Beauty

Orientation

2010-08-22T19:01:00.002-04:00

Tomorrow I have orientation. Needless to say, but I am stoked! Yes, it's a short post, but oh so sweet.

Message for the Fellas'

2010-07-15T00:41:00.003-04:00

Not my own work but I think the message is very clear and one that isn't shared often enough. I don't know who originally said/wrote those words, I just got them from the caption on a friend's picture.

"You may not be her first, her last, or her only. She loved before she may love again. But if she loves you now, what else matters? She's not perfect- you aren't either, and the two of you may never be perfect together but if she can make you laugh, cause you to think twice, and admit to being human and making mistakes, hold onto her and give her the most you can. She may not be thinking about you every second of the day, but she will give you a part of her that she knows you can break- her heart. So don't hurt her, don't changer her, don't analyze and don't expect more than she can give. Smile when she makes you happy, let her know when she makes you mad, and miss here when she's not there. "

- ~~Unknown~~ Bob Marley

EDIT: I shared this with another friend and they have informed me that this comes from Bob Marley.

The Miami Heat

2010-07-09T23:18:00.002-04:00

Well as could be expected there was a lot of fall out when LeBron James said that he would be joining Chrish Bosh and Dwayne Wade in Miami next year. Personally I feel that Chicago would have been the better choice, but either way LA is still going to win it all.

But here is a funny comment that my sister shared with me;

"in the lebron backlash, my favorite new nickname for lebron, dwade, and bosh from a comment on espn:

5. The Nazgul

The Nazgul were the characters in Lord of the Rings that were former kings who turned into demons that were constantly chasing the ring. It completely consumed them and robbed them of their humanity.... I think this sums up the situation in Miami."

Probability Blog

2010-06-12T21:09:00.001-04:00

I now have a blog that I will be devoting to all things probability.

http://probability101.wordpress.com.

Winning

2010-05-15T10:51:00.003-04:00

Am I the only one that was disappointed by the way the Cleveland Cavalires played the last 90seconds of the 2010 Eastern Conference Semifinals? They were down by less than 10 and instead of fouling and trying to make it a game (which is what you would expect to see from ANY TEAM in that situation), they just stood around and let the Celtics run out the clock.

Sure I was rooting for the Celtics to win, but watching the Cavalires give up like that was just pathetic. Here is a quote that they should take to heart,

"Winning isn't everything, but the desire to win is."

Clearly they didn't have this desire, and it showed in those closing seconds. Did they think that because they had the best regular season record and the NBA MVP that all they had to do was show up in order to win?

On the topic of winning, here is a quote from Vince Lombardi,

"If winning isn't everything, why do they keep score?"

Formspring

2010-05-07T11:53:00.003-04:00

If you haven't heard of it then read this article.

One thing I noticed was that some parents/adults were surprised at the kind of sexual content that teenagers made public. I'm not going to take a side and say whether this is a good or bad thing but I will say this. I remember being a teenager, and the kind of things that appear on Formspring are pretty "mild" compared to what is discussed in person. Also the topic of bullying is brought up in the article. Yes, this can be a real problem, but then you have to remember that they probably experience much worse in real life.

If you are a parent you should take the time to talk to your teenager about these thing and how they should deal with them. Additionally, make sure to let them know that they can come to you with any issues they have. And if they don't feel comfortable talking to you about it make sure that they know that there are other adults that they can talk to if it is more comfortable for them.

Take this chance to be parents and provide your kids with the tools and knowledge that they will need to get through life. Because as you know, there are things in life are much more difficult than being bullied in middle school or feeling sexually awkward.

Money

2010-04-24T20:30:00.003-04:00

Sorry to break the Graduate School Series, but I just had to share this quote from one of my processors.

"Money can either buy you freedom or chains."

Basically it was his way of saying, live within your means, to all of us graduating seniors.

The Graduate School Series: Part 2

2010-04-18T17:14:00.012-04:00

This is the second part in a series about applying to (mathematics) graduate school. You can follow this link to part 1 if you would like to start reading from the beginning.

The Application
You can be certain that every school you apply to will ask for a transcript and at least the General GRE. Some schools however, will require you to take the subject test, which is no joke. How many of you remember everything from your multivariable class? Or all the little tricks to go along with it. Then for the more advanced topics covered on the test you might not have taken a class. However, these are few such questions and they are usually pretty simple (take that with a very very large grain of salt).
My advice would be to not overlook the standardized test, since they are part of your application and do matter to some extent.
One last thing, don't forget that most schools will have some sort of application fee, so you should set aside some money to cover this.

Personal Statement:
Remember when you were applying to your undergraduate program how they made you write those essays on the most annoying topics? Well I have some good and bad news for you. The bad news is that you still have to write an essay. However, the good news is that the topic is actually relevant.
Since the word essay is such an undergraduate term, it is now called the personal statement. When you think about it, this is in fact a much better term to describe what you are being asked to write. In your personal statement you are asked to discuss why you wish to pursue a graduate degree in mathematics. So this generally involves talking about why you got interested in math, what you did as an undergrad. and then what you wish to accomplish after grad. school. Also if at all possible you would mention why you wish to attend the school to which this personal statement will be sent.
It should go without saying that you will want to write many versions of you personal statement. There should be no spelling or grammar errors, you have at least 2 months to work on it, so any errors reflect poorly upon you (especially if you misspell a faculty member's name). You should also try to have as many people read your statement as possible, and provide you with actual criticism. The worst that can happen is that they find a mistake or suggest a way to improve your statement.
By this point you should understand that the personal statement is quite important. And you most likely don't have any experience writing one. I mean sure you have written papers for classes before, but how many of those would you be willing to rest you hopes of admission upon? Well here is a site that can help point you in the right direction.

Recommendation Letters:
I doubt that there is a single accredited program that won't ask for recommendation letters. And if you manage to find one...then I suggest you take a much much closer look.
Well this is your last year as an undergraduate, and you have hopefully talked to a faculty member or two (understatement) in you time. Well this is where it finally pays off (just kidding, having a relationship with past professors is always a good thing).
Don't underestimate the importance of a strong recommendation. Some admissions personnel say that this is the most important part of the application. The opinion of one's peers can go a long way. Suppose there are two students both who are almost identical in all other areas. However, in one student's recommendation letters their profess says

"This student is as talented as Gauss was at their age."

While the other student was only described as

"A wonderful student with great potential."

Who do you think will be more likely to get acceptance letter?
That being said, it is obvious that you should ask professors with whom you feel will be able to provide strong recommendation letters. If you've made it to you last year and you can't think of any professor that meets this requirement, then you should really consider why you are even applying to graduate school.

Additional Funding
Wouldn't it be nice to have a little money for living expenses? This is where fellowships come into play. The simplest (though incorrect) way to describe fellowships is that they are basically scholarships for graduate and post-graduate students.
The process for applying for fellowships is more or less the same as that for applying to schools, well most of the time. Therefore, I won't say anything about applying for them. But you will find this site provided by NYU useful in your fellowship search. One thing that should be mentioned, in most cases fellowships are more competitive than schools, no disrespect to any school out there.

Well that's it for part 2, stay tuned for part 3.

The Graduate School Series: Part 1

2010-04-18T00:18:00.010-04:00

A few post back I said that I would document my experience with the whole graduate school application process. Well now that I have a little free time (only have 1 final to study for this semester) now is as good a time as any to write it.

Before starting I guess I should mention where I did and did not get into. Then I'll talk about the whole process, and a short part on what are some things to consider when you finally make your choice on which school to attend.

Rejected:
Carnegie Mellon University
Columbia University

Accepted:
Cornell University
Duke University
New York University (*)
University of Florida
University of Wisconsin-Madison
* accepted but without financial support

SELECTION
The first thing you have to do is select which schools you would like to attend. Talking to professor at your current (or most recent) institution is always helpful. So talk to them about what schools are strong in your area of interest, and which they think you have an reasonable chance of getting into. One way to group your schools is: dream schools, reasonable chance of getting in, and "safety". Now keep in mind these terms are pretty vague, since all programs are competitive when it comes to offering admission to applicants.
Now I am going to assume that you know what area(s) of mathematics you are most interested in, or even which area(s) you don't like. I can't really comment on the process for selecting schools when you are unsure since I did not fall into that category. Anyway, I suggest that you begin your research on potential schools during the spring semester of your junior year. A great place to start is looking at the U.S. News rankings, also here is another useful site, but keep in mind these should not be the end all say all. Also talk to professors and see which schools have papers published in journals you enjoy. Plus, you will be surprised at how many internet forums there are out there that discuss what schools are good in what areas.
At this point you should try to get a list as big as possible, put a school on the list if there is the slightest bit of interest in their program. For instance I had Washington University at St.Louis, and University of Michigan on my original list, even though in the end I didn't apply to either school. Another thing to keep in mind is that while you are in graduate school your interest might change, so you should also take into consideration the schools activity in other areas. More on this in the portion about making a final selection.

Then when you have some more "free time" in the summer you take more in depth looks at each of the schools on this large list. You can even send out emails to faulty and current graduate students expressing your interest in their program and if they could provide you with any information that isn't available on the website. That being said, you should throughly look through each website before asking questions about the program. Otherwise you might ask a question who's answer is easy to find if you had put in any effort, and thus come off as appearing to be lazy, and who wants that for a first impression?
Now either in the summer or the beginning of senior year you will shorten this list to contain only those schools to which you plan to apply. The size of this new list will vary from person to person so not much can really be said. Though I would suggest it contain more than one school.

With your list in hand you are now ready to move onto part 2.

Flash Mobs

2010-04-11T12:47:00.002-04:00

Hey here is a great idea for a flash mod that would actually help this country.
On election day everyone go to their local polling site and actually vote (if you legally able to).

Decision Time

2010-04-10T00:23:00.003-04:00

This should answer all questions.

Violin Tattoo

2010-04-04T17:20:00.002-04:00

Now this could just be my inner violin player talking but this is the most beautiful tattoo I have ever seen.

If I ever found a girl with this I would have to marry her right there and then. Well maybe not, but it would definitely make me want to get to know her.

Duke is Beauty

2010-04-01T08:20:00.001-04:00

Went on another campus visit last weekend. It was Duke University's turn this time around. Unlike Cornell they had a weekend where they brought in all of the prospective graduate students. I thought this was nice since you got a chance to mingle with your potential classmates as well as talk to the professors.

I got into Durham around 2pm on Friday and was picked up at the airport by one of the graduate students. I found it funny that she also said that you could easily find the math department on any campus by looking for the ugliest building. I suppose this is just a well known fact. However, the math building wasn't that "ugly", but that's probably because it is shared with the physics department as well. Unlike the visit to Cornell, this time we were put in an hotel that was relatively close to campus (and the university hospital). After we dropped our stuff off in our rooms there was time for us to sit in on one of the classes. It was a modeling class and they were talking about certain kinds of optimization problems. I was able to follow much of what was being said, though I wish I remembered more multivariable calculus.

After the class it was tea time. Apparently the graduate students and faculty have "tea" (really snacks) at 4pm each day. This was nice since I got to meet some of the other graduate students as well a professor. When tea time was over there was still a little time until dinner so we were taken back to the hotel to relax a little. It was at this time that I discovered that I can't send text messages while I'm in North Carolina (and South Carolina as well) for no apparent reason. I'm able to receive text messages and phone calls which is just weired. So if I do end up choosing to attend Duke I will have to find a new cell provider. Not sure if it's T-mobile or just my phone, everyone else had a different provider so not much help there.

The most exciting part of the visit was meeting my "twin". She was a University of Florida graduate and is currently doing research in probability. Wait, things get even better. So you remember the Denny's commercial about the "nannerpuss". The banana octopus that attacks pancakes, well apparently I was the only person (other than her friends she had told) that had ever seen this ad. It also doesn't hurt that we are almost the same height and both drive Hondas.

There was no shortage of food for the weekend. It almost got to the point that just hearing the phrase "there is food in the [location] for you" made me vomit. On Friday, the graduate students took us to a restaurant called Tyler's. Originally we had planned to eat at the Mellow Mushroom but things didn't quite work out that way. The food was alright, nothing special. However, the atmosphere made the dinner unforgettable. At this dinner I learned that 2 of the other students had received the same offer from NYU as me, admission without financial support. Seeing as how none of us are super wealthy there is no way we can afford to pay for at least a year of a PhD program AND to live in NYC.
After dinner we spent about 10min. outside in the cold deciding what to do next. Some of us ended up going to a local bar to watch the Duke basketball game, while others called it a night and went back to the hotel.

On Saturday some of the professors and graduate students gave talk about their research. The overall set up was pure mathematics talks before lunch and applied after. Naturally, I was more interested in the applied talk, especially the ones concerning probability. However, I found some of the pure talks nice. I even learned a little topology by the end of it all. There were a couple presentations on Mathematical Biology, and I must say that they made me wish that I had given that particular area a little more consideration earlier on in my undergraduate years.

At this point you should be able to conclude that I enjoyed the visit. This isn't going to make my decision any easier. Well I will keep you 'posted' (what a nice pun, even if I do say so myself).

Android

2010-03-21T23:21:00.002-04:00

First things first: Big ups to Cornell's men's basket ball team for making it to the Sweet 16. Hmmm now should I consider the quality of the basketball team in my graduate school decision (Duke or Cornell)? Let us see who goes further in the tournament. (I'm joking by the way)

Just got back from the IEEE Southeast Convention. Overall it was quite the experience. I went as part of the school's Software team. We expected the software competition to be structured more like the ACM ICPC since this is how it has been done the last...well always. However, this year they decided to change the format. This year teams would have to create simple Android applications in Eclipse. Another aspect would be that there would be no time component involved in the scoring.
Now, no one on our team had any experience writing Android applications, much less programs that needed GUI. Also we didn't have much experience developing "actual software". Our plan was to spend all of Friday learning all of this. But as you know, sh*t happens. Turns out the hotel internet was "overloaded" and thus insanely slow. We spent all day downloading about 300MB+ of files at about 15kb/s. Then there were all the installation problems we ran into since we were all using Ubuntu (thanks for the great Linux support Google).
When we did manage to have a working install of everything it was midnight, which meant that we had 7hours until the competition started. Luckily we somehow managed to read somewhere that we would have to deal with XML documents, so we spent a little time learning about those while obtaining everything else. For the 2hours after having a working environment we managed to create 2 simple applications. One just printed "hello android" to the screen while the other simulated a login screen. Nothing too complicated but it gave us a little feel of how things were done.

After we got some sleep (more like a nap to be honest) it was time for the competition. Now, the competition started at 7am...and the hotel's breakfast service didn't start until 7am as well. So you can imagine that none of the coders there were all to happy about that (in addition to them changing the competition set up). We managed to solve 5 of the 12-13 problems, which I don't think was too bad considering how much time we had to learn Android. The worst part of the competition was that we had to work on laptops which were running a virtual machine. This virtual machine was from a central computer (not a very good one since everything was super slow. Like pre 1995 slow).
My main problem with the competition was that they decided to inform us of the change a few days before hand. Now if they had given us a month or so to prepare it would be a whole other story. On the bright side, if I ever have some free time and feel like making an Android application I now have the tools.

NPSC Fellowship

2010-03-13T18:15:00.003-05:00

I meant to write this post earlier, and obviously that didn't happen.

As you should know by now, I spent a good part of my fall semester working on applications for graduate school. Well in addition to these applications I also spent time looking for and applying for external funding (which includes fellowships). Just as there are almost too many graduate schools you can potentially apply to, there are more than enough fellowships out there to consider. My bit of advice would be to become familiar with what is expected from you if you are chosen to be a fellow and end up accepting the offer. Needless to say, but you should also know just what kind of support they will be offering. Why waste your time on an application for an award that you know you would reject?
Anyway, one of the fellowships that I ended up applying for, and ultimately accepted, was one offered by the National Physical Science Consortium (NPSC). For information on the fellowship just follow the previous link. If you are too lazy I'll give you a brief overview; tuition covered, living stipend provided, and obliged to spend two summers with a NPSC Industry/Lab member. This list of might change from year to year so I can't say what your choices are.

