Wednesday, October 17, 2007

Putnam - 1

Well I have been spending between half an hour and one hour every day solving Putnam problems. Actually I should say attempting to solve Putnam problems, but it is the same concept I suppose.

Here is the most recent problem I have been able to solve on my own.


Overall I would say that it took me a little over an hour to come up with this solution. I have looked at other solutions and have yet to find one like mine which kind of makes me feel proud. It should be noted that in the following proof I leave out showing that the sum does in fact converge absolutely, something I would have done if under actually testing conditions.


Well the next time I manage to actually solve a problem that I think is worth posting I shall do so. Hopefully that won't be too far away.

Thursday, September 27, 2007

Faces Without Names

It happens to everyone at least once in their life. They are at an event with a friend and then they are suddenly introduced to a large group of new people. You honestly know that there is no way in hell you will remember everyone's names but you pretend to do so. Then after five minutes or so you realize that the only names you remember are those of the last person to be introduced and the member of the group you found most attractive. At the end of the evening when everyone is heading home you think to yourself, "Thank God, there is a chance that I will never see them again , and thus not embarrass myself by not remembering their names."
Well just when you thought the worst was over you run into at least one of the group members in public, and you are not with your friend. Damn they spotted you. Your mind races trying to remember their name, but with no success you resort to saying something along the lines of "Hey how are you?" and skillfully conduct the conversation in a way that lets you avoid using their name.

Well things like this happened to me a few weeks ago. While I was walking from my dorm to flag football practice I ran into someone who knew me. Now since I didn't recognize his face I was almost certain that we had never actually formally met. Well as it turns out we were both members of MAO in high school and he recognized me from there. Needless to say I had no idea who he was because he was not on stage often if at all. After talking to him I got to thinking about just how many people know me because of MAO. I'm fine with it if I am actually friends with the person now and talk to them on a semi-regular basis but it just scares me a little if I don't really know the person.

Classes are going alright so far. French is a lot of work, I am really beginning to wish that I had just taken either Spanish or Portuguese. Learning vocabulary is just taking up way too much time. It is becoming difficult to find time to work on programming or relearning Linear Algebra and Elementary Differential Equations. At least I still have the weekends. Putnam practices start tomorrow [a little late in my opinion but not much I can do about it, so I started my studying a while ago] and it should be interesting to see who will be there. Hopefully it will be more structured that it was last year where the professor really didn't have a plan for what material would be covered at what time. I would really like if my Number Theory teacher ran the practices since he is very enthusiastic and seems to communicate better with students. Sadly however, he is very busy so it is going to be extremely unlikely that he will be running the practices this year. Maybe next year will be different...or so I hope.

As things are now I am still uncertain about what I really want to do over the summer. If I have the choice to choose between attending and REU or and Actuarial Internship (and I hope I have to make this choice later in the year) I am not sure which I would choose. Really I suppose it comes down to which company/companies offer me internships and which REU(s) I get accepted for participation. In terms of internships I only have a list of two companies I would really like to work for, one is a consulting company and the other I like because of its location (yes there are other reasons for liking this company). In terms of REUs I would like to do one in any of the following fields (in order of preference); financial mathematics, stochastic processes and probability, differential equations, and number theory.

Wednesday, September 12, 2007

True Tolerance

I am not aware of how many of you actually watched the Emmy Awards, I surely didn't, but there seems to be some big story about Kathy Griffin and a Jesus remark. Before I continue I would like to warn you that some people might be offended by what they read and should continue with caution and an open mind.
After seeing the story headline on various sites I finally decided that it might just be worth my time to read one of the reports. At this time I was at Yahoo so I clicked on the "Griffin in trouble over 'offensive' remarks" link. For those of you that were too lazy, or were just so adsorbed in my post that you neglected to click on the link and read the article for yourself, you are probably wondering, "What could she possibly have said?" I know because that is exactly what I was thinking after seeing the headline millions of times. Well here it is;

