of town. That was a lot of fun. There are still several of us who haven't left.
Today we are probably going to watch The Incredibles. Isn't Spring Break great? Still lots of homework to do, though. But I'm making progress.
Sunday, March 13, 2005
17:21
My roommate's dad and brother got here Saturday night, and we all went to see National Treasure. When the grandfather was telling the story in the beginning, I thought the movie was going to be really stupid, but it wasn't that bad. As adventure/treasure hunting movies go, I'd rate it above Tomb Raider or The Mummy.
Nicole sent cinnamon rolls and grapes home with us last night so we could eat them for breakfast, and this morning I was up pretty early in order to use the shower and give it time to regenerate, so I cooked some potatoes, sausages and mushrooms, and we ate those as well.
Sunday school was about various Christological heresies that cropped up after the Council of Nicea (I'm going to the Church History class). Pastor Mike is back from the Israel trip, so in the main service we were back in I Corinthians. Chapter 13 this week.
The usual group Ultimate Frisbee this afternoon. I didn't get there for the first forty-five minutes, and it only went about another fifteen minutes before they switched to soccer. But I did play.
The evening service tonight is going to be on the predestination/free will issue. I've heard that one addressed plenty of times, including at every Grace Community Q&A session. Still, I'll go. I think Abe's trying to organize a game of Lord of the Rings Risk afterwards.
Nicole sent cinnamon rolls and grapes home with us last night so we could eat them for breakfast, and this morning I was up pretty early in order to use the shower and give it time to regenerate, so I cooked some potatoes, sausages and mushrooms, and we ate those as well.
Sunday school was about various Christological heresies that cropped up after the Council of Nicea (I'm going to the Church History class). Pastor Mike is back from the Israel trip, so in the main service we were back in I Corinthians. Chapter 13 this week.
The usual group Ultimate Frisbee this afternoon. I didn't get there for the first forty-five minutes, and it only went about another fifteen minutes before they switched to soccer. But I did play.
The evening service tonight is going to be on the predestination/free will issue. I've heard that one addressed plenty of times, including at every Grace Community Q&A session. Still, I'll go. I think Abe's trying to organize a game of Lord of the Rings Risk afterwards.
Saturday, March 12, 2005
12:26
So...interesting weekend so far. Late Thursday night I heard a couple of loud bangs and some sirens. I didn't think much of it, until I was walking to campus Friday morning and saw that the parking garage for one of the apartment buildings in the complex where I live had burned down in the night. The area was roped off and crawling with police officers and firefighters. There ought to be something in today's paper; I'll have to get one.
Last night there was no regular game night at Randy's, because they were doing something for his son Eric's birthday. Some of us got together anyway and watched the enhanced version of Star Wars Episode IV.
My roommate is not going to be back until after the break, but his dad and brother are probably coming down here today to pick up his sister, and if they do they will stay at my apartment tonight. Their grandfather died on Tuesday. I hope he does at least some schoolwork during the break, because it's going to be pretty hard for him to catch up after missing a week of classes.
Last night there was no regular game night at Randy's, because they were doing something for his son Eric's birthday. Some of us got together anyway and watched the enhanced version of Star Wars Episode IV.
My roommate is not going to be back until after the break, but his dad and brother are probably coming down here today to pick up his sister, and if they do they will stay at my apartment tonight. Their grandfather died on Tuesday. I hope he does at least some schoolwork during the break, because it's going to be pretty hard for him to catch up after missing a week of classes.
Thursday, March 10, 2005
21:14
I really need to figure out that remote posting thing so I can still post when the site feels like crashing. Bible study tonight was about not assuming that God owes us blessings in this life. Easy enough to see in the case of things that we want that might not be good for us. Harder to understand if it's something unequivocally good.
Spring Break is next week. I don't know if I'll visit my family or not, or for how long. Lots of homework to do.
Spring Break is next week. I don't know if I'll visit my family or not, or for how long. Lots of homework to do.
Wednesday, March 09, 2005
18:18
Hmm, I told Abe that I would be able to do something other than school at 20:30 tonight. I think maybe I can pull that off.
15:38
The math lab was almost empty today, which was really weird because we know of at least three classes with tests either tomorrow or Friday. It may have something to do with the fact that the weather is nicer.
Tuesday, March 08, 2005
19:56
Long day today. I got combinatorics turned in. Still more algebra to do. And my roommate is still out of town. I don't like living alone.
Monday, March 07, 2005
22:13
Wow, I'm not getting error messages every time I press a key! I got some algebra turned in, and still have to write up some more combinatorics.