I suppose in a future post I will describe my experience with applying to graduate school and for fellowships. I'll be sure to include what I wish I had done differently and what things I believed worked fairly well.

Ithaca is Gorges

2010-03-10T08:20:00.009-05:00

Yes the joke is overused, but very true. As you can guess I got back from visiting Cornell.

My host was a first year student in the OR department. She was really nice as well as knowledgeable. One for the first things I mentioned to her was that I expected Ithaca to be a lot colder. I could have gone the whole visit without my jacket (which was a hassle when dealing with airports/airplanes). She was quick to inform me that I was lucky and had chosen one of the warmer days for my visit. Just two weeks ago they had heavy snow fall, and I'm sure I would have died if I had to go through it. Also I got lucky in the fact that most of the walking areas had the snow and ice cleared at the time. My shoes had no traction what so ever; looking back I wish I had brought my Vans instead of the Adidas. Sure there would have been no extra traction, but they would have gone better with my outfit and I wouldn't be bothered by the tongue (I really should buy a new pair or just cut them off).
On the first night I got to meet some of my host's friends. One was a first year graduate student in CAM (Center for Applied Mathematics), they met each other through one of their classes. A plus in my book since it just shows that there is interaction between the ma

The town itself is pretty small, so that will take some getting used to if I decided to go to Cornell. In terms of size I feel that it is somewhere between Holland and Gainesville. The only thing worse than being a small town is the hills. To all you Floridians out there, you have no idea what a hill is. Compared to the hills in Ithaca, Florida "hills" are just slightly inclined paths. On the bright side though, I will get in shape...or die trying. Needless to say riding a bicycle is totally out of the question.
As I said in the first sentence (well the title really) the town is gorgeous. Just think of all those Christmas cards or postcards of small towns covered in snow with the sun either setting or rising. Ithaca is much better than those. For some reason while I was there I kept making connections to buildings I saw to those in the Harry Potter movies. There was a portion of one building that reminded me of the Quidditch towers for spectators in the movie. I guess this is a 'happier' comparison than my sister and I made between one of the towers at WashU and the one in Mordor.

The OR department was fantastic. The building looked amazing, and you don't get the feeling of being trapped inside a lab. Also it is kind of a big circle so it is pretty hard to get lost and easy to learn you way about (which is always good when you're on your own). The faculty were all nice and easy to talk to, so no problems there. The graduate students were just as easy to talk to and they all seemed to get along with each other. They said that for the most part there isn't much competition (if any) amongst the first year students, because what is there to compete for really? However, this does depend on the class. On Sunday I had dinner with my host at a Korean restaurant, while I had lunch and dinner with the rest of graduate students on Monday. It seemed as if every other restaurant was an Asian restaurant. This actually isn't a problem since I LOVE Asian food, the more authentic the better actually. However, I don't think I saw a Thai place, so I will have to continue my search.

Overall it was a nice trip, and I think I could be happy in Ithaca even though it would take some getting used to. Good news is that there is a bus that goes to NYC so if I ever really need to get out of town (and have the time to do so) I can always go there.
Now I'm just waiting for my Duke visit. I've been told that it is one of the most beautiful campuses I will ever see, but I think it will be pretty hard to beat Cornell.

Duke: Update

2010-02-09T20:43:00.003-05:00

As you should be able to guess from the title of this post it will be about Duke.

I GOT ACCEPTED!!!

Not much of a post but it is news worth sharing.

Update:

I also got into Cornell.

Best of 2009

2009-12-30T16:50:00.009-05:00

Well it is that time once again. Just like last year, I am going to provide you with a overview of what I have been listening to. All of the information will be coming from Last.fm: even though this isn't 100% accurate in the number of plays it does seem to provide the correct ordering in each of the list to follow. Similar to last year I will provide the names and play counts for the top artist, albums, and tracks (songs). However, this year I will provide the top 15 instead of the top 10.

Before I being I would like to say that this year I recently switched over from having Windows as my primary OS and am now using Ubuntu. Thus it was a while (probably a week or two) before I noticed that I could use Amarok to update my Last.fm listening trends. In addition I have used Grooveshark quite a bit and this fact isn't portrayed in the data below.

One last thing, in the traks section, each artist will only appear once. However, if they have multiple songs that are in the top 15 I will let you know. As a result this will cause me to list tracks that are not in the actual top 15. Don't worry, I will indicate their actual position.

Artist:

1: Portugal. The Man [664 plays]
2: Lil' Wayne [540 plays]
3: Nine Black Alps [409 plays]
4: Kanye West [395 plays]
5: The Hush Sound [360 plays]
6: Fabolous [357 plays]
7: Lupe Fiasco [341 plays]
8: T.I. [258 plays]
9: Muse [255 plays]
10: Eminem [251 plays]
11(t): Jay-Z [247 plays]
11(t): Rise Against [247 plays]
13: Ludacris [240 plays]
14: This Providence [232 plays]
15: Nada Surf [229 plays]

Albums:

1: Waiter-"You Vultures!" by Portugal. The Man [398 plays]
2: Everything Is by Nine Black Alps [244 plays]
3(t): Goodbye Blues by The Hush Sound [243 plays]
3(t): The Sufferer and the Witness by Rise Against [243 plays]
5: This Providence by This Providence [232 plays]
6: Loso's Way by Fabolous [230 plays]
7: Swan Songs by Hollywood Undead [208 plays]
8: The Cool by Lupe Fiasco [189 plays]
9: Love/Hate by Nine Black Alps [165 plays]
10: The Satanic Satanist by Portugal. The Man [155 plays]
11: Flying Colours by Bliss N' Eso [146 plays]
12: The Carter III by Lil' Wayne [144 plays]
13: Paper Trail by T.I. [142 plays]
14: Used and Abused by Danger Radio [137 plays]
15: Absolution by Muse [134 plays]

Tracks (songs):

1: Headlights by Nine Black Alps [50 plays] (also in real top 15: Ironside)
2: How the Leopard Got Its Spots by Portugal. The Man [44 plays] (also in real top 15: Gold Fronts, AKA M80 the Wolf, Stables and Chairs, House Warming Party, Kill Me. The King, Waiter, Marching With 6)
3: The Good Left Undone by Rise Against [38 plays] (also in real top 15: Roadside)
4: Always Strapped by Birdman ft. Lil' Wayne [34 plays]
5: A Wolf in Sheep's Clothing by This Providence [31 plays]
6: Plenty Money by Plies [30 plays]
7(t): Imma Do It by Fabolous ft. Kobe [28 plays]
7(t): The Diary by Hollywood Undeaad [28 plays]
9: Uptown by Drake ft. Bun B. & Lil' Wayne [27 plays] (actual position: 18)
10(t): Wasted by Gucci Mane [26 plays] (actual position: 22)
10(t): As You Cry by The Hush Sound [26 plays] (actual position: 22)
10(t): In Our Bedroom After the War by Stars [26 plays] (actual position: 22)
13: All of the Above by Maine ft. T-Pain [24 plays] (actual position: 30)
14: Imma Star (Everywhere we Are) by Jeremih [21 plays] (actual position: 40)
14(t): See These Bones by Nada Surf [21 plays] (actual position: 40)

Needless to say, but Portugal. The Man did this year what Lil' Wayne did in 2008...pwnd.

Another Fall Semester Gone

2009-12-12T22:47:00.005-05:00

So keeping to tradition I'll say a little bit about each of my classes this semester and then at the end mention what I hope from the next one.

Data Structures and Algorithms: (A-)
Quite possibly the worst presentation of the topic I have ever seen. Basically the professor read from PowerPoint slides and had the TAs do all of the work. The TAs; wrote and graded the homework, wrote and graded the test and also had to respond to any questions the students had (even if they were intended for the professor). Luckily I was part of the programming team so I already knew all of the material that would be covered in this class.
The homework assignments weren't difficult at all but rather annoying. Especially when they gave you defective code to use. I would have preferred if we have been told to solve a particular problem, and that a certain data structure/algorithm was necessary. Instead they gave us a template to modify, and you didn't even have to know how to implement a Breath First Search for instance. All you had to know how to do was make a method call to the super class which you were extending. It is quite disappointing.

Topology 1: (A)
Well it doesn't help that about 3 weeks into the course we got a new professor (the original instructor had a stroke). The new professor expected that we knew more than was previously covered and also in much more detail. Needless to say, much of the semester was spent playing catch up. Normally I am a fan of the Moore method (students present all the work/answer questions) but I don't feel that it is appropriate for an introductory course. Especially one quite this abstract. In the end I am ashamed to say that the only thing I took away from this course were the portions that had direct applications to analysis.

Analysis: (A)
Not much to say, we started with a quick (1 day) review of basic things such as the monotone and dominated convergence theorems. After this it was some pretty cool stuff about signed measures. Which lead to the Lebesgue Differentiation Theorem and the Lebesgue-Radon-Nikodym Theorem. At the end of the semester we started with some introductory Functional Analysis (kind of like infinite dimensional Linear Algebra) and talking about Banach spaces.

Set Theory: (A)
The class wasn't that difficult. However, unlike most other easy classes I did like the way this was set up. This is not to say that it didn't have its flaws. This was another class that was taught with the Moore method. The professor would post the problem sets on his websites and then the students chose which problems they wanted to present to the class. The problems, at least the ones that didn't deal with the axiom of choice, weren't that difficult. Mainly it was a class to get students used to providing rigorous proofs to generally accepted facts. I will say however, that some of the results from this class I was able to use right away in some of my other classes, so that was nice. My main problem with the class was the test. All the questions came from the problem sets, so you really only needed to memorize the presented proofs and not actually understand the reasoning behind it. I would much rather have preferred the questions to make us apply something we had seen before, but oh well.

Overall I would say that this was a very successful semester. I managed to get my grades, manage work, do some reading for my honors thesis (which I need to read a lot more for), apply to graduate schools, and see friends every now and then. I'm actually looking forward to next semester, even though it will be my last.
At the moment I am currently signed up for 6 classes. However, I will only be taking 4 (2 will be dropped during drop add), the only problem is that there are 5 that I would like to take and am not sure which to drop. The choices are Theory of Measure and Integration 2, Operating Systems, Theory of Probability and Stochastic Processes 2, Partial Differential Equations, and Moder C++. The problem is that I can't decide between PDE and C++, which I would rather take. I can see both being useful, but one is going to be more work (C++) but it will be more enjoyable.

My Final Putnam Exam...2009 Edition

2009-12-11T04:32:00.003-05:00

Well a few weeks ago I took my last Putnam exam. And I can say with a smile on my face that not only did I perform just as well as last year, but I have even exceeded the expectations I held when first entering UF. Initially I expected that I would only be able to answer two questions on the whole exam by the time I graduated. However, this year I answered (though probably not in enough detail for full credit) 4 question. The amazing thing is that even of the questions that I didn't answer I was headed in the right direction for most of them. For instance, one question asked you to find all possible values for some variable given some conditions. Finding the upper bound was rather trivial, but the lower bound wasn't quite as obvious. During the contest I found the correct lower bound, but didn't realize that I had arrived at it by evaluating a Riemann sum. Oh well you win some you lose some.

I'll post the problems and as much of a solution for each problem (if possible) on my other blog. I would have done it here but sadly I don't have LaTex enabled, so it would not only look ugly but also be a pain for me to write (as well as you to read).

One last thing, on the off chance that I haven't mentioned it earlier, I am applying to graduate schools. At the moment the list consist of Columbia, Carnegie Mellon, Cornell, Duke, NYU, and Wisconsin-Madison. All would be great places to attend, so fingers crossed.

Code Reuse

2009-11-12T00:58:00.003-05:00

So here is a pretty useful trick/hack.
Say you need to create a max-heap. However, the code that you are forced to use will only create a min-heap. What do you do?
Well one solution is to just negate all the input entries, and then create a min-heap. Then the most negative (or most positive depending on how you view things) will be at the top.

I used this trick on my last Data Structures homework assignment. The code that we were allowed to use would create a tree with the smallest element as the root. But we needed to find the largest element. Now I could have easily written my own code, but why should I when code has already been provided? So all I had to do was negate the input and then copy the given code (though I did have to change a few inequalities around). Overall it was a great feeling, like I was "beating the system".
I prefer to look at this as being creative and not as being lazy.

Sadly, I can't take all the credit for this method. I had seen it before while reading a TopCoder tutorial on the C++ STL. They were talking about how to implement Dijkstra's algorithm with a priority queue. In C++ the priority queue container will always put the largest element at the top by default (though you can easily change this).

Being In Control

2009-08-15T01:25:00.003-04:00

So whenever I ask someone why they chose to drive a manual transmission instead of an automatic, the response usually sounds something like this. "Because I like the feel of being in control. It's like you, and not the car, are doing the actual driving." Now the funny thing is that this is also the reply I get from some people when asked why they prefer Windows over Linux. Well, they don't say driving, but rather talk about being in control of the computer. Guess that being in control means accepting that there are things you can't control.

Super Freak

2009-08-10T22:25:00.002-04:00

I was talking to Ashley yesterday. The conversation was going pretty well. She was talking about how she is enjoying her time in Chicago before going back to MIT. Then somehow we got to talking about programming languages and physics. Personally, I'm pretty surprised that she didn't complain about having to learn to program. Back in high school she would avoid anything that involved using a computer, that wasn't looking stuff up on Google or Wikipedia. But I suppose you can only avoid it for so long while being at MIT.

Well after talking to her, for some reason I started to really freak out about the whole graduate school application process. I still have to write a draft of my personal statement, and take the Math GRE subject test. I have gotten all As in my major classes, participated in a summer research program (paper under consideration for publication), and also plan to do a senior thesis. All this on top of what I am sure will be strong recommendations. Yet for some reason I am still worried. I suppose that I am worried that this won't be good enough to get into the school(s) that I really want to attend.

Correction

2009-08-07T21:57:00.003-04:00

Well I fixed my algorithm and managed to solve the problem (see previous post). Here is a general overview.

Create array of cumulative sums
Create Segment tree
Answer queries using segment tree

Each node of the segment tree contained about the location of the max and min elements of the cumulative sum array, that was spanned by the interval. For instance, the node that pertained to the interval [2,4] would contain information about the max and min elements of Sum[2...4], where Sum[] is the cumulative sum array. Also other information might need to be stored in each node, but I'll leave that up to you to discover. Don't want to spoil all the fun now do I?

Now I'm moving onto GSS3, which is more or less the same problem but with the ability to update sequence elements in addition to making queries. At the moment I plan to use the same code but modify certain parts so they they use binary indexed trees.

Found this to be a pretty interesting problem. Think I might try to implement a version for working with 2D arrays. Really it's not too hard to extend to more dimensions but the code just gets longer though the thought process stays the same. To me this is probably the major advantage of using segment trees over sparse arrays. But I must admit that I am not all that comfortable with the sparse array method, so it might extend just as easily (though I don't see it).

Range Minimums and Maximums

2009-07-29T19:27:00.009-04:00

WARNING!!! The following algorithm is incorrect! For a counter example consider the set { 9 , -10 , -10 , 5 , 5 }. It will say that the answer to Q(1 , 5) is 9, but it is fact 10. However, though it is incorrect it does provide you with a good place to start.

At first I was going to talk about the SPOJ problem ORDERS in this post, but decided to put that off. Mainly because I found something else more interesting in addition to the fact that I still haven't completely finished ORDERS.

First off, here is a link to a TopCoder tutorial on RMQ (range minimum query). This post is by no meant a substitute for the tutorial. I would recommend reading the tutorial after this post (only because you are already here) to see more on the topic. Now the problem I will be discussing is GSS1. I would like to point out at this time that the solution I am going to give WILL NOT GET ACCEPTED!! It is far too slow, but should give you a good idea on where to start or proceed.

So suppose we were naieve and decided to do all our preprocessing at the beginning and then ansewr each query in O(1). Obvioulsy the first data structe we think of is an array. So we will let Ans[i][j] be the answer to the query Q(i,j).
Now how does one go about creating this array? Well obviouly the answer to Q(i,i) is the input[i], where input[] is the given array, so

Ans[i][i] = input[i].