"A lot of people come up here and thank Jesus for this award. I want you to know that no one had less to do with this award than Jesus, suck it, Jesus. This award is my god now."
If it is not totally obvious from the quote, and it should be, this is what she said when she accepted her Emmy. Now I am sure that opinons on this comment are very polar, and it is easy to understand why. On one side you have the people who are either indifferent and/or find it funny, then you have the die hard "Christians" who are outraged.
Personally I fall into the former group. I am not sure if this is because of my sense of humor, failing sense of religion, or realizing that there are better things to get enraged about. Sure I'll admit that I do find it funny and you know why because it is true. Just about every time you see someone win one of these awards they go up to the stage and when they open their mouth they just regurgitate typical, "Oh my gosh I never expected to win this...this is one of the best moments of my life...I would like to thank;(insert names of produces, directors, family members) and most of all God..." I for one am just plain sick of this verbal vomit. We all know that they had that speech, and a rather poor one at that, when they learned that they were nominated. As for those who chose not to prepare a speech and honestly wing it, I say it is even worse because it not only shows a lack of preparation but also an astonishing lack of originality.
It should be noted that I am not saying that her method for breaking the mold to go was the right way, but hell it did the trick and managed to piss off some people at the same time. The same people who are always pushing for tolerance. Sure her comment wasn't tolerant towards most steadfast Christians but who are they to judge her and not be open to tolerating her opinion?
This reminds me of the MTV incident with Kanye West that occurred after Hurricane Katrina when he said, "George Bush hates black people." Now yes this story did get a lot of coverage but I don't remember reading about large groups of people that were upset with him, or even being outraged by the media's constant replaying of the clip with out edits. Whereas Kathy Griffin's Jesus remark will be edited out of just about every future television broadcast of the Emmy Awards.
Now this might just be me but shouldn't we be a little more concerned when a well known media icon, who's words reach many different audiences, claims that the leader of our country "hates black people", than we should be when some comedian, who makes a living by getting under people's skin, says "suck it, Jesus"?
I wonder what kind of response she would have gotten if she had instead said, "suck it, ____", where the blank is filled with one of the persons she beat in order to win the award, or even some other religious figure such as Muhammad, Buddha, or Abraham. These are the kind of things that make me wonder just how tolerant our society is, and if we are "tolerant" because it is what we truthfully believe or if it is because if we are not perceived to be tolerant we wil be looked down on by the rest of society.

Saturday, September 01, 2007

Dawn of the First Real Week Back

Now that the first real week of school has come to a close I new have a better gage of exactly what I am in for this semester. Some classes seem as if they are going to be a little easier than first anticipated, while others are going to be just as much work.

To begin with it French looks as if it is going to be easier than I thought. This does not mean that I won't put in as much time, it just means that my A will be even higher.
Wildlife Issues is alright I'm still not sure if I absolutely need to buy the $70 course packet since he did not make it seem like it was required.
Number Theory and E.E.C. is still a toss up because no one has the book yet. This is bad planning on the professor's part because he did not tell us what book we would be using until the first day of class, and it turned out that Amazon was sold out. So it will be at least another two weeks until everyone has their books.

Well in French I randomly met this girl who went to the same high school as me. One day she walked into class and I thought to myself, "wow she looks really familiar, have I seen her before?" We look at each other for a second before she says, "Did you go to...?" Well it turns out that we were most likely in the same Spanish 3 class my junior, her sophomore, year of high school. Then through her I met another girl who went to school in the same county as us but a different high school.
In Wildlife I have met one new girl. She's a first year student majoring in Finance. Seems like a nice person and on top of that she's really cute. Yeah yeah I know, you shouldn't judge a book by its cover, but really who wants to sleep with a book. No really I've talked to her and she's really cool.
In Number Theory and E.C.C. I really only know one person personally, and she is the person who talked me into signing up for the class to begin with. Most of the other people I either recognize their faces or know of them because I have heard their names often in the past.
Advanced Calculus on the other hand I am surprised at the number of people I know in there. At least three of the students were in my Linear Algebra class last summer and then there are people I know either from Pi Mu Epsilon or Nu Alpha Theta.