Bible study was at my apartment, as usual. The most recent chapter in Disciplines of a Godly Man (by R. Kent Hughes) was on the Discipline of the Mind. Even though my roommate was gone, we had six guys, which is more than usual. Good discussion. Interesting to hear different ideas about entertainment and Bible reading strategies. One of the things the author did was survey a bunch of Christian leaders about books they had read. The questions (along with my own anwers) ran something like this (in each case I'm listing books other than the Bible):
1) What five books, sacred or secular, have had the greatest influence on you?
Listed in alphabetical order:
The Chosen, by Chaim Potock
The Fight, by John White
Gödel, Escher, Bach: An Eternal Golden Braid, by Douglas Hofstadter
Lès Miserables, by Victor Hugo
The Story of Liberty, by Charles C. Coffin
2) Of the sacred books that have influenced you, which is your favorite?
Currently: Holiness, by J.C. Ryle
3) What is your favorite novel?
Lès Miserables, by Victor Hugo
4) What is your favorite biography?
Call of Duty: The Sterling Nobility of Robert E. Lee, by J. Stephen Wilkins
Bible study was at my apartment, as usual. The most recent chapter in Disciplines of a Godly Man (by R. Kent Hughes) was on the Discipline of the Mind. Even though my roommate was gone, we had six guys, which is more than usual. Good discussion. Interesting to hear different ideas about entertainment and Bible reading strategies. One of the things the author did was survey a bunch of Christian leaders about books they had read. The questions (along with my own anwers) ran something like this (in each case I'm listing books other than the Bible):
1) What five books, sacred or secular, have had the greatest influence on you?
Listed in alphabetical order:
The Chosen, by Chaim Potock
The Fight, by John White
Gödel, Escher, Bach: An Eternal Golden Braid, by Douglas Hofstadter
Lès Miserables, by Victor Hugo
The Story of Liberty, by Charles C. Coffin
2) Of the sacred books that have influenced you, which is your favorite?
Currently: Holiness, by J.C. Ryle
3) What is your favorite novel?
Lès Miserables, by Victor Hugo
4) What is your favorite biography?
Call of Duty: The Sterling Nobility of Robert E. Lee, by J. Stephen Wilkins
Sunday, March 06, 2005
20:37
Okay, it appears that the site is going to let me post this time. Earlier it kept crashing. My roommate went to Portland with his family, and I'm not sure when he'll be back. Sometime next week. I think he emailed all his professors, but I'll also talk to his math professor for him in person. Speaking of which, I need to finish my homework for that professor.
Saturday, March 05, 2005
19:40
I don't like this whole phone-not-working thing. I think I'm going to have to get a new one.
Other than that, I'm doing algebra. No details that I feel like recording. Just algebra. I should have done some laundry too, but I forgot. That's okay; I can do it tomorrow or something.
Other than that, I'm doing algebra. No details that I feel like recording. Just algebra. I should have done some laundry too, but I forgot. That's okay; I can do it tomorrow or something.
13:23
My roommate is out of town this weekend. He left late this morning with his sister. They may be gone more than the weekend, because their granfather's health is failing and they might go up to Portland. He said he would let me know if they are going to be gone longer, which might prove difficult since my cell phone hasn't been working consistently for the past couple of days. Before he left we cooked breakfast -- potatoes, sausages, mushrooms and pancakes. We like to do that on Saturdays.
Enterprise wasn't even on last night, but we watched one of the Section 31 episodes from DS9, Monk, and the first half of The Two Towers extended edition. I think that was the first episode of Monk where no one actually died. Personally, I think it would be cool if he did more than just homicide investigation.
Enterprise wasn't even on last night, but we watched one of the Section 31 episodes from DS9, Monk, and the first half of The Two Towers extended edition. I think that was the first episode of Monk where no one actually died. Personally, I think it would be cool if he did more than just homicide investigation.
Friday, March 04, 2005
14:02
Okay, so I've got algebra and representation theory to finish by Monday, and combinatorics to finish by Tuesday. Should be a fun weekend.
The usual group will want to play Ultimate Frisbee on Sunday, but I think it will still be too muddy. I don't like playing in the mud.
Yesterday was a quiz deadline, and it's a Friday, so it's quiet here in the lab. Most of the students are learning how to simplify radicals, convert between radical and exponential notation, and all that good stuff.
There are at least five different computers that someone labeled with papers that say, "Kick student out during certification of 5.4b." I'm assuming this is meant to be a description of a problem the machine has, rather than a suggested course of action. I wonder if anyone was actually notified of the problem. My guess is they weren't. People don't seem to realize that putting a paper on the keyboard keeps students from using the computer, but utterly fails to inform anyone who can fix the problem. Five computers down is bad. That's almost 1/6 of the total stations...fine for right now, but bad right before the next deadline. I guess I'd better tell somebody.
The usual group will want to play Ultimate Frisbee on Sunday, but I think it will still be too muddy. I don't like playing in the mud.