Now suppose that we know the value of A[i][j] how would we find Ans[i][j+1]? Well, there are three possibilities.

Ans[i][j+1] = Ans[i][j]
Ans[i][j+1] = input[j+1]
Ans[i][j+1] = Ans[i][j] + Sum(input, k+1, j+1)

In the above k is the index of the last element that is used to make A[i][j] (more on this in the example later on). So using this we can build our array Ans[][] in O(n^2), which actually isn't that bad for small cases.

EXAMPLE:
input = { 1 , 2 , -2 , 4 , -1 , 1 }

So Ans[][] will be a 6x6 array.

Ans[1][1] = 1 clearly. Now for Ans[1][2], we can either use Ans[1][1], only use input[2] or add to Ans[1][1]. So in this case we will want to add to Ans[1][1], thus giving Ans[1][2] = 3. Note that k was 1 so Sum(input, k+1, j+1) = 2

Now for Ans[1][3] we have the following cases;

Ans[1][3] = Ans[1][2] = 3
Ans[1][3] = input[3] = -2
Ans[1][3] = Ans[1][2] + Sum(input, 3, 3) = 3 - 2 = 1

So trivially we want Ans[1][3] = Ans[1][2] = 3.

Just for good measure consider Ans[1][4];

Ans[1][4] = Ans[1][3] = 3
Ans[1][4] = input[4] = 4
Ans[1][4] = Ans[1][3] + Sum(input, 3, 4) = 3 -2 + 4 = 5

Thus it is best to take all the elements in this case giving Ans[1][4] = 5. And you continue this process.

Well here is the C++ code that you have been waiting for (unless you like some other language). Once again I would like to say that this method WILL NOT WORK!! for the case on SPOJ. (note I assume that the first element of the array input[] is 0, just to make things easier to code)


Ans[n+1][n+1];
memset(Ans,0,sizeof(Ans));//not needed but I just like to know what's in my arrays

for( int i = 1; i!=(n+1); ++i)
Ans[i][i]=input[i];

for( int i = 1; i!=(n+1); ++i)
for( int j = i+1; j!=(n+1); ++j)
   Ans[i][j]=my_max(Ans[i][j-1],input[j],Ans[i][j]+Sum(input,k+1,j));

I'll leave the implementation of my_max( ) and Sum( ) up to you, along with a way to keep track of k. Note that you will need to be "creative" when making Sum( ) so that the above stays O( n^2) and doesn't become O( n^3).

In the link to the tutorial at the beginning of this post he describes other methods to solve this problem. Some have much better performance. The one I plan on using has preprocessing time O( n) and answers queries in O( log n). Some of the other methods that he claims are easy to code (though I would disagree) have preprocessing time O( n) and answers queries in O( sqrt(n)) and preprocessing time O( n log n) and answers queries in O(1).

DAGs and DP: aka one thing I'm good at and another that I'm not

2009-07-21T21:06:00.004-04:00

So I haven't solved an SPOJ problem in a while. Mainly because I've been doing other things. Well today the drought is over. I managed to solve RENT.

I'll just describe how I went about solving this one. I should mention that the idea was not totally mine. Anyway, I will assume that you have either read the problem or are familiar with it's statement.

Well first off there is the obvious O(2^n) algorithm but obviously this is out of the question considering that the program has 3s to run and n can be as large as 10000. So the next thing to try is looking for a DP solution. This is where DAGs (Directed Acyclic Graphs) come into play, though it might not be obvious.

You construct the graph in the following way. There is an edge between vertex U and vertex V if there is an even starting at time U and ending at time V. Also the weight of the edge is equal to the amount of money you will get for selecting that activity. At this point you execute the DP portion by using a variation of a DFS (So as to not spoil the problem completely I'll let you figure that part out yourself). Just remember that you are looking to make the MOST money in the alloted time.

This method is O(E+V) once you have created your graph. I think the way I created my graph is close to O(E). With a few optimizations the above will work (at least in C++), my solution finished in 1.71s so if you are using Java or another language that isn't particularly "fast" some additional tweaks (or a completely different algorithm) might be necessary. I would like to mention that there are other methods to solve this problem but I didn't find them to be quite is intuitive or obvious. Plus I like working with graphs, and thought that transforming this into a graph problem was rather interesting.

EDIT: Now I also want to edit my algorithm so that it will also tell you which events to select. I don't see this being all that difficult, so I'll probably think about it later this week, and hopefully have an solution (an efficient one that is) by Sunday.

New News

2009-07-15T22:02:00.003-04:00

Not sure if I mentioned on here before, but I have a job for the summer. Sure I'm glad to have a job but I really would rather be doing something that is more math or computer related. And more computer related than using MSOffice. This has further motivated me to become quant. Also I'm preparing for the GRE, ideally I would like to take it before I start school again. However, I am not sure I'll be able to learn all the vocab (random words and roots) by that time; as well as do lots of practice problems and test. Then I get to take the math subject test in October, and again in November if needed.

In some of the free time I have I've managed to start another blog, start leaning regular expressions, learn Bash programming, read a few chapters from an algorithms book, and learn a little more about C++. So not too bad if I don't say so myself, however none of these topics has really been explored to much depth. Notice the lack of math on that list, it's pretty depressing. I'm considering buying a book on Measure Theory (either with relation to probability or integration) and another on Stochastic Processes.

Well that's all for now. Just though I'd drop by and give a brief update since I've been somewhat busy recently.

Facebook Quizzes

2009-06-29T22:57:00.002-04:00

For some reason these things are just so addicting, even though the results can be total BS at times.

Quiz : What is Your Secret Innermost Desire for Your Life...?
Result: Sexual Stimulation
Your subconscious mind is driven most by sexuality. What this means is that when your unconscious mind sees an opportunity to remind you of your sexual desires, it takes full advantage of it. Because of this, things that have very little sexual content or that seem sexually neutral to others, may register as sexually charged to you, at least on an unconscious level. Your unconscious mind recognizes the value of sexuality. The reason it may do so, is because of a deep-rooted fear of the opposite living a life that is numb to sexual desire or is turned cold by it. You unconscious mind may be trying to avoid this sexual dullness, and so it reacts by swinging to the opposite extreme, strong sexual desire. By sending you these sexual messages on a regular basis, your unconscious makes sure you don't forget about sex. Demure who can resist your seductive charm? You have mastered the art of flirting so well that all you have to do is sit there and look pretty and they come to you.

Quiz: How Dateable are You?
Result: Completely Dateable
You are the perfect gentleman/lady and you know everything anybody needs to know about dating and flirting

Quiz: What are you Born to Do?
Result: Best at Everything
you are the social person who make usefull contacts. you introduce important people to influencial people and always reap some sort of reward as a result...but you dont enjoy the spotlight as much. you prefer to stay in the back as there is more room to strech and you like the feeling that you are the one with the power and most of the time that is true... you will do well in almost anyfield you know how to flater without being to obivous and you can make just about anyone like you

Quiz: Which Transformer are You?
Result: Bumblebee
Bumblebee is a cautious, yet brave warrior of the Autobots. He is the symbol of friendship with mankind because of his bond with his human; Sam Witwicky. His feelings are sometimes hurt very quickly if put down or harassed. He is loyal to Optimus Prime and Sam. His original vehicle form was a 1976 Chevy Camero, but upgrades it to a 2009 version. Motto: "The least likely can be the most dangerous."

I'm Not Into Dating

2009-06-28T17:59:00.002-04:00

Below is and edited version of a conversation I found.

(05:48:36 PM) Person1: wow. yeah, I've been there. I dated a guy last year who wasn't "big on relationships"....which I discovered was code which really meant "you're not worth me making a big deal out of what we have". Once I realized that, I wasn't sad to see him go
(05:49:11 PM) Person2: oh wow never though of it that way
(05:49:16 PM) Person1: if someone doesn't think you're worth dating officially, then they're not worth you wasting your time over them.
(05:50:38 PM) Person1: yeah. Even farther back in time, a few years ago, I was one of those people. It wasn't that I didn't want a relationship, because nobody is going to turn down a relationship with the person that they think is right for them. The fact is that I didn't like the guy enough to commit to him.
(05:51:52 PM) Person1: [EDITED], but learn from my mistakes: get rid of this girl and don't waste more time on her, time that you could spend finding a girl who treats you well
(05:52:54 PM) Person2: wow that was really helpful. more so than the usual "move on/get over it" from others. thanks
(05:53:10 PM) Person1: you're welcome, I'm glad I could help.

Just Friends...Forever

2009-06-10T23:17:00.002-04:00

This was good for a small laugh. Not sure where it came from since a friend sent me the article and not a link. Anyway enjoy, oh and I don't feel this way about anyone so don't think that it's personal in anyway. Though my past would beg to differ.

"I really like you. I do. You're so nice, and sweet, and you listen to all my problems and respond with the appropriate compliments. But, well, I don't really see a relationship in our future. It would be terrible if we let sex destroy this great friendship we have where I get everything I want and you get nothing you want. Don't you think?

I knew you would understand. You always do.

We're so perfect as friends, you know? I can tell you anything, and you know you can always come to me anytime you need to hear me bitch about work or how ugly I feel. You wouldn't want to ruin a friendship like that just so you could be my boyfriend, and have me look at you with desire and longing in my eyes, if only once—would you? Of course not. Well, if we started dating, it would only complicate this wonderful setup I've got going here.

It's just…you're like my best friend, and I would hate for something you desperately want to change that. I mean, sure, we could go on some dates, maybe mess around a little and finally validate the six years you've spent languishing in this platonic nightmare, but then what? How could we ever go back to the way we were, where I take advantage of your clear attraction to me so I can have someone at my beck and call? That part of our friendship means so much to me.

No. We are just destined to be really, really good friends who only hang out when I don't have a boyfriend, but still need male attention to boost my fragile and all-consuming ego.

Anything can happen once you bring romance in. Think about how awful my last relationship was at the end, remember? The guy I'd call you crying about at 3 a.m. because he wouldn't answer my texts? The guy I met at the birthday party you threw me? I had insanely passionate sex with him for four months and now we don't even talk anymore. God, I would die if something like that happened to us.

Plus, ick, can you even imagine getting naked in front of each other? I've known you so long, you're more like a brother that I've drunkenly made out with twice and never mentioned again. It'd be way too weird. And if we did, then whenever you'd come shopping with me, or go to one of my performances or charity events, or take me for ice cream when I've had a bad day at work, you'd be looking at me like, "I've seen her breasts." God, I can't think of anything more awkward that that.

Oh, before I forget, my mom says hi.

Anyway, you would totally hate me as your girlfriend. I'd be all needy and dramatic and slowly growing to love you. If I was your girlfriend, I would never be able to tell you all about the other asshole guys I date and pretend I don't see how much it crushes you. Let's never lose that. That's what makes us us.

Don't worry. You're so funny and smart and amazing, any girl but me would be lucky to date you. You'll find someone, I know it. And when you do, I'll be right by your side to suddenly become all flirty and affectionate with you in front of her, until she grows jealous and won't believe it when you say we're just friends. But when she dumps you, that's just what we'll be.

Best friends. Friends forever."

1984

2009-06-09T19:44:00.003-04:00

Currently reading 1984 and am about half way through so far. Can't say that it has lived up to the hype as of yet but who knows. Well I think I have found the best line in the whole book, yes I am willing to bet that it is better than anything I will read in the second half.

"If you loved someone, you loved him, and when you had nothing else to give, you still gave him love."

Personally I feel that it would be better if 'him' were changed to 'them' but that's just a minor detail.

How to Separate Interface From Implementation

2009-06-07T13:43:00.004-04:00

Well I've finally managed to see how to separate implementation from interface. The basic idea is pretty simple and that only took about a minuet to understand. This was mainly due the fact that it was easy to find lots of examples online. Really the only problem was that they didn't tell you HOW to use this to make a functional program.

So I'll just put together a quick "how-to", where I'll walk through a simple example.

We will create a class called Base, below is the base.h file.


#ifndef BASE_H
#define BASE_H
class Base
{
   int value;
   public:
      void set_value(int);
      int get_value();
};
#endif

So that's the interface for our class, not to create the implementation. This will be in a file called base.cpp


#include "base.h"
void Base::set_value(int x)
{
   this->value=x;
}
int Base::get_value()
{
   return this->value;
}

Finally here is the main program. Since we don't want to be original we shall just call it main.cpp and it looks something like this.


#include< iostream >
#include "base.h"
using namespace std;
int main()
{
   Base X;
   X.set_value(120);
   cout<< X.get_value()<< endl;
}

Now to we create an object file from base.cpp by entering g++ -c base.cpp into the terminal. Then to link this with main.cpp we type g++ main.cpp base.o into the terminal. If all has worked you should see the number 120 printed to the screen when you run your program. (with ./a.out in cause you were wondering)

Progress Update II

2009-06-03T17:40:00.004-04:00

Well I ended up starting over. My original plans were a little too complicated for a first attempt at a game. However, the way things are set up it is moderately easy to make any desired updates. One "mistake", well more of a not sticking to convention, is that I did not separate the interface and implementation of things in my header files. Right now I'm reading more on why this should be done, but haven't gotten far enough to be able to see much real benefit.

Here are all the header files I use as well as a brief description of what they do.

Hero.h
Used to make the hero class, also known as the character you control.

Enemy.h
Basic information that all enemies in the game share; such as health, a name, and strength.

Save.h and Load.h
Used to save and load game data.

Fight.h
Control all the aspects of combat. This would include things like if an attack hits, how much damage attacks do, and knowing when a fight is over.

Menu.h
All the menus that appear in the game are in this file. It contains a number of functions that return characters or strings, to let the game know what the user has decided to do.

Engine.h
Contains the Play_game( ) function that more or less controls the flow of the game.

Derrick Rose

2009-06-02T13:09:00.002-04:00

Found this article to be quite though provoking. Don't think I'll say where I stand on the issue but he does raise a few good question.

My two favorite excerpts are below.

This isn’t to absolve the people involved, but the question shouldn’t just be did Derrick Rose cheat on his SAT?

It should be why the heck did he have to take it in the first place?

No one cared when Danica Patrick went pro as a race car driver at 16. No one tried to prevent Shawn Johnson from winning an Olympic gold at the same age or Miley Cyrus from making millions singing and acting with her dad even younger than that.

And no one ever required them to recognize analogies before doing so.

So why do we make Derrick Rose?

Progress Update I

2009-05-27T12:17:00.007-04:00

So far everything is going pretty smoothly. This is due largely in part to having created a UML, and doing some documentation before I started coding. However, I feel that I will have to go back and change and/or add somethings. The biggest problem right now is memory management. I don't yet fully understand how the delete keyword works, so my classes at this point don't have deconstructors (yes I know wasted memory, but the game shouldn't be that big so I will worry about it later). This is the main reason that I considered writing the game in Java and not C++.

Creating and using my own header files is actually easier that I had first assumed. Every now and then I will make sure that they work by trying to use them in a small test program that I wrote. Most of the time if there is a problem with a file it is because of a stupid typo or forgetting to include another needed header file, so nothing too detrimental.

Even though everything works so far, and by that I mean compiles with no errors or warning, I still have no idea if they work as intended.

I'll post a quick overview of all the current and planned header files in the next update.

Y-Game

2009-05-25T16:35:00.002-04:00

So I have come up with a personal summer project. I am going to recreate "Y-Game". Basically this was a text bases RPG that my friend created back in high school for the TI-83/84.
Right now it will still be text based, but that might change depending on how much time I end up having. Also it will be more elaborate since I will be writing the game in C++ (or Java, but not likely).
From this I am basically hoping to become more familiar with header files, linking files, and most of all writing and reading data from a file. I already know how to read and write to a file, I would like to do that so that it is possible to save your progress in the game and then come back at a later time and continue.
More than likely the next few post will be updates on how things are coming along.

Moving Through Trees

2009-05-12T21:15:00.005-04:00

Well this week has been pretty successful so far. I've managed to solve 4 SPOJ problems I think, though one was just applying a "basic" geometry formula.

