Uberman's Sleep Schedule

For those of you that do not know what Uberman's sleep schedule is I advise that you go look it up on Google or Wikipedia or just continue reading this post.
This is how the sleep schedule works. You take 20-30 minuet nap every four hours. Lets say that you chose to take your naps at 12, 4, and 8, the nice thing is that no matter what times you choose the time are the same regardless of am or pm. Obviously to stay on this schedule you need to be able to either adjust your daily schedule or take care in choosing nap times. Also at first it is going to be difficult to adjust from the normal mode of sleeping, where you get all your sleep at one time. Some sources claim that it takes about a week to get adjusted and even then you still need a lot of self discipline to remain on schedule. According to "Steve Pavlina" this purpose of this schedule is to help the user enter what is known as R.E.M. sleep faster.
After reading more about this from various sites and my friend's personal account of trying it, I have decided that I would like to try it. Unfortunately I will not be able to start this intense task until I am done with finals because right now I do not have a week to "waste" while getting adjusted to the new sleep pattern. As things are now I plan to start the week between finals and the start of summer classes. Hopefully I can find a job where I will be able to fit my naps in during my lunch hour. The only foreseeable to actually doing this is going to be convincing my mother that I will be "perfectly fine". Once I get past that staying awake is going to be a pain since I do not have anyone else who is willing to do it with me as of right now. Hopefully once I start I will not miss any of the naps because that will really fuck things up as you can imagine.
Wish me luck and if you are interested in doing this with me and will be in Gainesville over the summer feel free to let me know. I know that doing this while studying for the first Actuary exam isn't the smartest thing ever but the exam isn't till August so by June I should realize if this is for me or not.

Integration Technique

Today I was helping out at the Buchholz calculus team practice and there was only one problem that they had no idea how to solve. The problem was similar to the one below.

I have left of the limits of integration because for this kind of problem they are not very important. There are several ways to proceed when solving this, first you can write the denominator as one sine or cosine function. This is the most obvious way to proceed but is certainly not the best, I am not sure where it will lead but just with a little mental computation you should quickly realize that you have not made the problem any easier. The method I suggest is that you make an appropriate substitution. When I first mentioned to them that there existed a convenient substitution they looked at me in disbelief. I suggest that you try and think of the substitution before reading any further.
The substitution I am referring to is,

After some algebra and trigonometry you will arrive at the following,
After you replace each trigonometric expression with its corresponding algebraic one you should have an integral that is much easier to solve.

Peanut Butter Jelly Time

SHAKE, SHAKE, SHAKE,...

These past two days were a very much needed break from studying and stressing over REU. First off I did not get accepted to the REU program, but I am not too upset because the program was designed for students with more mathematical experience. This summer I will spend taking classes either at FSU or UF. Most likely at FSU assuming that the math department allows me to take Linear Algebra and have it count towards my major; if not then I will have to stay in Gainesville and find a summer job to help cover the cost, since my scholarships only pay for the spring and fall semesters.
Now that I have discussed that it is time to get back to the original topic.
On Friday I went to the Hands Down Showcase, which was a hip-hop dance competition. All of the performing groups did an awesome job. Yes Trina, I'll admit that the Assins performance was good, but only on a performance level. I think Sarah's description of their dance is the most accurate one that is possible with the English language (the description was: SEX, not sexy, it was sex). After the Hands Down event we (Trina, Joe, Gene, Sarah, and I) decided to have a wholesome meal at Subway. We had conversations about things I don't remember anymore, I hope that none of them were about anything serious. Boredom set in so we decided to go to "Club Joe". That was fun until we had to turn down the music because some girl on the second floor complained that our music was too loud. Her exact words were, "Could you turn it down, or at least the bass. I mean EVERYTHING IS FUCKING MOVING!" Honestly, what could she possibly have been doing that would require silence? It was Friday at around 11p.m. she needs to get out and have some fun. Well after she left we had some fun with the lights, hopefully no one in the room was prone to seizures because then I would feel bad about us putting them through that. We even watched about three or four episodes of Happy Tree Friends, if you do not know what that is then I suggest you go to YouTube and find out. Sarah had the best reaction to these videos. Trina was laughing at them which was something that I was not expecting at all. Later at around 3a.m. on Saturday we decided to watch Battle Royal at Beaty in Matt's room. The movie was somewhat disturbing, but overall I thought it was alright, definitely something that I would consider watching again in the future. The movie was bases off the manga which was bases off a book. I don't think that I will ever read the book but if I can ever find the manga I would love to read it and hope that it will help to clarify some of the things in the movie. By the end of the movie everyone was tired so we decided to call it a day and all went back to our respective rooms. I got back to my room and fell asleep around 5:00a.m.
After I woke up I went and saw The Man of Mode with Trina, Sarah, and Gene. The plot was somewhat original and very humorous. The only problem was that since I am not very good with names I do not remember the names of all the characters, I had to identify them by how they acted and the clothing that they wore. Medley turned out to be my favorite character in the whole play, because it was through him that many of the events were set into motion. Also everyone in the play was almost always willing to share their "secrets" with him. After watching the play we went at ate then went back to Weaver and watched a few episodes of Robot Chicken and Aqua Teen Hunger Force. The days events were concluded with about an hour of pool at the Reitz.
Well I need to head to bed now since I have to wake up early for church tomorrow.

Video 1:


Video 2:

A Well Spent Day

Today was the first time in about a month that I have actually had the time to do math problems that I actually find interesting. When I say I have time I mean that there was not a test that I needed to be studying for, or an assignment that must be completed. Sure I have a differential equations test on Friday, but it's going to be easy so no need to waste time with studying for that.
I started off the free time by solving this problem;


If you are unable to read the above problem then just click on it and it will be displayed in a larger format.
The problem did not require too much insight. It was basically a routine exercise with Lagrange multipliers. Also if you did not know any calculus the problem was still solvable thanks to the Cauchy-Schwartz inequality. This about two minuets to think up the solution and then another five to write it all down.
The next three hours were spent doing problems that were more challenging and took a little more insight. However, there was one problem that took the majority of the time. The disappointing part is that I was not able to solve the problem.



I was able to develop a recursion formula and initial conditions but after this point i was not able to generate a closed form. My answer is split into cases depending on the parity of n and then it has the solution in the form of a product of terms.
Hopefully, I will be able to solve this problem, and the other problems on the three sheets (a total of 29 problems) before the end of the semester. This is the second set of problems that I am attempting. In the first set I was able to solve six problems on my own, I needed help on four, and have incomplete proofs for one. The source of the problems is the first compilation of 100 Mathematical Problems by Yang Wang, a professor at Georgia Tech., so I am working on the first fifty-one problems, and find it very rewarding even if I have to ask others for help. Asking for help and learning something new is better than being clueless for eternity. Obviously I only ask for help after I have put in a considerable amount of effort (normally a weeks worth at least).


Well I need to sleep now, early class tomorrow, so I shall leave you with a parting quote.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of a sculpture.
-Bertrand Russell