Yesterday was a quiz deadline, and it's a Friday, so it's quiet here in the lab. Most of the students are learning how to simplify radicals, convert between radical and exponential notation, and all that good stuff.
There are at least five different computers that someone labeled with papers that say, "Kick student out during certification of 5.4b." I'm assuming this is meant to be a description of a problem the machine has, rather than a suggested course of action. I wonder if anyone was actually notified of the problem. My guess is they weren't. People don't seem to realize that putting a paper on the keyboard keeps students from using the computer, but utterly fails to inform anyone who can fix the problem. Five computers down is bad. That's almost 1/6 of the total stations...fine for right now, but bad right before the next deadline. I guess I'd better tell somebody.
Thursday, March 03, 2005
22:41
There was a guest speaker at Bible study tonight, because Brad is at the Shepherd's Conference in California. Dan was gone also, so Greg had to lead music and M.C. The message was about joy. One thing that stood out to me was the fact that joy is listed as a fruit of the Spirit, right after love. We talk a lot about loving people, but not so much about being joyful.
I've been reading a book called A Thousand Suns, by Dominique Lapierre. The author is a French journalist. The chapters all stand alone -- each one is about either a person or a historical event. So far I've read about a pirate, a bullfighter, and the liberation of Paris during WWII. The next chapter that I haven't read is about the founding of modern Israel.
I've been reading a book called A Thousand Suns, by Dominique Lapierre. The author is a French journalist. The chapters all stand alone -- each one is about either a person or a historical event. So far I've read about a pirate, a bullfighter, and the liberation of Paris during WWII. The next chapter that I haven't read is about the founding of modern Israel.
13:15
Well, we finally got people lined up to move the tables, I think. I can't be there on Friday because it has to be done at 15:00 and I run the math lab until 15:30, but my officemate will be there and the department head said he could find a faculty member to help out as well. I guess I'll help on Saturday, though. I also found out that I can still register for the conference, which is good. My work schedule will make me miss the Friday session (which is apparantly why it was so hard to find table-moving volunteers) but I can still go to the others.
It turns out that problem was way more complicated than I thought. The map I needed to define is a map from a group onto the dual space of a vector space. So you plug a group element into the top-level map, and you get a functional. Plug a function into that, and you get another function. Plug a vector into that function, and you get a vector. Three fun-filled levels of complexity. I was trying to prove that the map was a homomorphism on the wrong level.
It turns out that problem was way more complicated than I thought. The map I needed to define is a map from a group onto the dual space of a vector space. So you plug a group element into the top-level map, and you get a functional. Plug a function into that, and you get another function. Plug a vector into that function, and you get a vector. Three fun-filled levels of complexity. I was trying to prove that the map was a homomorphism on the wrong level.
Wednesday, March 02, 2005
15:58
In case you haven't noticed, my blog posts will tend to be short and frequent. This reflects the nature of my schedule, which is busy but varied. When I am in a fixed position for a long period of time, I am likely to be interrupted at any moment. When I am not likely to be interrupted, it is because I'm going to interrupt myself shortly in order to go somewhere. Also, I do homework. It's kind of like an obsessive hobby.
Hmm, it looks like the Blog engine keeps track of date and time, but it doesn't have the right time zone. I'll have to try to fix that.
Hmm, it looks like the Blog engine keeps track of date and time, but it doesn't have the right time zone. I'll have to try to fix that.
15:24
I turns out one of those homomorphisms was actually guaranteed to have an inverse, so I can set up the map I need as a composition. Then I just need to prove that it is actually a representation. Shouldn't be too bad.
In other news, I just checked my school email for the first time in a few days, and found out that the department head asked me to coordinate some guys to move tables on Friday and Saturday for a conference we're having. Wish I'd realized this before today...so far only one guy from the department has emailed me. I might have to recruit my roommate.
In other news, I just checked my school email for the first time in a few days, and found out that the department head asked me to coordinate some guys to move tables on Friday and Saturday for a conference we're having. Wish I'd realized this before today...so far only one guy from the department has emailed me. I might have to recruit my roommate.
Tuesday, March 01, 2005
22:32
Well, I think I understand what a linear functional is, at least in this context, but what I'm left with is a diagram that I need to commute and no way to say that the required map exists. What I've got are two automorphisms, A: V -> V, B: V -> V, and I need C: V -> V such that C(A(v)) = B(v) for all v in V. Obviously this isn't going to work without some kind of restriction on one of the existing maps. I'll have to consult with the professor. Meanwhile, I can turn in the rest of the assignment and go home.
21:22
I am typing this from the computer lab in the Physical Sciences Building. Mostly I'm here because I need to find out a precise definition of the dual of a vector space, so I can try to finish a problem and get the homework turned in before I head home. That may or may not happen, depending on how difficult this problem is. My roommate is also here. He appears to be listening to music, chatting on MSN, and not studying physics.