Of the remaining problems the first was about playing a game optimally. Usually I detest doing these kinds of problems, but once I noticed that there were solutions in Brainf**k I knew that there was something I was missing. Here is the link to the problem, as far as hints go all I will say is play the game by hand for the first few (under 30) numbers and you should notice a pattern.

The next two problems are pretty similar. Since I am going be describing how I actually solved them I will not be providing a link. They were both asking you to find the longest path within a given tree. The naive approach (and probably more difficult to program) approach would be to find the distance between very possible pair of vertices. This is going to result in an O(n^2) algorithm, and not to mention that it isn't immediately obvious how to find the distance between two given vertices. Naturally the next I idea was to use a depth first or breath first search, the issue now becomes knowing if you have found the longest path. Well here is the approach that I used; start with any vertex of the tree and then use DFS (depth first search) to find the vertex that is farthest from it, call this vertex X1. Now do another DFS starting with X1 and find the vertex X2 that it is furthers from. The distance between X1 and X2 will be the longest path in the tree (though I don't feel like proving rigerously or even using hand waving to explain why).

Here is a sample of the code I used to solve the case where all the paths had the same length. It isn't too difficult to modify for weighted trees.


pair< int,int > dfs(vector< int > >&G,int v)
{
   stack< int > S;
   S.push(v);
   vector< int > visit(G.size(),0);
   while(!S.empty())
   {
      int parent=S.top();
      S.pop();
      tr(G[parent],i)
      {
         if(visit[*i]==0)
         {
            S.push(*i);
            visit[*i]=visit[parent]+1;
         }
      }
    }
    vector< int >::iterator    i=max_element(visit.begin(),visit.end());
   return make_pair(i-visit.begin(),*i);
}

The first entry of the returned pair is the vertex farthest from the starting point, while the second entry is the distance. Thus you will run the DFS two times as previously mentioned. So the complexity of this method is O(n) which is much better than the other approach.
It should be noted that the following is at the beginning of the code


#define tr(a,i) for(typeof(a.begin()) i=a.begin();i!=a.end();++i)

Summer Job

2009-05-09T01:27:00.003-04:00

So I most likely will have to find a job this summer. I am pretty set on avoiding fast food and being a waiter. As of now the list of potential places of employment are as follows:

Kohl's
ACM
Boston Market
Jo-Ann's
Sears

I don't really consider Boston Market to be quite as bad as normal fast food restaurants so that is why it is included on the list.

In addition to possibly working I will also be preparing for the GRE and hopefully start studying for the FM actuarial exam. Oh and I should also email my thesis advisor asking him if there are any papers he would like me to read over the summer.

Terminal

2009-04-28T13:12:00.004-04:00

A little while ago I installed Ubuntu 8.10 onto my desktop, along with Windows XP. Truthfully speaking, the only reason I boot into Windows more often is because I have a program that lets me watch tv on my computer (which is nice seeing as how I don't currently have a real tv).

Anyway, after changing most of the Ubuntu settings so that things are the way I like them; I realized that I still hadn't "fixed" the terminal size. Well at first I did a little Google search to see what the necessary command(s) I would have to run were. However, most of what I found required me to make a launcher, which I didn't want to do. Though I have a feeling that this is the way I solved this issue when I installed Ubuntu onto a portable HD for my laptop.

Finally I found a much nicer way to change the default terminal size. Here it is;

1) Open up a terminal

2) Tyep the following:

sudo gedit /usr/share/vte/termcap/xterm

*in the above you could replace gedit with vim if you wanted, but I just like using gedit personally.

3) Find the following line:

:co#80:it#8:li#24

4) Change it to the following:

:co#A:it#8:li#B

Where A and B are the dimensions you desire. (Your teminal will have dimensions A x B)

Daydreamin

2009-04-23T15:17:00.002-04:00

Yesterday I went to a Lupe Fiasco concert. Definitely not an experience that will be forgotten any time soon. My only complaint would have to be the excessive use of strobe lights, though after a while I did manage to get used to them.

There was one song in particular that he performed that stood out more than the others. Not because of the lyrics or the beat, but rather because of a past experience that involved the song. I won't go into what the experience was on this blog, but you will get a video of the song, along with the lyrics.

Lyrics:

Daydream
I fell asleep beneath the flowers
For a couple of hours
On a beautiful day
Daydream
I dream of you amid the flowers
For a couple of hours
Such a beautiful day

[Lupe Fiasco]
As I spy from behind my giant robot's eyes
I keep him happy 'cause I might fall out if he cries
Scared of heights so I might pass out if he flies
Keep him on autopilot 'cause I can't drive
Room enough for one I tell my homies they can't ride
Unless they sittin on the shoulders but that's way too high
Let's try not to step on the children
The news cameras filmin
This walkin project buildin
Now there's hoes sellin hoes like right around the toes
And the crackheads beg at about the lower leg
There's crooked police that's stationed at the knees
And they do drive-bys like up and down the thighs
And there's a car chase goin on at the waist
Keep a vest on my chest
I'm sittin in my room as I'm lookin out the face
Somethin to write about
I still got some damage from fightin the whitehouse, just a

Daydream
I fell asleep beneath the flowers
For a couple of hours
On a beautiful day
Daydream
I dream of you amid the flowers
For a couple of hours
Such a beautiful day

[Lupe Fiasco]
Now come on everybody, let's make cocaine cool
We need a few more half naked women up in the pool
And hold this MAC-10 that's all covered in jewels
And can you please put your titties closer to the 22s?
And where's the champagne? We need champagne
Now look as hard as you can with this blunt in your hand
And now hold up your chain slow motion through the flames
Now cue the smoke machines and the simulated rain
But not too loud 'cause the baby's sleepin
I wonder if it knows what the world is keepin
Up both sleeves while he lay there dreamin
Me and my robot tip-toe 'round creepin
I had to turn my back on what got you paid
I couldn't see half the hood on me like Abu Ghraib
But I'd like to thank the streets that drove me crazy
And all the televisions out there that raised me, I was

Daydream
I fell asleep beneath the flowers
For a couple of hours
On a beautiful day
Daydream
I dream of you amid the flowers
For a couple of hours
Such a beautiful day

Daydream
I fell asleep beneath the flowers
For a couple of hours
On a beautiful day
Daydream
I dream of you amid the flowers
For a couple of hours
Such a beautiful day

Drains

2009-04-21T00:24:00.001-04:00

This post just made my day. The next time I have a blocked drain I am totally going to try this.

http://hpuew.blogspot.com/2009/04/bi-carb-soda.html

Christina Aguilera

2009-04-13T09:32:00.004-04:00

I was on Yahoo reading an article about someone's 10 Finest DIVAS. Here is what they had to say about Christina Aguilera.

She almost made my pop list, since I enjoy her as a radio pop star, but you know the inside line on Ms. Aguilera is how unlike so many of her contemporaries, she can actually sing! Imagine how exciting that must be for the studio engineers and record producers who work with her. It's like hiring an electrician and discovering after he leaves that your house now has actual electricity and the light switches all work! Such competence in this day and age? What next? A CD player that doesn't break after only four years? Crazy!

And I'm not afraid to admit that I am a fan. Honestly talent is sexy and you and I both know that she is a damn good singer.

BigInteger

2009-04-07T00:24:00.002-04:00

Well I now have a working C++ BigInteger class. The only problem is that so far it is only able to do addition and multiplication. I am fine with the speed of the additions since you can't do any better. The multiplication is where the main problems are located. Sure the method works but it is way too slow. I just need to figure out how to convert a string that represents a number in base 10 into a string that represents the same number in binary. Once I am able to do this I know how to perform faster multiplication algorithms. A similar problem will be converting the answer (which will be in binary) back to decimal.

Regardless I would still like to add a method for modular arithmetic and possibly division, these would just be nice to have but not necessary. Also I should probably work on getting it to handle negative numbers as well.

Printer Simulation

2009-03-31T17:44:00.002-04:00

PQUEUE

The question above was my "SPOJ victory of the day." On my first attempt at the problem I was thinking too hard about all possible cases. Needless to say this resulted in WA. However, today I looked at the problem and noticed that the bounds were extremely low. So I thought about just simulating the process, and realized after a little thinking that this would be O(n^2) in the worst case, which was not a problem considering the fact that the upper bound on n was about 100. After getting my solution accepted I noticed that there were relatively few TLEs, this should have alerted me sooner that a "trivial solution" was possible

I think the problem would be more interesting if they gave you the times that each job was added to the printer queue. The problem would still be solvable by simulation but it would require a little more "creativity" in doing so. However, the way I coded my solution, it wouldn't be too hard to adapt it for this variation. Basically I used a double-ended queue to keep track of the order of each job request. The reason for using this structure is that it has the ability to quickly add and element to the back and delete and element from the front. In addition I used a heap to keep track of which job currently had the highest priority.

Nice Quote

2009-03-27T14:45:00.003-04:00

I was talking to my analysis professor about which classes I should take next semester. We were both clear that I was taking the 6000 level analysis, but then for my other class there was a choice between Functions of Complex Variables and Elements of Topology. His opinion on the subject can be summed up in the following quote,

"If we (the math department) were to only offer one course this (complex analysis) should be it."

Hashtables

2009-03-27T00:12:00.005-04:00

Well I was looking for a hash-map in C++ since doing something like

myMap[i];

Where myMap is an std::map<> takes logarithmic look up.

So after some looking around I did manage to find that there were hash-maps for C++, but after that I had to do some more searching to see what libraries I needed to include in order to use them.

Below is a little program that just prints the integers 1 to 10 followed by hello world, that makes use of a hash-map.


#include<iostream>
#include<ext/hash_map>
#include<string>
using namespace std;
using namespace __gnu_cxx;

int main()
{
 hash_map<int,int> myhash;
 for(int i=0;i<10;i++)
     myhash[i]=i+1;
 for(typeof(myhash.begin()) i=myhash.begin();i!=myhash.end();i++)
     cout<<i->second<<' ';
 cout<<"hello world\n";
 return 0;
}

Certainly not the most user friendly stuff to type at the beginning but I suppose it is worth it. I should mention that when I wrote the second for loop I had no idea if it would compile or not since I didn't know that you could use iterators on hash_maps. Also unlike std::map, __gnu_cxx::hash_map does not store the keys in an ordered fashion, just something to be aware of.

As a side note, if you didn't add the line


using namespace __gnu_cxx;

you would have to type


__gnu_cxx::hash_map<Tyep&key,Type&value>;

This should be obvious but you never know when/if you'll one day forget.

My 2008 Putnam Results

2009-03-24T16:43:00.002-04:00

As expected I managed to score a 20/120, in addition to this I finished 616/3627, so top 17%. To be honest I was hoping that I would have been in the top 15% but I'm not going to complain.

Oh in addition to this our school finished 12th, which is our best finish ever from what I've been told. Sadly I wasn't on the team (I had class at the time of the T.S.T), but hopefully I will be next year and we will finish just as high if not better.

Hello World

2009-03-21T13:15:00.007-04:00


#include <iostream>
int main()
{
   cout<<"Hello world.\n";
   return 0;
}

You have no idea how long it took to get that to look nice. The part that caused the most problems was getting the '<' and '>'signs to display properly, thanks HTML. After that it was pretty straight forward, you just put the code in between either

<blockquote> ... </blockquote>
or
<code><pre> ... </pre></code>.

In case you were wondering, in order to display '<' you typed &_l_t_; (without the underscores). For some reason you can make '>' with the one on the keyboard, but you can also do &_g_t_; (once again without the underscores).

Units Actually do Matter

2009-03-20T00:19:00.004-04:00

Just another reason no one likes biased news; be it liberal, conservative, 'Apple', or whatever.

You might remember this from a while back, if not then enjoy it now.

[Inert Your Title Here]

2009-03-14T00:50:00.002-04:00

Well it is almost the end of another Spring Break. I had originally planned to copy the Measure Theory portion of my Analysis notes into my new notebook, study look over some Differential Equations, and get in some SPOJ time. Needless to say things didn't go as planned. Pretty much all my free time was spent working on SPOJ.

Most of the problems were ones that I had previously started but for some reason was unable to generate an acceptable solution. The only totally "new" problems were JAVAC, SUMITR, and TRICENTR. None of these were all that difficult, but the source limit on SUMITR did cause some issues. I ended up writing the solution for that in C rather than C++.

Here are the other solved problems and my remarks.

ADOMINO: Exactly the same as AGGRCOW but there are some cases that AGGRCOW didn't have so some modifications needed to be added in order to work around these. Not sure if this should even count as a "new" problem really, but why not, it did take me more than 1 submission.

SBANK: I just needed to use a faster way to read the input. To think that I had this problem unsolved for about half a year only because of this.

SHPATH: I had to implement Dijkstra's with a priority queue (a heap like data structure) rather than a set. Personally I prefer to use the set solution but I can see why the priority queue method is faster.

STABLEMP: My idea of using a greedy algorithm was correct. The problem was in the way I was storing the necessary information. Just imagine my embarrassment when I discovered this small but important mistake.

Back From a Hectic "Vacation"

2009-02-27T23:33:00.004-05:00

Wow it has been a while since I have updated this blog. Quite a bit has gone on in my life since then, but I won't go into those things on this blog (that's what the other blog is for quite frankly). As far as school goes I am discovering that learning measure theory is almost as confusing as learning basic topology was the first time through. Luckily the professor makes comparisons to continuous functions, and other topological things that we are familiar with. So it could be worse I suppose. I tried reading the chapter in Rudin and needless to say I was left wondering, "what did he just say, and how am I suppose to show that?" Intermediate differential equations is pretty simple, the only bad thing is that some of the problems are quite computationally involved and they bore me to be honest. At times I wish the course was more proof based but I know that in order to do so you would need high level analysis (real or complex I'm not sure) and most of the people in that class (myself included most likely) aren't up to that.

The computer science classes are quite the bore. Though Intro. to computer organization has its interesting moments.

Well that's enough about classes. This Sunday there is going to be a programming contest. Hopefully everything will run smoothly *fingers crossed*.

Also I'm a lot more active on SPOJ now that I was before. I should start looking at more problems that just those I find interesting if I really want to increase my knowledge (or at least that's what I believe). The last problem I solved that required some thinking was a little DP problem. Building the solution wasn't all that bad, what made it a little challenging was making sure you caught all the cases.

Annoyance

2009-01-10T16:07:00.003-05:00

Well I decided that this year I would like to keep better track of what I listen to, so that when I make the "Best of 2009" post the numbers will be more accurate. Only problem is that I can't for the love of me enable the Last.fm scrobbling program while using Ubuntu. Well that's not entirely true. I've gotten it so that it recognizes the song, the only problem is that when I get it to do this I am unable to actually play the song with my media player. I've looked around and have a general idea of what is causing this problem. Only thing is that I haven't been able to find a solution, well I'm sure I could but right now it's not at the top of my priority list. In addition to this I use pandora quite a bit, and I'm not sure if it keeps track of your listening trends the say way Last.fm does. Oh well.

So I'm using my Windows XP computer for the first time in a few months. One thing I will say is that I miss having a gcc compiler. I have Dev-C++ which usually pretty close to being the same but it's just not the same. I looked around and found a way to get the compiler I want for XP but don't really feel like doing all the necessary work right now, I'll probably end up doing it around the time of finals. The only reason this is a bother is because when I submit solutions to SPOJ problems there is a small chance that there might be a compilation error. It would be really cool if there was an online "compiler" so that I could check before submitting (this is when I'm not writing the program under Ubuntu of course).

One last thing, for those of you who continually ask "What are you going to do with a math degree?" or "Why math?" Here is an answer I'm sure you'll like. Notice how the top rated jobs are mostly math/science related.

Best of 2008

2009-01-07T20:15:00.004-05:00

Well yes I know this is a little late but I don't care. I'm going to list the top 10 artist, albums, and songs I listened to in 2008 according to Last.fm Note that when I get to tracks I will only list each artist once. Thus if they actually appear more than once I will only list their top ranking track (just to add some variety) I will however say how many tracks they had in the top 10 and if they actually were in the "official" top 10.