AASA (Asian American Student Association) had a presentation last Friday. All of the performances were spectacular. Sadly many of my friends were in the show and I was not able to tell mainly because I did not have seats that allowed me to clearly see their faces. I can't wait for the next general AASA event.

Saturday, August 25, 2007

First Week Predictions

What follows are my predictions about each of my classes.

French 1: Learning a new language should be fun. There are only a few foreseeable problems that I believe this class will give me. One is learning the new pronunciations and not confusing them with Spanish pronunciations. Also spelling will be a major problem early on because some words have letters that are not pronounced, which will take a lot of getting used to.

Wildlife Issues: Seems like it will be an easy class if I keep up to date with the work or just work with others since all the assignments are online it seems.

Number Theory and Elliptic Curve Cryptography: Lots of work considering that I did not take the Elementary Number Theory class in the spring. Professor is really cool and the topic is interesting.

Advanced Calculus 1: Working through Rudin so that right there lets you know that it isn't going to be a walk in the park. On the first day of class we got the "...this class is where some of you will start to hate math..." speech. I have already worked through the first and a majority of the second chapters on my own and have been frustrated at time but not to the extent of ever wanting to quit math.

Wednesday, August 08, 2007

On to a New Year

Yesterday was my last day of official summer classes. All that remains is for me to get back my test and pack.
As far as I can remember this is one of my best and most enjoyable summers ever. This is however, not saying that it didn't have its low points because that would just be foolish to assume. The first few weeks were easily the least interesting since I had not started working at Buchholz and my linear algebra class was going over material I was already familiar with. Since I am currently not feeling very creative I think that I will just give general overviews of each aspect of this summer, and hope that I do not leave out anything important.

WORK:
Started working with the pre-calculus group at Buchholz around June 4th. It was obvious from working with them and seeing their past performance at competitions that they were the strongest group. This made the job more interesting since whenever they had a question I was sure that I was going to be one of the more difficult questions on the test we were reviewing. I'll admit that there were times when we would get to a problem that I did not know how to do so we would either talk through it or look at the solutions. There would also be a questions to which I would know one method of solving, but my method would be very inefficient and banked on the hope that you had at least five minutes to dedicate to the problem. Working there was in some ways a break from the usual theorem-proof format I have grown to love. Another plus was that I got to solve problems that did not assume knowledge of calculus. So I had to rely on other tools, such as trigonometry, geometry, basic formula manipulation, and some basic knowledge of sequences. Just in case you were not aware Buchholz places first at the National Mu Alpha Theta convention in Tampa, Florida. Yes that is right, they beat Vestavia Hills. The Theta, Alpha, and Calculus teams all places first in their respective divisions, so they pretty much mopped the floor with Vestavia.
Of all the sections I feel that this is the best place to insert the information about my studying for the P/1 actuary exam. I am feeling pretty confident that I will pass. I have taken numerous practice exams and done other online problems. Of all the practice exams the lowest score I have ever gotten was a 20/30, where I usually average around 24-25/30 correct answers. There are just a few topics that I am not very familiar with but they almost never show up, this is not to say however, that I will not at least look them over before the actual exam. A few days ago I was going to watch the review DVD that I have but unfortunately the DVD player software on my computer is not working properly. It displays the images but it refuses to play any audio which is just slightly important. Well I am going to watch the DVDs during my week between summer and fall.

