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IMPORTANT NEWS November 22, 2008

Posted by putnam120 in Life Events, Math Related.
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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.

Minor Incidents November 2, 2008

Posted by putnam120 in Life Events.
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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 October 27, 2008

Posted by putnam120 in Life Events, Programming Related.
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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 October 19, 2008

Posted by putnam120 in Life Events, Programming Related.
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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.

Blinded September 26, 2008

Posted by putnam120 in Life Events.
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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 September 21, 2008

Posted by putnam120 in Life Events, Math Related, Programming Related.
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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 September 13, 2008

Posted by putnam120 in Life Events, Programming Related.
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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).

Shopping Can Actually be Fun August 15, 2008

Posted by putnam120 in Life Events.
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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 August 11, 2008

Posted by putnam120 in Life Events.
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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.

From the Integers to Infinite Series July 30, 2008

Posted by putnam120 in Life Events, Math Related.
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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.

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