Artist:
1- Lil' Wayne (1444 plays)
2- Linkin Park (902 plays)
3- Yngwie Malmsteen (838 plays)
4- Maroon 5 (817 plays)
5- Alter Bridge (768 plays)
6- AFI (700 plays)
7- Stratovarious (687 plays)
8- Nada Surf (681 plays)
9- Kanye West (680 plays)
10- Muse (471 plays)

Songs:
1- Far Beyond the Sun(95 plays) [Yngwie Malmsteen] (also in real top 10: Black Star)
2- A Milli(91 plays) [Lil' Wayne] (also in real top 10: La La, Got Money, Phone Home, 3Peat, Lollipop, You Ain't Got Nuthin')
3- See These Bones(84 plays) [Nada Surf]
4- Blackbird(73 plays) [Alter Bridge] (actually at position 11)
5- Put On(70 plays) [Young Jezzy]
6- Prayer of the Refugee(62 plays) [Rise Against]
7- Papercut(61 plays) [Linkin Park]
8- Prelude 12/21(60 plays) [AFI]
9- A Beautiful Lie(58 plays) [30 Seconds to Mars]
10- Shiver(55 plays) [Maroon 5]

Albums:
1- The Carter 3 (804 plays) [Lil' Wayne] (was there really any doubt?)
2- Lucky (655 plays) [Nada Surf]
3- Songs About Jane (453 plays) [Maroon 5]
4- Hybrid Theory (401 plays) [Linkin Park]
5(t)- Absolution (364 plays) [Muse]
5(t)- Three Cheers for Sweet Revenge (346 plays) [My Chemical Romance]
7- Late Registration (350) [Kanye West]
8- Concerto Suite for Electric Guitar and Orchestra in E flat (319 plays) [Yngwie Malmsteen]
9- Rising Force (314 plays) [Yngwie Malmsteen]
10- Like Vines (303 plays) [The Hush Sound]

*IMPORTANT: The numbers displayed might not (and most likely are not) be correct. This is due to the fact that I often have music playing and for some reason or another Last.fm is not keeping track of this. This is not Last.fm's fault, but mine since I either choose not to log in or am on a computer that doesn't have (or doesn't support) the software necessary to keep track of played music.

Efficient Finals

2009-01-03T18:10:00.003-05:00

Well I was reading an algorithms book and here is something that was pointed out that I never considered before.

Assigning times for Final Exams is equivalent to coloring a map.

How so? Well assume that we only have the following restriction, two finals can not be at the same time if they share at least one student. Now let the classes be the vertices of the graph, and place an edge between any two vertices if they share a student. So basically you assign colors (or times) in a way such that no edge has vertices of the same color.

Obviously the four color theorem does not apply when coloring this graph. Just consider the case where a student is taking 5 classes. (go and look up to see how this breaks the necessary assumptions for the theorem). None the less it is still an interesting connection, though I am sure Universities do not use this method to schedule their finals (for some obvious reasons).

Greed

2008-12-20T00:22:00.006-05:00

Well I didn't manage to completely solve a SPOJ problem today, what a shame. I managed to think of a method of attack but didn't have the time or motivation to try and code it up or even write pseudo-code. The problem statement can be found here, since I don't want to accidentally leave out any details.

The method I am going to try combines a binary search and greedy algorithm.
First create a sorted array of all the locations of the stalls, then a second array that will keep track of which stalls have cows. Call these arrays A and B respectively. Through out my explanation assume that both arrays are always sorted. Now if you only have 2 cows you place them in the extreme left and right stalls, so add these stalls to B. The general idea is that the best location for cow (N+1) can be built from the best location for cow N. For example, to add the third cow look at the stall that is "half-way " between the 2 stalls with cows. Is the minimum distance at this point less than if you were to move it left or right by one stall? If so add this stall to B. If not do the same thing by looking at the midpoint of the left and right halves (some case work might be able to be applied to minimize this but I haven't thought about it yet). After doing this you can find the best spot for the third cow. To add the 4th cow look at the "interval" between cows 1 and 3, and the interval between cows 3 and 2, and apply the above method.

I haven't really considered the time constraint and input sizes but I might be able to get away with a linear search for the best spot (though I doubt it). I suppose that TopCoder article I read on binary search is coming in handy. Well I probably won't be able to work on this again until Tuesday so hopefully I'll be able to work out any "bugs" before I sit down to code.

*UPDATE: Well I managed to actually write up the code for this earlier than expected. However, there was a change in how I went about doing it. I instead did a binary search on all the possible distances between the stalls, in order to find the largest possible minimum. Basically given a distance and the number of cows I would perform the following operation;

bool(stall, distance, cows) //where they are all the appropriate data type
num=1;
prev=stall[0];
for i from 1 to one less than the number of stalls
. if stall[i]-prev is less than distance do nothing
.else prev=stall[i] and increase num by 1
end for loop
return true if num is at least as big as cows, else return false

This basically tells you the maximum number of cows you can place so that the distance between any 2 is "distance". So if I remember correctly the possible distances between stalls were between 1 and 1 billion. So the above should only needed to be run no more than 30 times.

Making a Fence

2008-12-18T23:06:00.005-05:00

Another day and another SPOJ problem complete ( link to problem). In this one you had to implement a way to find the convex hull of a given set of points. This one wasn't that horrible since I already knew a method to perform the desired task. The only problems I encountered were, 1) what do you do about collinear points and 2) what about one and two point sets? Luckily there were examples that covered both of these issues so I adjusted my code accordingly.

The method I used is known as the Graham Scan. First you find the most lowest point, or furthest left point (I personally like to chose the lowest, but going with the furthest left doesn't really change anything). After this is done you sort the remaining points according to the angle the line connecting them and the lowest point, makes with the x-axis. Then create a stack, and add the first two points (the lowest point and the one with the smallest angel measure). I should clarify that this is not actually a stack since we will need the ability to access both the top and second elements. What you do next is easier to explain with pseudo-code in my opinion at least so here it is:

for i=3 to the size of P //P is the collection of points
. while stack.size>=2 and cross(stack.second, stack.top, P[i])<=0)
.. s.pop //remove the top element
. s.push(P[i])

Basically if a right turn is made (cross product less than 0) or collinear points (cross product equal to 0) the point at the top of the stack is not part of the convex hull. If you don't follow draw some points, if you ever make a "right turn" you are moving "out" and thus it is more efficient to not consider the point at where you turned right. (hope that helped). Supplementary stuff: This could be improved by first finding the points with the largest and smallest x and y coordinates. These four points will form a quadrilateral (assuming you have at least 4 points that is), if any point is inside this quadrilateral it is clearly not part of the convex hull, so you only need to consider the remaining points. I would like to get around to adding this to my code by I am a little stuck at finding a way to determine if a point is in the quadrilateral or not.

In case you were wondering this is a O(n*log n) algorithm.

Minimum Spanning Tree

2008-12-17T22:38:00.004-05:00

While online I realized that I visit the same sites on a regular basis. So I decided to look through my bookmarks to see what sites I haven't visited in a while. Hey look what I found, SPOJ. Why not try to solve as many problems as I can over this break? I already have bookmarked a few problems I have found to be particularly interesting or will make me implement an algorithm I know but have not coded before.

Well I decided to start with a problem where I was asked to find the minimum spanning tree of a given graph. This falls under the "found to be interesting" category. After thinking about it for a while Dijkstra's Algorithm came to mind, and I said "instead of adding the vertex that has the shortest path to the starting point, why don't I just add the smallest weight?" So I wrote a program to solve the problem this way, with out caring about how efficiency. Then testing it against the example they gave I saw that it worked. So now time to do some improvements, but first to look around the internet (aka Wikipedia) to see what other attacks there are that I might not have considered.

Turns out that the method I though of is known as Prim's Algorithm. Unfortunately the pseudo-code that Wikipedia provided was difficult to follow, but luckily I didn't have to search hard for a site with pseudo-code I could understand. However, there is one thing I still don't understand. Each of the sites mentions how you can put the edges into a heap to help make searching faster. First I don't see how this helps and second how does one decide how one edge comes before another in the heap? Well I guess I'll have more time to consider this.

Here is my implementation of the algorithm, I believe it runs in O(EV) time. Sorry for the horrible formatting, I really wish that blogger would just not auto-format stuff the way MSWord does, so annoying.

void mst(vector&E,int N)
{
vector found(N+1,false);//vector of already solved vertices
found[0]=found[1]=true;
long long wgt=0;//total weight
tpl temp=tpl(-1,-1,-1);

while(N-1>0)
{
vector::iterator II=E.begin();
int sh=2000000;
for(vector::iterator I=E.begin();I!=E.end();++I)
{
tpl R=*I;
if(found[R.first]==true && found[R.second]==false)
{
sh=R.third;
temp=R;
II=I;
break;

}
else if(found[R.first]==false && found[R.second]==true)
{
sh=R.third;
temp=R;
II=I;
break;
}
}
N--;
found[temp.first]=found[temp.second]=true;//another vertex has been solved for
wgt+=temp.third;//update total weight
E.erase(II);
print(found);//print found vertices, used to debug
}
printf("%ull\n",wgt);
}

Another Semester Down

2008-12-12T16:16:00.005-05:00

Finally this semester is over. Not that I didn't enjoy it but the classes didn't provide me with enough of a challenge. I don't see too much changing next semester but you never know. I don't see any reason for not making all As since I pretty much destroyed every test and project. Well here's the expected break down of each class.

CIS 3020: Quite uninteresting. All the object oriented stuff we learned in class I already knew, and that was because I spent about an hour reading the OO portion of a C++ tutorial. The lab sessions were quite useful since you actually learned concept, thank god for graduate students. The two things I got out of this were learning some Java and finally switching over to Linux (as far as my laptop, I still have to get around to putting it onto my desktop).

Fourier Analysis: Worst mistake ever. Easy class, but so uninteresting. I was expecting a theoretical approach to the topic, or at least an applied one where theorems were stated and then proofs sketched. However, what I got was "here is what a fourier series is, now here is what MATLAB can do". Needless to say I didn't really learn anything I would consider worthwhile.

Numerical Analysis: Seemed like a computational approach to linear algebra. Though the class did make us use MATLAB he would explain where the equations and algorithms came from before showing how to perform them in MATLAB. Overall could have been a better class but I guess I was expecting too much since I had already started reading a Numerical Analysis book a few years ago.

Modern Analysis: Good review of what I did all last year in Adv. Calc. The problems he assigned were pretty interesting and required some thought, but nothing to the point where you would be banging your head on a desk two hours before the assignment was due. He's a pretty cool guy and an amazing teacher. The phrases of the semester were "blindingly obvious" and "it's easy", so as you can imagine we had some fun with those. OH before I forget he has agreed to be my faculty adviser (or whatever it's called) for my honors thesis. So after the second semester of the course we will get together to discuss thesis topics; looking forward to it.

On a non academic side, today I found out that I was chosen to go through the selection process for an NSA internship. Hope everything goes well and I am chosen, this is honestly my dream internship.

Also if you have lots of time to waste here is a really good site, though I warn you there are a lot of graphs.
Procrastinate

Steven A. Smith on Burress

2008-12-04T23:13:00.000-05:00

What more is there to be said.

Oh Java

2008-11-29T13:13:00.002-05:00

Well I have been doing a project in Java (obviously not my choice, I would rather be using C++). I have started to get annoyed with how verbose Java can be at times. For instance say you have two string, string1 and string2, and you wanted to see if they were the same; instead of just typing string1 == string2 like you would be able to in C++ you have to type string1.equals(string2). I should note that string1 == string2 is allowed in Java but it checks to see if the two objects point to the same location in memory, and in most cases this is not what you want to check. But check this out, apparently if you want to compare two characters using the == operator is perfectly fine, gosh Java just make up your mind already. Well that's enough Java bashing for a while, I suppose that I just prefer C++ because it is what I learned first and have been using for much longer. I will admit though that Java does have its upsides (this will be left for another post).

The other day I got around to wondering why I never needed to defragment. the drive with Linux. I have just had people tell me this and have read it online but never actually got around to seeing why. So I got on Google did a quick search and found my answer, and was quite pleased with the result. Here is a link to probably the easiest explanation to follow. After reading that article I saw on the page a link to something about how to "properly delete files", something I have always wondered about and now was just as good a time as any to read about it. I won't go into it too much here, but when you just hit the delete button it is similar to just deleting the pointer that tells you where the information is stored and not the information itself. If you want a better explanation and information on how to "delete" the information just follow this link (you will see why I put delete in quotation marks once you read the article/post).

Why Teachers Weep

2008-11-28T01:20:00.002-05:00

This is not mine but I found it to be quite funny and true at the same time. I am glad that I am finally in classes where students are honestly interested in learning the material and not so much about knowing just what will be on the test.

Then Jesus took his disciples up on the mountain and gathered them around Him. And He taught them, saying: "Blessed are the poor in spirit, Blessed are the meek, Blessed are the merciful, Blessed are you who thirst for justice, Blessed are you who are persecuted, Blessed are the peacemakers...

And Simon Peter said, "Do we have to write this stuff down?"

And Phillip said, "Will this be on the test?"

And John said, "I'm sorry. Would you mind repeating that?"

And Andrew said, "John the Baptist's disciples don't have to learn this stuff!"

And Matthew said, "Huh?"

And Judas said, "What does this have to do with real life?"

Then, one of the Pharisees, an expert in the law said, "I don't see any of this in your syllabus. Do you have a lesson plan? Is there a summary? Where is the student guide? Will there be any follow-up assignments? How will this affect the bell curve?"

And Thomas, who had missed the sermon, came to Jesus privately and said, "Did we do anything important yesterday?"

And Jesus wept.

A Follow up on Amendment 2

2008-11-27T17:27:00.002-05:00

Now this article from isn't about Florida but it is about the same topic so in my opinion it is just as good.

Here is a link to the article, please actually take the time to read it and the links that it sends you to.

Intermediate Value Theorem

2008-11-26T21:49:00.002-05:00

Well I have stared looking over some analysis problems in preparation for the Putnam exam. Though I will admit I have not prepared as much this year as I have in the past, or would have like to.
Well here are some of the problems I have worked on, none of them are particularly difficult but they make you think for a few seconds.

Here are the solutions.

Integral Test

2008-11-22T15:47:00.002-05:00

Here is my post on the integral test. The post is located at my WordPress blog.

Integral Test.

IMPORTANT NEWS

2008-11-22T14:45:00.002-05:00

Well for unknown reasons (well not totally unknown) I can no longer use LaTex on this blog. I did look up ways to get this back but ran into a few problems. Most of the solutions only worked for Unix like systems, and I would like to be able to use LaTex on the blog even if I was on a Windows machine. Also most of these solutions would have required me to add another version of Tex to my linux system and I didn't really want to do that. There was however, one solution that would work with all systems (supposedly). All I had to do was edit the source code for a GreaseMonkey script, but after doing that I was still running into the same issues as before so I quickly gave up on that dead end.

I will still be using this blog but whenever I want to post anything mathematically related I shall post a link to my WordPress blog in the post. The reason I am using WordPress is becasuse it has LaTex built in and thus less work on my part.

Welcome Home Steve Spurrier

2008-11-15T23:40:00.002-05:00

Well I finally went to a UF football game. I was pretty much forced into it by Veronica and Juliana. Really it wasn't a bad choice for a first game really, UF was playing USC (South Carolina, not Southern Cal), so I got to see Steve Spurrier.

We had pretty good seats for the game, right behind the band. I admit it was quite the experience, though not all that people have talked it up to being. The game itself was not really worth it since it was a blow out (56-6 UF) and really who want's to watch that?

The half time show...oh how I miss half time at FAMU games, and that is all I have to say about that.

Before:

After:

Amendment 2

2008-11-05T23:41:00.002-05:00

Sometimes I am just shocked at how closed minded and "selfish" Americans (in this particular case Floridians) can be. Look at the title, if you don't know what I'm talking about follow this link.

Below is what one of my friends had to say about this topic. I would have to agree with him 100%, yes even the willingness to leave America and live somewhere else.

It is not often enough that something happens in this country that makes me ashamed to be a part of it. However, there has been a growing trend which has stopped me dead in my tracks. With the recent Florida elections, I have witnessed first hand the bigotry that continues to permeate our society.