CLASS:
When I started this class I was not entirely sure how difficult it would be, since I had many conflicting reports. Some would say it was "a joke" while others would swear that it was the most difficult class that they have ever taken. I was pretty sure that I would agree with those that were saying the class was a joke because I knew the kind of mathematical background they had and knew that it was very similar to my own. However, I was not going to make any assumptions too early on because I did not want to pay the consequences if I happened to be wrong (yeah I know me being wrong, it's almost laughable). After the first few weeks I came to the conclusion that this was in fact going to be an easy class. Now just because I found it to be easy does not mean that I did not learn a lot. When I say easy I mean that the class moved at a rate that allowed me to work ahead and cover additional topics that were either glossed over or skipped entirely in class. Each person's grade in the class consisted of three exams, homework, and classwork. Homework and classwork are pretty self explanatory so I will not bother talking about them. Each of the exams had the same structure; a true/false section, 2-3 application problems, and then the rest would be recreation of proofs. Now for those of you that know me, I HATE recreation of proofs since it does not show that the student actually understands the material, but rather has a good memory. There are however, some cases where proof recreation is important, and this is when you are asked to recreate the proof an important/"classical" theorem. So I would have rather the proofs on the test have been things we had not ever seen before but would be able to tackle using what we already knew. O well I guess this is asking just a little too much for this class since even with the recreation people were still having problems.
Hopefully, the other upper level undergraduate classes will not give me this same feeling of dissatisfaction with the test. Well I only plan to take three more undergraduate math classes; the other eight or nine will be graduate classes. Needless to say I got an A in this class. Even though it was easy I didn't realize just how much I had learned until I started answering questions from other students on the Art of Problems Solving forum.
For those of you that plan to take this class (MAS 4105) pay special attention to the chapters on diagonalization, linear transformations, and inner products. Personally I found these to be the most important chapters in my understanding of linear algebra. Not to down play the importance of the other chapters, you should by no means disregard them since you need them to build the theories used in the mentioned chapters, but in comparison I found them to be more "small details" necessary for a fuller understanding.

SOCIAL:
Well I played more pool that I thought possible. Yet due to the inconsistent nature of my playing I never seemed able to get noticeably better and stay that way. Regardless playing was always fun. Then there were the seven or so weeks that Ann was here; we pretty much watched a different movie every week...now weather we were watching legal copies or not is another thing, and shall be left for discussion in a different post. PARTIES! No more needs to be said for fair of what information might get to who. Spent a lot of time hanging out with Nancy, JP, Mike, and others who I didn't get the opportunity to hang out with as much during the regular school year. Just in case any of you out there are drinkers of that lame thing called whole milk I am sorry but your beliefs are wrong. You need to turn away from the red cap and come to the light, preferably the side of the green cap but any other color is fine. Actually any color that is not associated with skim or soy milk. Trina finally turned 19 and I still need to buy her a present so if any of you have any suggestion please let me know as soon as possible, thanks. Also I feel that under this section I should place a big WHAT THE FUCK WAS I THINKING AT THE TIME!?! (if you have any idea what this is about then the chances are that you are correct)

Monday, July 16, 2007

Liquids Control My Life

A few days ago I was browsing around Yahoo.com and saw the most outrageous story. Before I start please sit down and try not to laugh too hard. The article headline read "The Most Expensive Bottled Water". Now when I saw this I was expecting to see around $10 per bottle. Astonishingly I was no where close. The actual price for the most expensive bottled water was about $55 per bottle. Now honestly how do you convince people to buy this? I don't remember the product name or the name of the company that made that specific "drink" but luckily there were others on the list. One of the more memorable brands on the list of outlandishly priced water was Bling H2O. Here is a link to their product homepage, BlingH2O. If you happened to click on the "Buy Now" link at the bottom of the page you should see some bottles with their respective prices. Now don't worry if you can't afford to buy the $552.20 limited edition, I am sure that the $20-40 variants will be just as satisfying. Hell it might even be the same as the $1 20oz. bottles that you can buy at just about any vending machine.
If you can manage to find the article on yahoo or with any search engine, you will notice that they sell almost exclusively to celebrities and people in Los Angeles. Just thought that I would put that out there. Exactly what I needed, another reason I would rather live in Chicago or New York, instead of California.
If you are not thinking that it is sad that people are willing to spend $20+ on bottled water, most of that money is really going towards paying for the bottle, then there is something wrong with you. Lets put things into perspective a little. You hear "$20+ for a bottle of water" and you think so what. Now if someone told you that you would have to pay $4 for a gallon of gas, you gather the towns people and march on city hall. Interesting isn't it. Unless things have drastically changes I think that water is just a little, not much actually, more important to sustaining life than gasoline was and ever will be any time soon. So unless you havea master plan to get America free oil then I suggest that you save that $552.20 and either put it towards an iPhone, a PS3, or buying gasoline and a Brita filter.