My personal statement essays for my Berkeley application.

```Describe the world you come from — for example, your family, community or school — and tell us how your world has shaped your dreams and aspirations. (630 words available)

The most critical component of my upbringing was my first ten years of education at a Montessori community school. Having the freedom to manage my own time in the classroom from an early age cultivated my interest in independent studies and catered to my love of Science and even made my love independent pursuit of knowledge part of what it is to be me. My interest in the Sciences, especially Astronomy and Physics, was sparked in the 6th grade when one of my teachers introduced us to a new book, Universe, which I immediately to read and soon after, convinced my parents to buy. This exposure to cosmology began my interest in understanding the complexity and immensity of the universe, and in learning the means by which we understand the universe: science. The most important lesson this environment taught me, however, was that one can only be intellectually satisfied when they follow their interests and stick with them despite discouragement from peers or even teachers.

At Montessori, I also learned the value and importance of a strongly bound community and the role of trust in the learning process. Montessori’s inclusion of students from three grades in every classroom taught me that the intellectual playground is an even platform and that any subject can be understood at any age. This reinforced my interest in independently driven study of Physics during my elementary school years. Additionally, Montessori’s treatment of teachers as general guides to learning rather than instructors designated to one subject or another allowed me to see the connections between subjects and gave me access to multiple perspectives on mathematics. I also believe that Montessori was enormously important in developing my visual interpretation of Mathematics; a unique outlook that has enabled me to make insights otherwise impossible.

To this day, my interest in Science has prevailed. I have completed many independent projects and I’m still driven by my passions. (Something like that).

There are three constants: a,b,c. If for only each unit of c can the amount a be subtracted from b, what is the relationship between a,b,c? Hint: The values are tangible (i.e. representative of something real).

Tell us about a personal quality, talent, accomplishment, contribution or experience that is important to you. What about this quality or accomplishment makes you proud, and how does it relate to the person you are?

How I approach learning (370 words)

“It is a miracle that curiosity survives formal education.” - Albert Einstein.

By the beginning of my sophomore year in high school, I had become intensely dissatisfied with the rote, mundane methodologies of conventional education. I was tired of giving priority to the topics on which I was going to be tested. I was unfulfilled by my unquestioning acceptance of knowledge. Ultimately, I was afraid of becoming just another cog in the machine. I decided I was going to learn my own way.

This personal reformation was the result of questioning the personal value of receiving a good grade. I realized that I had been aspiring to meet someone else’s standards and ignoring what was truly important: my learning. A more accurate way to gauge personal progress was through introspection. When I finally began to question my own progress, I discovered gaps in my understanding covered by a carefully placed film of facts. This discovery led me to my new and current goal: to fill those gaps with well-founded understanding and to ensure that no more form as I continue my formal education.

In the interest of creating and maintaining a concrete foundation of understanding, I now seek a visual and intuitive understanding of rules and concepts. I glean far more by pursuing this understanding independently than by simply learning and accepting the common proof or explanation. My results and methods are personal and thus most in tune with the way I think and reason. They are in the words I best understand: my own. This personalized understanding sometimes allows me to provide the unconventional outlook necessary to solve a problem simply whose solution would be more complex with the mainstream approach.

In retrospect, the work I am the most proud of and that I have found the most enjoyable was the work I completed in the pursuit of this personalized understanding. I know this work is unique and my understanding is profound. It’s not the same essay that the past five generations have written, nor is it just another annual class project.  It's the work that was formulated, executed, and completed by only me. It has my personal element instilled in it, my cognitive fingerprint.

If you wish, you may use this space to tell us anything else you want us to know about you that you have not had the opportunity to describe elsewhere in the application. (550 max.)

The following summaries of some of my larger scale independent projects will show how I have supplemented by formal education over the past few years.

I wrote a program that takes the friends of any given Facebook user and stores the list in a database and subsequently takes the friends of each of their friends (eliminating mutual friends) in order to discover the rate of growth of the network after starting from a given node. The objective was to compare rate of growth to the postulated 6 degrees of separation between any two individuals. Additionally, I generated formulas to compare the interconnectedness of a node and its connections, of a given section of a network, and of an entire network.

Analyzing the Network of Words

Similar to the Facebook network analysis program, I wrote a program that uses words listed as synonyms in a common dictionary resource to form a network and then calculate the number of words that can be reached from any given word through its synonyms, and its synonyms' synonyms, etc.

Accidental discovery of the normal distribution curve

In an attempt to understand the nature of permutations, I found all the permutations of a four-digit binary number (0001,0010, etc). I noticed that if I tallied the number of times a given number of 1’s appeared for each permutation, I would get a much higher occurrence of two 1’s than four or zero 1’s. I also found that if I graphed these tallies, the results had a bell shape. I subsequently wrote a program that does this tallying for a much longer binary number and found similar results. I hypothesized that if I were to take the limit as the length of the permuted binary number approached infinity, I would get a perfect normal distribution curve. When I brought this hypothesis to a math teacher at my high school, he said it was valid and pointed out that I had been calculating rows of Pascal’s triangle.