I am speaking of course about the Florida Constitutional Amendment number 2. This amendment passed on November 4th, and it prohibited homosexual marriage and stripped rights from a domestic partnership. For those of you who are ignorant on the subject, domestic partnership has not been an exclusively or even predominantly homosexual union. It is merely what the name says. Two beings entering in a legal partnership in order to relieve stress of financial situations among many other things. Now, domestic partnerships across Florida have been reduced to a mere shadow of the benefits a man and a woman may have by being legally married.

This ignorance is gut wrenching. Imagine a similar amendment, one which prohibited interracial marriage. That's right Florida, let's all vote on whether our constitution says I can marry a black woman. Such a proposition would be met with instant hostility and cries of overwhelming racism. Hell, lets take it one step further. Black people can't marry. Period. There is no alternative to give them equal status of being "married". By the simple fact that they were born black, they are denied the rights which are extended to another race.

If you think there is a fundamental difference between those two examples and amendment 2, you are blinder than I ever thought my friends could be.

There is no excuse for this. There is no justification. This, and the progression of 29 other US states is fueled by nothing but sheer bigotry towards homosexual people. In the process, states such as Florida have crippled many non-homosexual partnerships, all in the name of preserving the American family.

I cannot and I will not tolerate this. My desire to complete my education keeps me in the US, but I vow that if such blind hatred continues to be entwined into the very constitutions of the states that make up this nation, I will be leaving. I love America, and I have always thought how lucky I was to live in a nation that was for the most part, better off than most others. But this is not an issue I will compromise.

Normally, I would be open for debate on an issue, but I'm afraid I am making an exception to this. I am not gay, and honestly this decision will probably never affect my personal life. It is the principle itself which is evil. If you think this could have been defended by saying that the domestic partnership was abusable, then I counter with allowing homosexuals an equal equivalent to marriage. If you counter with marriage only being between a man and a woman by decree of God, I will counter with an absolute declaration of your stupidity.

My only salvation is to hope that in the future, children will read about this is textbooks, much as we read about the injustices against black people in America and their faces will be filled with shock. Shock that at one point in the not so distant past, their country, their grandfathers and grandmothers, could have believed in such bullshit.

Also I would like to mention that I am not gay and just like my friend this will most likely not affect me in my life. But it is the principle of the matter, who gave the government to power to say that marriage is the union of one man and one women? Some people will say something like "...it's in the bible...", well I am still waiting for someone to actually show it to me. Also since when was the bible the doctrine that governed this country? The bible also says to turn the other cheek...and yet we are in a war over a particular even that happened a few years ago. So don't tell me that we are a "Christian nation", because being a Christian is about more than just reading the bible, you also have to follow the lifestyle, and so far this country isn't doing a very good job. Yes I know that homosexuality is looked down upon by the bible (this I have actually read and/or been shown) but so are the 2 commandments Jesus gave us (for crying out loud he cut the 10 down to 2, at least have the decency to try and follow them both). Here they are, "The first commandment is this: Hear, O Israel: The Lord our God is the only Lord. Love the Lord your God with all your hear, with all your soul, and with all your mind, and with all your strength. The second is this: Love your neighbor as yourself. There is no other commandment greater than these." (Mark 12:29 if you need a reference). Now I don't know about the first one, but this Amendment surely goes against the second.

I shall leave you with the following quote, and if you don't see how it relates then I truly do feel sorry for you.

If mankind minus one were of one opinion, then mankind is no more justified in silencing the one than the one - if he had the power - would be justified in silencing mankind.
- John Stuart Mill

Minor Incidents

2008-11-02T16:24:00.004-05:00

Well I have decided to tag a Computer Science minor to go along with my Mathematics major. After this semester is over I will only have 4 more CS classes to take before I have completed the minor, this basically comes down to 1.3333... CS classes per semester. The classes I have to take are; Applications of Discrete Structures, Intro. to Computer Organization, Data Structures and Algorithms, and Operating Systems. Due to prerequisites I will be taking the fist two next semester, then Data Structures fall of next year, and finally OS my last semester (because this seems to be the most difficult of the 4 and I would rather not to have to worry about it while working on graduate school applications).

I came to this decision after realizing that there weren't any outside of major classes that interested me, other than Economics, Finance, or CS. Honestly, I find all these disciplines to be just as interesting and rewarding. However, what made me choose CS was the kinds of people that would be in the classes. In my experience most of the people in the Economics or Finance classes don't seem to have any interest in the subject and are only there because they have to take it for the major. In addition they constantly complain about the work and other consequential details about the class. While the CS majors are very adamant about their classes and willing to learn. Also there isn't as much complaining about the class (unless it is to say that they aren't learning enough or that it's not challenging enough).

In addition to the above issues there are some other personal "problems". Now that I think about it problems really isn't the most appropriate phrase to use. Here is the general overview: A little while ago (2-3months) stopped talking to one of my friends because I felt used. A few days ago I was pretty bored and lonely (most everyone I knew was out of town) and I considered giving them a call. After thinking about it I didn't mainly because I would feel that I was using them, and that's just something I refuse to do, even to someone I no longer care about. Well I care about them but it is basically at the same level I care about a complete stranger. The day after this happened I talked to one of my friends and basically what I remember from the conversation was this, "...you will constantly be filtering people in and out of your life. It sucks at time but it is just something you have to learn to accept."

Homecoming Weekend

2008-10-27T22:58:00.002-04:00

Well I was not on campus, as a matter of fact I wasn't even in Gainesville, for homecoming this year. Instead I was attending the ACM ICPC Southeast Regional (a programming competition for college students). We took four different teams this year. It was my first time going and I didn't do all that well on the placement test so as a result I ended up on the 4th team. At the competition we managed to answer 3 of the 10 questions and finished 21st out of abut 62 teams. Also we beat the 3rd team. Our school's first team answered 5 questions and got 2nd place (the fist place team also answered 5 questions), while our 2nd team answered 4 question and I am sure that they were in the top 10. Overall I believe that we did very well, considering we were with out the aid of the C++ STL and Java API refernce sites which we were promised.
Any case, it is time to prepare for next year's competition. My goal is to be on the fist team and get 1st place.

Comfortable in an Open World

2008-10-19T01:03:00.003-04:00

Now when I use my laptop I mostly boot into Ubuntu Hardy (8.04). The only time I boot into Windows Vista (which I still think is a better OS than XP) is when I need to use MATLAB. However, this is becoming more of a rarity since I have started using Octave and have become quite comfortable with its interface. In addition I find that compiling and running programs is much easier under Ubuntu. I suppose I could set it so that it is just as easy under Vista but that would require some work. All of the applications I use on Ubuntu are Open Source, with the exception of Adobe, and this is only because I find that it is considerably better than any of the Open Source aternatives I have found thus far. I used to have WINE installed but removed it once I realized that I had no need for it sicne it could not install MATLAB and I'm not much of a gamer so really everything I need can be done with Linux compatable programs.

As far as programming goes I have started using Java. It isn't that difficult to pick up since I know C/C++ it just takes a little getting used to. I might go back and try to convert some of the solutions I did for SPOJ problems and convert them to solutions in Java (they are all in C++). Learning a new language really can't hurt since there are some problems I see and am like "I know how to do that but I can't fit the necessary data into as a long long (64 bits) is C++, if only I could use Java's BigInteger."

Next week is the South East Regional Programming Competiton for ACM. Wish me luck. I feel pretty prepared, I have a grasp of most of the basic algorithms we coverd. It is just coming up with the correct data structures to use that is giving me problems now, but that should soon be fixed.

Post 100 and about 900 days later

2008-10-02T00:00:00.000-04:00

Well this is post #100.
Unlike other post this one will be dedicated to someone (you will know who you are after reading).

I know you have done nothing to deserve what I am doing (well that's not entirely true but this isn't the place to discuss that). I just want you to know that it was a wonderful 3 years and a portion of my life I will not easily remove from my memory. In that time you became one of my best friends, if not the best friend. But that isn't enough for me anymore so I am saying goodbye.

Blinded

2008-09-26T09:00:00.002-04:00

First I would like to mention that the generalized statement in my previous post is incorrect. I shall in the coming days post the correct version with proof. Now for the real post.
------------

Without you in my life, brightening the days
I might as well be blind, crawling in the dark
Searching for a light switch I'll never find

But there you are
And it's like God said, "Let there be light"
No, more like
"Let there be [her name]"

And now I'm obsessed
I might as well be blind
Because all I see is you
But that's alright by me
Since with you there what else is worth looking at?

I Have Wireless

2008-09-21T03:30:00.002-04:00

So I have finally managed to get my wireless card working with Ubuntu 8.04. You have no idea how happy I am about this. I have been wanting to really give Ubuntu a try but have always been reluctant to because of the fact that it wouldn't work with my wireless card and I would need an ethernet cable in order to connect to the internet. Now I know this happiness will not be too long lived because once I update to the next version of Ubuntu (which in my case will probably be 9.04 and not 8.10) I will most likely have to go through the same process again and hope that it still works on the new version.

On a more "depressing" note; I managed to finish only half of one my my 5 analysis homework problems. They all seem to be about connected sets. One of the funny things is that in Rundin for a set to be connected it must not be able to be written as the union of two separated sets. However, on Wikipedia, Mathworl, and one of my other analysis text they also say that the separated sets must be open sets. Now I know that if two open sets are disjoint they are separated so I don't see the real need for this extra assumption. In any case the problem I managed to solve was as follows.

Let A and B be two connected subsets of a metric space X. Show that is A and B have nonempty intersection then their union is also connected.

The second half of the problem asked us to state and prove a generalized version of this for the union of arbitrary connected sets. I came up with:

Let {A} be collection of connected sets. If for each F in {A} there exist a G in {A} such that the intersection of F and G is nonempty then the union of all the members of {A} is a connected set.

Voting and Coding

2008-09-13T22:18:00.003-04:00

Well as the title indicates, this post will be mainly about two thing; voting and coding.

Voting:
Don't you just find it a little discouraging that when you turn 18 you are finally able to vote and be drafted into the military (assuming you are male). What really bothers me about this isn't so much the service aspect but rather the fact that when I turned 18 I was sent a card saying that I had registered for the selective service. Now I don't remember doing a damn thing for this, I'm not complaining, but still. On the other hand when I wanted to register to vote I had to go out of my way in order to do so. And you wonder why so few young people decide to vote. It's viewed as a burden, I mean if they can register for the service on their own they sure as hell can register you to vote, even if it's as an independent and then you have to go and change your party affiliation if you so desire.

Coding:
This year I think I am going to take programming team practices a little more seriously. I guess it is because now I know that in most competitions I will be able to solve about one or two problems "easily". However, I would like to be able to do more and in order to accomplish this goal I will have to learn more algorithms (or at least the thought process behind them). At the most recent practice I learned a pretty efficient algorithm for finding the longest common substring between two strings. Before seeing the algorithm I would have been able to do this problem but my method would have been very inefficient and complicated to code.
Also I have finally found a blank CD for me to make a Linux boot CD. I am going to install Ubuntu on my portable hard drive instead of partitioning the hard drive on my desktop or laptop. I really don't have a problem with having Ubuntu being the main OS on my laptop but I am not sure how to go about installing MatLab on that system so I am going to avoid the potential problems. Also one of my classes works primarally in a Linux environment so having Linux on my comptuer will make things easier (although I could still do most if not all of the work under Windows if I really wanted to).

"Low-Tech" But Creative I Must Admit

2008-09-11T09:27:00.002-04:00

Just another thing you have to worry about in the world. When will people try not get ahead by screwing over others? Whoever it was that came up with the concept of money must be rolling over in their grave now thanks to all the problems it has caused through out history. I suppose if it wasn't money then it would be something else that would cause people to react in the same fashion.

Why can't we just go back to the bartering system? You know, when things were simple. I'll admit that this system has its flaws but personally I think that the advantages definitely outshine its pitfalls.

Well here is the article you have been waiting for.

Just Another Problem With America

2008-09-10T21:45:00.003-04:00

A citizen of America will cross the ocean to fight for democracy, but won't cross the street to vote in a national election.
- Bill Vaughan

As if I needed more of a reason to vote. This quote is just so depressing but then when it gets worse when you stop to think about it and realize just how true it actually is.

Shopping Can Actually be Fun

2008-08-15T23:24:00.005-04:00

Decided to do some last minute back to school shopping. Really all I needed was a new pair of shoes and a few other minor things. The only real thing I needed was shoes, everything else I could have bought once I got back to campus, but why not buy now instead of later.

Since I knew that I needed shoes, the first place we (Ann and I) went was to the shoe section of Sears since I had seen the shoes I wanted there before. The shoes I got were Adidas Samba's, I had actually been wanting a pair for the longest while but never got around to actually buying them. They only came out to be $42.99, and I just happened to have $40.00 cash in my wallet, so I ended up putting the other $2.99 on my credit card, I'm sure that I looked pretty weird.

After buying the shoes we just walked around the mall for a while before deciding that I could actually buy some more cloths. Really a fun experience, trying on everything and getting a good laugh at how ridiculous I looked or how amazing it was. The two things that stick out the most are the pink shirt that Ann wanted me to try on even though I told her that I would not buy it. I must admit though that it didn't look all that bad, however, I stand by my decision to not buy it. Then there was this set of brown shorts with white vertical lines, and another set of brown pants. Both were too big so I didn't have to put up much of a fight as to why I wasn't going to buy them. After all of this I just ended up buying a white button down shirts with grayish vertical stripes/lines.

This might not seem all that interesting to most of you but to the parties in attendance it was quite the memorable day.

Time Flies

2008-08-11T23:25:00.005-04:00

Last night before going to bed I was talking to one of my friends on AIM. I hadn't spoken to them in a while so most of the conversation was about what we each had been up to for the summer. However, we managed to move to a totally unrelated topic and some of their comments left me just a little depressed. So I did what I normally do when this happens, I end the conversation, put up a witty away message and then go to bed.

Wham! I feel better in the morning and it's like the event never happened. Also when I woke up I was thinking about another math problem (similar to #2 in the previous post). After sitting in bed for a while reflecting on last night's conversation and trying to come up with a proof for this problem, I decided that it was time to go and eat breakfast. Then a few hours later I went over to Ann's.

Well I basically spent all day (well really 10.5 hours) with her. We played Guitar Hero 3, something I have so missed from my days in Holland. I convinced her to start playing on the hard difficulty setting. Things went a lot better for her once she got used to the added button, I think now all she has to work on is "reading" and getting used to the speed. Oh and she also needs to get comfortable with "pull ons and hammer ons". After the Guitar Hero session we went to get lunch at the same place we went for my birthday (Far East Cuisine I think). Then we basically messed around online until dinner.

Extracurricular Affairs

2008-08-10T18:10:00.001-04:00

Well by this time I am sure that just about everyone has heard about the John Edwards affair. If not, or you for some reason want to read more about it, just click on the previous link and it will take you to an article in the New York Times. Now I am not supporting this kind of activity but really why would you put something like this out when your family is in the public eye? To me it just seems like something that you would want to keep between yourself and your spouse. Regardless, what was he thinking? He is married and even has children. Luckily his two youngest children are not that old, so the kids they will interact with most of their lives will not remember this, but it will still be one of those "family secrets" you are ashamed of. As for his oldest child (who is at Harvard Law) good luck to her and dealing with this, since you know people will want to talk to her about it and how she feels.

Also this not only hurts him and his family but also a certain democratic candidate who happens to be running for president. It also doesn't help that Edwards chose to endorse Obama and not Hillary Clinton. I am sure that the McCain campaign will you this to their advantage when the time is right.

In any case it seems that democrats seem to take part in "extramarital activities", weather holding office or not. Kennedy, Clinton, and now Edwards, just to name a few. Let's see if (and hopefully not) Obama will keep the tradition good.

solution

2008-08-02T16:57:00.003-04:00

This is the solution for problem #1 in my previous post.

Let , since is a Cauchy sequence there exist an such that if if Similarly since a subsequence converges to we have that when . Now let be the larger of and .

Now .

Here is the solution for #2 in my previous post (this one took a little longer for me to think of).

Let be a sequence in such that . Now from properties of we have that for all Now let , and since we have that for large enough. So since is complete. Additionally, is a limit point of each , so .

From the Integers to Infinite Series

2008-07-30T22:24:00.005-04:00

In the upcoming fall semester I will be taking the first year graduate analysis class. Hopefully, this class will be more "rewarding" than the undergraduate analysis sequence I completed last year. The undergraduate sequence was not a total waste of time since I actually did learn some new things, but the class moved so slowly and the test were not all that difficult. I never really had to exert myself in order to obtain my A. As a result in the second semester I tried to get a 100% on every assignment and test. I almost achieved this goal, however, I did not make a small clarification on one of my proof thus resulting in me losing 1 or 2 point for the problem.

The graduate class will be using the same book as the undergraduate sequence. However, we will hopefully cover all of the sections. Last year the professor would pick and choose which topics he though were necessary and possible for the majority of the class to understand. As a result some of our proofs were longer than needed but I suppose knowing multiple ways to prove something isn't all that bad.

Right now I am reading through as many chapters as I can and working all the exercises. My only requirement is that I can only be working on problems from at most two different chapters and that I can only be reading one chapter ahead of the problems I am solving. So basically right now I am working problems from chapter 2 and 3, and reading chapter 4. I am almost done with the problems from chapter 3, but the ones from chapter 2 are going to take a little more time. I suppose that it has to do with the fact that dealing with topology is still a little "new" to me.

Tomorrow I will hopefully be able to do the following problems:

1) Suppose is a Cauchy sequence in a metric space , and some subsequence converges to a point . Prove that the full sequence converges to .
2) Let be a sequence of closed, nonempty, bounded sets in a complete metric space . Also and . Prove that contains exactly one point.

I will eventually get around to making a post about my REU in Michigan. Sorry to disappoint, but I just need some more time to better collect my thought on this topic so that I will have a post worth reading.

GIMP

2008-07-14T23:27:00.003-04:00

Well in my free time I have decided to learn how to use GIMP. For those of you that don't know, GIMP stands for GUI Image Manipulation Program. Basically it is an open source version of Photoshop.
Yesterday I started reading the online manual (which I should probably download to my computer sometime soon) and was somewhat insulted by the simplicity of the first few sections. However, I can see why they are needed. As of now most of what I know to do was discovered by playing around with the program and reading random portions of the manual.
Right now my goal is to be able to create a cool banner for the portion of this blog with the title. I already have a few done but none of them are "amazing" so they are not going to be used. I think the first thing I should find out is the necessary dimensions for the banner.
The program seems pretty straight forward so far, however, I would like to learn how to make manipulations to text.

Short Computer Post

2008-06-21T11:25:00.007-04:00

I don't really feel like making a complete post at this point in time so I will post a a few pictures of the new desktop.

This is a shot of it in use. Running programs include: Windows Media Player, Firefox, GoogleTalk, Google Desktop, Trillian, and ObjectDock.

This is a screen shot with all windows minimized or closed.

Finally, in case you were wondering I am running Windows Vista Home Premium. There is no way in hell I would EVER get a Mac or have their OS running on my computer. As a matter of fact I try to avoid all apple products, but sadly I have to use Quicktime Player every no and again. Anyway, I don't know when but I will be trying to dual boot Windows and Luinux sometime in the future.

A New Take on Purity

2008-06-12T23:47:00.001-04:00

Best xkcd comic strip ever.

REU 2008 - Week 1

2008-06-07T21:11:00.002-04:00

Don't expect an entry for every week of the REU but I figured that the first week was important enough to have its own.

When I first moved into my apartment I was pleasantly surprised by the size. My first impression was that it was way too small for four people to live comfortably. However, after spending some time here I quickly realized that I was mistaken. The roommates are pretty cool, well actually I have only met 2 of them, the last one will be arriving on Monday. The first one I met had just recently returned from Africa where he was helping install water filtration systems in a village. I don't remember the name of the country but it was a French speaking one. The other roommate is a year younger than me and it kind of shows in ways, mainly when we are working in groups (he is a member of my group in addition to being my roommate). The three of us that live here so far are all math majors and the one remaining roommate is an engineering major.

The research is going extremely well. At the beginning we would "play around" with the problems and find a solution. Then our mentors (I can't think of a better term for them, I guess advisers works but that makes it seem like we are PhD students) would present us with a paper which contained the result we had just discovered. You would think that this was disheartening but it actually was not. Having actually come to the conclusion ourselves made reading some of the proofs much easier since we had a better understanding of what they were doing and could relate some of their ideas to our own. However, we have so far have come across a result which we have not been able to find stated in any paper. I guess you could say we have our first theorem, and it's quite a wonderful feeling. We were surprised by the theorem actually. This is because based on the question we were answering one would expect the result to be complicated. However, it is quite the opposite. When we first saw it we were all skeptical and furiously searched for a counterexample but could not find one. After going through it again we were certain that it was correct. All that is left to do for this finding is to actually write up the proof of the theorem and the necessary lemmas.

Well I'll keep this one relatively short and end by saying that it seems like I will be going to the beach quite often (even though we have to climb over a "mountain" to get there). So far this week I have gone three different times.

From Big to Bigger

2008-05-29T19:00:00.003-04:00

I would like to start this post off by saying congratulations to all the 2008 graduates; high school, college, graduate school, medical school, etc. it doesn't matter. The road has been long and hard (some harder than others) but you have finally made it. Looking back on the last four or five (or more in some cases) years, wonderful memories rush to the forefront of you mind at incomprehensible speeds. Times spent with friends doing "stupid" things, things you regret ever happening but because they did you are a better person. (We all have things we regret it's just a matter of how we deal with it, so I don't want to hear any "I don't have any regrets about my life" bull s**t) So of you will be continuing your education or looking to work in academia, while others will be starting "life". Which ever category you fall into I wish you the best of luck.

A few days ago (May 22nd) I attended my siblings' high school convocation, well actually many of my friends were there but it would take too much time to list them, so I'll just list a few: Ann, Clara, Roland, and Jeremy. Now that the event is over I am glad that I decided to attend. Ever time someone I was close to won an award it made me proud since I would be able to say "I know them and we are great friends" in addition they deserved the award for all of the hard work they put forward both in and out of school. I can only imagine how their parents must have felt.

Today was my sibling's graduation. It's not until you have to sit through one of those as a nonparticipant that you see how fast they move. For some reason I remember my graduation taking forever, but then again I was anxious for it to all finally be over. The speeches given by the saluditorian and valedictorian were both quite good. The saluditorian is a good friend of mine and a funny guy so naturally there were some (well really many) hidden comments in his speech. The only part I regret is that my parents decided to show up only five minutes before graduation started so parking was hell and it was near impossible to find seating. We ended up sitting above the tunnel where all the graduates entered and left, so as my siblings were leaving they were able to see us. Also there was no way to get any good pictures of what was happening on stage because we were so far away. Oh well, being there is what really counts, and I managed to get a few good pictures.

Sum of Two Squares

2008-05-23T22:14:00.003-04:00

I know that I haven't had a post about math or anything math related for a while, so I think it is time to change this.

Well the problem discussed here really isn't that difficult but it is interesting enough to mention. "Given an integer determine if can be written as the sum of two squares." For example if , however, if instead we had it can be shown that it is not possible to have where .

Sure you could try using "brute force" to solve this but that is boring and definitely not worthy of its own post. The necessary key insight is a theorem by Fermat. The theorem states that a prime number can be expressed as the sum of two squares if and only if . The proof of one direction is not that difficult but a proof of the other direction (that if then is the sum of two squares) requires a little more work. I don't feel like posting them here but feel free to look on Wikipedia, where you will find numerous proofs. The proof by Euler is quite straight forward but is quite long and split into many sections (your call on whether this is a good thing or not). My personal favorite is the first proof by Dedekind using Gaussian Integers.

Now another important fact to know is the following. If two integers, and , can each be written as the sum of two squares, then their product, can be written as the sum of two squares. The proof is just a basic exercise in equation manipulation, if you have not proven this fact for yourself I suggest you try to in your spare time.

Using these two facts the problem basically boils down to "factor ." Actually our task is even easier than this, we only need to find the prime factors, , of such that . Thus if factors as and for some , we have that and is odd, then can not be expressed as the sum of two squares.

Pretty simple, now writing a program to actually do all of these things is a little harder but not by that much.

Deja Vu

2008-05-16T21:09:00.004-04:00

Today just like any other day had its ups and downs. A few days ago I decided to try Wubi, which is a way to try Ubuntu before you decide on whether or not you actually want to install it on your computer. Well I was not able to get my wifi working, a serious issue for any computer user in these times. I spent basically all day trying to get this right but it seems that my efforts were all in vain. Thus I decided to uninstall Wubi, however, even after this when I started my computer there would always be an option to start up Ubuntu (which of course didn't work with out Wubi). So I reverted my laptop back to the factory shipped condition. The next few hours were spent removing all the unwanted programs and reinstalling those which I had saved before the restore.

I wasn't at the computer during the entire restore process. Went out with Ann to a restaurant, but am not able to recall it's name. the food was pretty good and not over prices. For some reason I let her talk me into having the sweet potato side. Honestly it wasn't all that bad but not as good as the sweet potatoes that my mom makes when I come home. Looking back the only negative about our lunch outing was that almost as soon as we got to the restaurant it started to rain, so we were wet while we waited to be seated.

After lunch we went back to my place and had some fun with the internet and learning about phone numbers. Just in case you were wondering it is not possible to have pi and "e" as phone numbers. They both violate some rule about the placement of the number "1". Well now I will have to find a new mathematical constant to have as my future phone number. If you know of one that is available feel free to leave it in a comment.

Today I downloaded the new Lupe Fiasco album, The Cool. I haven't really had the chance to listen to all of the tracks but some stand out more than others. As of now my favorite is Go Go Gadget Flow, and the one I skip most often would have to be Superstar, due mainly to the fact that I hear it everywhere I go. Below is a video of another one of the better songs called "Little Weapon", listening to the lyrics makes you think how sad and it is even worse because it is true.

Sales Tax and Apples

2008-05-11T20:35:00.008-04:00

A few days ago I was standing in line at a Subway looking at the prices of the menu items; $4.99, $5.89, $0.99, etc. This just got me thinking, why don't they just give you the price after tax? Just imagine being an immigrant and going to the store and buying two products both listed at $5.99. You go to the register and expect to pay $11.98, but you have to pay $12.82 after 7% sales tax. The first thing that you think is "What is going on here? Why do I have to give you more money than the listed price?" The truth of the matter is that most other countries the price that is shown is the one after tax, so you can imagine how this would cause confusion. Honestly, how difficult would it be for stores to just calculate the tax and add it on to the already listed price? Not very I hope.

I know that no matter how much I, or anyone else for that matter, rants about this, this stupid policy is not likely to change.

Just browsing around the internet I came upon an all too familiar forum discussion topic: "Why are Macs better than PCs". Of course as expected I saw the typical "viruses" claim. What made this thread interesting however, was that there were other claims that were made, some of them irrational but at least they tried to be original. After the virus statements, I would have to say that the next most popular claim was that Macs had better graphics. Now I don't know how true this is since I have never sat the two down side by side and compared so I have no real opinion on this. Some other listed reasons included, easier to use, being faster, and just look better. Now Macs looking better is obviously not a reason that they are better than PCs so I will just disregard this one. Whoever made the being faster claim obviously knows nothing about computers. It's not the computer, but the processor, RAM, and amount of programs running that determine speed. Finally, as far as being easier to use this is really just a matter of getting acclimated. Every time I have to use a Mac I have the hardest time navigating, not because I don't know how to find what I am looking for, but because the keyboard shortcuts are different. This and the way you interact with open windows is a little different when it comes to maximizing/minimizing and other such task.

Amidst all this PC bashing there was the occasional "voice of reason". One of the reasons for the "lack of Mac viruses" is obviously the small portion of market power they have but also because of how the OS and software are closely integrated. One of my favorite statements in the whole thread went something like this, "I don't have anything against Macs, however, what I do have an issue with is the air of superiority that seems to surround almost all Mac users. They seem to think that just because they own a Mac that they are so much better than all PC users. Really, from the looks of things it seems that the extra money you pay for a Mac is not for a better computer but rather for this false sense of superiority." I would have to agree with this statement. Almost all the Mac users I know seem to always try to mention how much better their computer is than mine. Even though it is true it's not because I am using a PC but because I have less RAM, a slower processor (which is about to change), and the amount of programs I run simultaneously. When I was looking for laptops I originally though about getting an iBook or Powerbook. However, as it turns out they were selling for about $2,000 and if I wanted to get the same thing on a PC I would only have to pay about $600-700. So it's no surprise I went with my HP Pavilion dv6700.

Small Intermission

2008-05-05T23:13:00.007-04:00

Finals ended last week and I am glad that I will never have to see some of those classes again. Looking back on the semester, I realize that French was not all that bad. Honestly I am going to miss the subject, but not the having class every morning. Another class I'm not going to miss all that much is Abstract Algebra. Now I know that I might regret this but for some reason the topic doesn't appeal to me quite as much as number theory, analysis, or other branches of mathematics. The funny thing is that algebra and number theory are very closely related. Just about every theorem we learned in algebra could be stated in terms that wold make it applicable to a number theory class. Overall the semester wasn't that bad, surprisingly advanced calculus turned out to be ,what I considere, my easiest class. I still have to wait another week or so to find out my final grades but I am pretty confident that I made As in all of my classes.

When I returned home I found my laptop waiting for me. In case you are wondering I mentioned the laptop in one of my last two post. Setting everything up was pretty straight forward, no real surprises. The only real issues were getting used to the new feel of vista and removing all of the unnecessary preinstalled software. Really I could group these into the same problem since it took me a while to find the "add/remove programs" function in vista, which happens to be called "programs and features". After finding this I spent the next hour or so finding unwanted material and then waiting for Windows to uninstall them. Overall Windows Vista isn't all that bad, I would rather be using XP but after spending some time with it you realize that in all actuality it isn't as bad as some reports make it out to be.

Here are a few screen shots of my new set up.

In use:

Desktop:

As you probably noticed this is not the usual Windows set up. I have "replaced" the task bar and system try with an application called ObjectDock, which imitates the thing that is used my Macs. On the side is Google Desktop's side bar, personally I prefer it to the one that comes with Vista.

Finally, my birthday was a little while ago. I didn't really do all that much, just had lunch with two of my best friends and then spent time with the family. Even though it doesn't sound like much it turned out pretty well.

Finally Time For Finals

2008-04-16T15:51:00.006-04:00

Just finished what I hope was my last Abstract Algebra test. The take home portion of this exam was hell. Even though there were only 3 questions it took a little under a week for us to complete. The first two questions were pretty simple and we finished in about an hour (most likely less). They day before the exam was due my team and I spent around 12 hours working on the sole remaining problem, and we didn't feel too confident about any of our proofs. What frustrated us the most was that the material covered in the final question did not have any major connection to algebra. This combined with the professor's poor wording of the problem left us wanting to kill people. Today was the in class portion of the exam which surprisingly was not all that bad. I did however, make a few mistakes. One problem I got the right answer but used the completely wrong method, luckily this was a short answer and not proof bases test. Another problems I used the same incorrect method but this time I am sure I go the wrong answer. Other than those two questions I think that I got everything else correct.

In addition to the abstract test I had an Advanced Calculus test the following period. Luckily the theorem he wanted us to prove was not all that difficult, since I did not bother studying for it due to the abstract test.

Before you get the wrong idea, today was not a horrible day. In fact it was and most likely will be the best day of this week. I woke up this morning thinking that I would have to go to French. However, during my shower I remembered that we didn't have class today because we had the oral portion of our final the previous day. During this new found free time I studied a little for abstract and watched some television. This got old after a while so I resorted to doing a few SPOJ problems, which is something I haven't done in about a month. During the period of about one hour I finished a previously started problem relating to Fibonacci numbers, started and completed a problem on finding the centroid of a region, and finally started a problem on strings. This last problem I have though of a method but am not sure exactly how to program it just yet.

One final bit of good news, I ordered my laptop a few days ago. Here are its "stats":

- Genuine Windows Vista Home Premium with Service Pack 1 (64-bit)
- AMD Turion(TM) 64 X2 Dual-Core Mobile Technology TL-60 (2.0 GHz, 512KB+512KB L2 Cache )
- 15.4" diagonal WXGA High-Definition HP BrightView Widescreen Display (1280 x 800)
- 2GB DDR2 System Memory (2 Dimm)
- 256MB NVIDIA GeForce 8400M GS!!
- HP Imprint Finish (Radiance) + Webcam + Microphone
- 802.11b/g WLAN and Bluetooth from 802.11b/g WLAN!!
- 160GB 5400RPM SATA Hard Drive
- SuperMulti 8X DVD+/-R/RW with Double Layer Support
- High Capacity 6 Cell Lithium Ion Battery (3hr 30min)

This only came out to $847.09 and $59.10 of that is tax (shipping was free).

Finals and Work

2008-04-05T18:24:00.004-04:00

Well the semester is winding down, I only have a few more test and then I'm "free". Now that I think about it I have quite a few test to take actually. Two in Abstract Algebra, either one or two in Advanced Calculus 2, two in Managerial Economics, and one in French. None of these should be particularly difficult, but some count more than others so I will actually have to study.

Right now I am really looking forward to my REU. I still have to book a flight but that shouldn't be a bit issue. Earlier today I received an email from the coordinator informing us about who was going to be in our groups as well as how we were to sign up for housing (which is provided free of charge). Interestingly there will also be other undergraduates participating in research in other natural science areas. If I am correct I believe that the email said that there would be somewhere around 200 undergraduates, and only 15 of us will be working directly with the mathematics department. Apparently we will be getting pain $800 minus taxes every fortnight.
While on the topic of money I think it is appropriate to mention that I might be teaching the discussion section for a Precalculus class next fall. I found this out on Friday after my Advanced Calculus 2 class. The professor talked to me and another sophomore, he wanted to know if we would be around next fall since the department was looking for more TAs to help teach discussion sections. He said that he would refer us to the person in charge in order to set up our interviews, which are just a formality according to him. It was mentioned that we would be getting paid but nothing much was said about this topic, and I'm fine with that.

It's been a while since I've done this, but here is a video to accompany this post.

Linux in my Windows

2008-04-02T10:05:00.003-04:00

A few days ago I tried to dual boot Windows XP and Ubuntu (a Linux distribution). At first I was just booting Ubuntu from the boot CD I had created, and things were running smoothly. Eventually the time came where I decided that I wanted to boot Ubuntu from the hard drive and not the CD. Well I started the process and things were running smoothly, me hitting next and Ubuntu doing what it does best (rocking). So I come to the end of the installation and when I restart my computer I realized that I had not partitioned my drive so that it would run BOTH XP and Ubuntu, but instead I had installed Ubuntu on the whole drive, which means no more Windows XP. This wasn't all that bad since I was planning on replacing XP eventually in any case. However, problems arose once I realized that I was not being able to connect to the campus internet (they have some new long and stupid process which I believe is out to get Linux users). Thus for the weekend I didn't have internet, I did however, have a lot of fun games that came with Ubuntu so I was entertained.
Yesterday I managed to get a copy of an XP boot and installation disk. So right now I am in the process of reinstalling all the applications I will need and all of my other hardware to work with XP again. So I have been frantically downloading things left and right.
Things I still need to get include;
a C++ compiler, Adobe Reader, WinTV, a few Firefox add-ons, and other minor things like anti-virus software.
In any case I shall be reattempting to dual boot XP and Ubuntu in a few days, wish me luck.

Codes

2008-03-27T21:01:00.002-04:00

Well this semester is almost over, and I could not be any happier about it. Classes are starting to get on my nerves. Really it is just the non-math classes but this general feeling of resentment is being carried over to the math classes and that is never a good thing. Economics should have been interesting but it turns out that he spends a semester teaching you how to do basic optimization problems. By basic I mean only require calculus 1 and there are no round off errors. French is being as some would say, "French". It isn't so much the class in this case as much as it is the having a test every other week or just about. By the end of the semester you are just burnt out and would rather get a 50 on a test than look at another word of French.

Registration for the next semester is coming up soon for me, I think my registration date is either the 30th or the 31st. In any case I still have to narrow down my class choices. Right now the only classes that I know I will be taking for sure are; Modern Analysis 1 (a first year graduate class) and an Advanced Programming Fundamentals for CIS Majors, which is an introduction to computer science for students with prior programming experience. As for my other classes I am still torn between Introductory Numerical Analysis and Numerical Linear Algebra (another first year graduate class). Regardless of which class I take in the fall, I will be taking Numerical Analysis (the graduate level) in the spring, so chances are I will be taking the Into. Numerical Analysis. Finally there is a Fourier Series and Transforms class being offered which I would really like to take, but after talking to an adviser, I was informed that the class might be canceled if not enough students register.

Things have gotten to the point that in my copious spare time I decide to work on SPOJ problems. The problem that I have just recently completed after about a week is BITMAP, for those of you that are interested. My initial approach was to solve this problem with dynamic programming which seems reasonable. However, it was a few days ago that I learned about what I think is called a "breath first" search. I am not sure if this method is actually faster than the dynamic programming idea I had but it is definitely easier to program for this particular problem. I suppose that actually having a class in C++ would have it's benefits, mainly in that I would get a better idea of how particular ideas can be used to solve problems. For instance, before I knew about queues but they never seemed useful since it appeared that anything they could do, vectors could do better (I am sure you could create a vector that acts like a queue but it would require unnecessary amounts of code). This is the main reason I am taking the
Advanced Programming Fundamentals class.

Right about now I should be getting back to finishing my take home Abstract Algebra test, which is due tomorrow around 12:30.

Overdue Spring Break Post

2008-03-18T11:32:00.004-04:00

You don't realize just how much you need a break until you get one. Mine wasn't too eventful, I just went back home and decided to relax a little (honestly it was more like a lot). Even though I didn't do all that much it was still enjoyable.

Firstly I heard back from the REUs that I had applied to last month. I got an offer from one of the REUs and will be working on one of the more interesting problems in my opinion. Here is the description of the project that is provided on their website:

In the mid 1990's an electronic puzzle called "Light's Out'' became popular. The puzzle consists of a grid of lights, and at the start, some of these lights are on. Pressing one of the lights will toggle it and the four lights adjacent to it on and off. (Diagonal neighbors are not affected.) To win, one must switch off all of the lights. This puzzle can be reformulated in terms of graph theory with vertices representing lights and edges representing adjacency. One can then study graph theoretic properties of the puzzle, as well as optimal winning strategies and "always winnable'' graphs.

This project will deal with adding a probabilistic element to the puzzle. One question relates to the expected number of moves required to win under a strategy of randomly pressing vertices on a winnable graph. Another avenue of research would involve assigning probabilities to various edges, so that lights are only toggled on or off with a certain probability when any vertex is pressed. The study of these questions may lead to other interesting variations on this theme.

This program runs from June 2nd to July 25th and is in Holland, Michigan which is only about two hours away from Chicago.

In addition to this great news I got to hang out with some friends. Don't think I will need to play Guitar Hero for at least another 2 months. Also went and saw Definitely Maybe with Ann, the movie was fantastic until the ending where it all sort of fell apart. I suppose they couldn't have thought of a better ending. The next movie I want to see is 21, this is kind of a big deal since I normally don't set out to see specific movies.

Bernstein Polynomial

2008-03-17T10:12:00.005-04:00

Recently in Analysis we learned about a famous theorem due to Weierstrass. This theorem asserts that ANY continuous function on a closed interval can be approximated by a polynomial. The proof in Rudin's Principles of Mathematical Analysis was kind of easy to follow but really required that you fill in many gaps, as is usual with many of his proofs. However, over spring break I was reading A First Course in Numerical Analysis by Ralston and Rabinowitz and they provided a proof that was not only much easier to follow but seemed more natural to some extent. It should be noted however, that some of the steps in their proof assumed that you have some background in analysis in order to justify some of their claims. Anyway what follows is their statement of the theorem and its proof.

Theorem:
If is continuous on a finite interval , then given any , there exist and and a polynomial of degree such that , for all in .

Lemmas: The following lemmas are easily proven by the binomial theorem, and thus left to be done so by the reader. (Don't you just hate when books do this to you)
1:

2:

3:

Proof:
Define the polynomial . From the lemmas we have that

, from this we have that

. Let on (we can turn any finite interval into by a simple rescaling). Now if . We

next proceed to define two sets, for any x in the interval and , and is the set of remaining points.

Using the above identities we have that .

For the set we have

for large enough. (note that on )

Thus .

Compared to Rudin's proof this one is much easier to follow if you actually prove the lemmas. The above proof was given by Bernstein in 1912, it should be mentioned that I might have left out a few details but the general idea is there. In case you didn't do it, the rescaling done with the interval is just , so and and anything in between and maps to with .

Challenge Problem:
If is a periodic continuous function of period prove that for any there exist such that . Where .

My Solutions

2008-03-08T14:24:00.004-05:00

Well spring break officially starts today, even though I started on Thursday after my managerial economics test. After the exam I went out to a club with a friend and her neighbor. It was the second time that we went to this particular club, luckily this time was more enjoyable than the previous visit. Even though I had a great time, I would not say that this was my best clubbing experience. It had nothing to do the people I went with since they are some of my best friends, it's just that they are not the group of friends that I normally go to clubs with so it was just a little awkward for me and took some getting used to. The next morning I woke up feeling horrible, the only way I know to describe it would be as hung over, but I haven't had any alcohol in about two to three months. In any case it was not fun getting up and going to my 8:30 class on Friday. Even though I felt like crap class was well worth it, since there were very few people there we got to practice our speaking (this is French class by the way).

As of now I am not exactly sure when my ride back home is leaving, all I know is that it will either be on Sunday or Monday. With the free time I have while waiting to leave I should really be doing the homework so that I won't have to do it later. Guess I will start on that once I finish this post. Right now I am just reading some C++ books and working on SPOJ problems. I have solved three more problems the only issue is that I need to find a way to improve my method so that I can fit in their ridiculous time constraints.

Well I am going to post my solutions to some of the problems in the previous post.

1:
Choose , then by the mean value theorem there exist an such that . From the given it follows that , and being uniformly continuous trivially follows.

2:
part 1: Since is continuous at , for every there exist a such that when . Now choose an and its corresponding , then
. Thus is differentiable at and .

Part two follows with ease.

6:
Let , so is also differentiable on , and . Thus there exist a such that and when and . Since is compact, we know that attains a minimum value somewhere on the interval; and because it is differentiable on this interval its derivative at this point is 0. So there exist such that .

Analysis Midterm

2008-03-06T00:15:00.009-05:00

Well I had my undergraduate analysis midterm today. I think it is pretty safe to assume that I dominated that test. When I first saw the test I began to worry, but as I started to work on the problems thing began to settle down. The test only covered material from the chapters on differentiation and integration.
Here are the problem statements as I remember them, I might post my solutions later on.

1:
If for some interval , show that is uniformly continuous on this interval. (Note that need not be closed, or bounded)

2:
part 1: Suppose that is continuous at . Prove that is differentiable at .
part 2: Define a function by if and if . Find the value of and prove your result.

3:
Define when and 0 at the origin. What is the minimum value of that causes to be bounded. Also for this is continuous at 0? Prove your result. Finally characterize the values of such that is continuous on .

4:
Prove that if and only if for every there exist a partition such that .

5:
Suppose that is continuous on , and . Prove that,
.

6:
Let be differentiable on the closed interval such that . Prove that there exist a such that .

As you can see, nothing really difficult about the exam. I don't know why I panicked at the beginning, maybe I was anxious or something.

Miller-Rabin and Primes

2008-03-04T11:03:00.003-05:00

For those of you who do not know, Miller-Rabin is a probabilistic algorithm for testing the primality of numbers. This is different from a deterministic algorithm since with Miller-Rabin there is a change that even if the test says a number is prime that it is in fact composite. However, we can make the probability of this happening so small that we are not worried. On the other hand, if the algorithm says that a number is composite then there is no doubt that it is so.

Here is how the algorithm works. You are given a number and wish to find out if it is prime. So we choose a random integer . First we compute , if this is not 1 then we know immediately that is not prime. If this is in fact 1, we then proceed to calculate where is an odd integer. Next we calculate , if this is we choose another random integer. If it is not then we proceed with the following "cycle". Let and continue to iterate in the following manner, , until . If none of these , then is composite. But if one does satisfy this criteria then is a probable prime.

Now for the reasoning behind the algorithm. From Fermat's Little Theorem we know that where is a prime and . Using this and a few other techniques we can see that we must have that . Now if is a prime number then is a field and thus there are only 2 square roots of 1, namely 1 and negative 1. Thus if none of the is equivalent to negative 1 modulo then we have found a third square root and can immediately conclude that is not prime.

It can be shown (not it this post) that after running the algorithm with "testers" (the random integers) which all point to being prime then the probability that is composite is . Also the algorithm has runtime of where is the number of testers. It should be noted that this can be improved to if we use the fast Fourier transform to do the multiplications.

Well below is my C++ code for the Miller-Rabin algorithm.

//a plays the role of N and b is the tester
bool MR(long long a, long long b)
{
if(gcd(a,b)!=1)
return false;
unsigned long long Y;
int B=0; //a-1=M(2^B)
long long M=a-1;
while(M%2==0)
{
B++;
M=M/2;
}
Y=RS(b,M,a); //I use repeated squaring, instead of FFT, to calculate b^M
if(Y==1 || Y==a-1)
return true;
int j;
for(j between 0 and M) //this is not real code it just did this so that it would show up in blogger
{
Y=RS(Y,2,a);
if(Y==a-1)
return true;
}
return false;
}

Yes I know this looks ugly (thanks a lot blogger) but it is still readable. Below is the code for the repeated squaring function.

unsigned long long RS(long long a, long long b, long long c) // a^b mod c
{
if(b==0)
return 1;
if(b%2==0)
return (RS(a,b/2,c)*RS(a,b/2,c))%c;
if(b%2==1)
return (a*RS(a,(b-1)/2,c)*RS(a,(b-1)/2,c))%c;
}

This algorithm calculates in time.

Well if any of you are compelled to try using this here are a few cool "easy" problems you can try.
Prime Generator
Prime or Not
(Note: Using Miller-Rabin might not be the best method to solve both of these problems)

Dodged a Bullet

2008-02-26T13:47:00.003-05:00

Well this is the fist time I have managed to avoid the "blah blah blah just friends blah blah blah" conversation with someone.

This is all attributed to my decision to become more assertive/definite when it comes to making decisions. Before I would just be indifferent about most choices when someone else asked me make a decision. It wasn't that I didn't care what we did, it was just that I did not feel comfortable calling the shots because I would feel as if I were imposing my will on them. I guess this also might explain a few other aspects of my life, which I will not divulge into on this blog. In any case, I was talking to the girl that I had a small crush on a few days ago. I had known her for a while so I knew there was a pretty good chance that I had been placed on the "shitty ladder." (some people refer to this as the friend zone) Regardless I decided to find out weather or not my intuition was correct. Since I knew that I didn't want to have the talk which was outlined at the beginning of this post I went about gathering the information in a more subtle manner. Either way I got what I was expecting but wishing would not happen. So I have given up on pursuing that relationship any further.

It was not until today that I realized just how close I had cut it. I was talking to her and she mentioned that she was going on a date with some guy. This only a few days after asking me for advice on how to tell someone she only liked them as a friend, but not hurt them. Honestly, she was asking for the impossible. It's understandable that she would not know just how unrealistic this is because she never been, and most likely will never be, in the other person's position. Well I gave her an honest answer, which she seemed to take quite well actually.

Well I am glad that this will no longer be an issue. I can finally move on and not have any regrets about what could have been. Sorry if you are reading this post and it seems that things don't like together very well, I am just writing as things pop into my head.

Until next time. I am off to do more programming.