PS Comments & Suggestions: From Grade School to Graduate Study in Mathematics

[xunoname]

Please comment on my PS and provide your valuable suggestions. Thank you.

In my arithmetic class in grade one, I once was requested to recite the multiplication table. “…five multiply nine equals to forty-five. Six multiply nine equals to fifty-four.” I got into silence suddenly. I was just wondering why five multiply nine equals to the digit reverse of six multiply nine. My silence annoyed my teacher. She said that I was so stupid that I even could not remember the multiplication table.
Anyway, I don’t think I was stupid or not suitable for study. From elementary school to high school, I usually took No. 1 in all kinds of mathematics exams and contests in my city. However, I had two shortcomings, one is that I viewed the world too realistic and could not tolerate any flaws, and another is that I lacked persistence, since I got excellent performance too easily.
In Sept, 1998, I entered the Department of Mathematics, y University. It was not my ideal college. No wonder, I felt a little disappointed and did not concentrate on my study for a while. Nevertheless, I tried to get out of the depression. In my senior year, I planed to go to the US for further study, and I got an offer from x University. However, my visa application was refused. Afterwards, due to financial pressure, I did not seek graduate study in China, but found a job in y University first.
Years past, I had got a lot from my job: working experience, decent pay, promotion. However, they were far from what I want. I like imagination and discoveries, so I decided to pursue a valuable graduate study.
My action was not easy since my job duties and some other things took up much time. However, the pleasure of learning and imagination gave me the necessary motivation and courage. Consequently, I began to look at mathematics from a totally new angle. For example, I noticed that Weierstrass Theorem and the Nested Interval Theorem basically refer to one thing in different ways.
I took GRE sub twice, and got 680 (63%) and 760 (79%) consequently. I had planed to get 90% at the second time. However, I had to help my wife with her PhD study application, MS degree thesis, visa application, and etc. It was August when she successfully went to South Carolina. Furthermore, I was a little nervous at the second time. Anyway, the score itself is not as important as what I learn from the course of my study.
A graduate student in Philosophy once said to me” Mathematics is totally different from other natural sciences, because it is absolute truth, precise and flawless. ” I partly agree with him. Yes, mathematics is a precise science, and it maps to the real world very well. But it is not perfect at this time. Based on some axioms or self-evident truths, we derive theorems by logic reasoning. But this method is not always effective. Sometimes we even can not decide the authenticity of a proposition in our predefined logical system. We have to find answers outside the existed system.
The department of mathematics at z University has many creative faculty members. They are the most precious resources for a graduate student. That’s the most important reason of my application. It is a long way for me to go. At Newton’s time, a genius can master mathematics, Physics, and Astronomy together. But today, only a few people can keep up with the rapidly advancing frontier of knowledge, and they have to devote their whole time to it and specialize in a small area. I am just a beginner at this time, and do not have a fixed direction yet. I also know that my academic background is not the best. But I believe my determination, persistence, and intelligence can help me achieve my goal – discovering more mysteries on mathematics. Yes, I can. I wish sincerely I could study and perform research here, and gain a broad vision of mathematics.
P.S. A writing sample is attached with this statement. It is very simple. But you may take a look at it if you wish.

 

[xunoname]

New version:

It is complex for me to explain why I like mathematics. The internal causes maybe are: A. I like the feeling of discovery and imagination. B. I realize that mathematical principles govern the universe. The external causes come from many resources: wonderful books such as The Emperor's New Mind, by Roger Penrose, Mathematics’s past, present, and future, by Jincai Zhou and Xi Liang, as well as the prizes I won from various mathematical contests. In the 1992 National Olympic Mathematics Competition for elementary school students, I got successive champions of my city in the first round, second round and final. In the 1997 National Mathematics Contests for high school students, I got No. 38 in my province.
My career did not go smoothly. I was good at finding new methods and initial ideas, but I was too realistic and poor in emotional intelligence quotient. In Sept, 1998, I failed in the national college entrance examination and had to go to x University. It was top 40 in China, but was not my ideal college. No wonder, I felt a little disappointed and did not concentrate on my study for a while. Nevertheless, I tried to get out of the depression and gradually found a right path. In my senior year, I sought overseas graduate study and got an offer from y University. However, life struck my again. I was a little nervous and the situation was tough. My visa application was refused. Afterwards, due to financial pressure, I did not seek graduate study in China, but found a job in x University first.
Years past, I had got a lot from my job: working experience, decent pay, promotion. Unfortunately, they were far from what I want from my boyhood. I missed study. Therefore I decided to pursue a valuable graduate study.
My action was not easy since my job duties and some other things took up much time. Luckily, the pleasure of learning and imagination gave me the necessary motivation and courage. Consequently, I began to look at mathematics from a totally new angle. For example, I noticed that Weierstrass Theorem and the Nested Interval Theorem basically refer to one thing in different ways. Furthermore, I began to pay more attention to the meaning of basic concepts and ideas instead of methods and proofs, and I found there are some many connections between different mathematics branches. I became more eager to know the essential beauty of mathematics. It is the most important motivation for my further study.
I took GRE sub twice, and got 680 (63%) and 760 (79%) in turn. It seemed that I had a lot of time to prepare for the second chance. However, I had to help my wife with her PhD study application, MS degree thesis, visa application, and etc. It was August when she successfully went to South Carolina. Furthermore, I was under great pressure at the second time. Anyway, I tried my best, and I learned a lot, both in knowledge and emotion from the course of my study. So I am satisfied with the outcome.
A graduate student in Philosophy once said to me” Mathematics is totally different from other natural sciences, because it is absolute truth, precise and flawless. ” I partly agree with him. Yes, mathematics is a precise science, and it maps to the real world very well. But it is not perfect at this time. Based on some axioms or self-evident truths, we derive theorems by logic reasoning. But this method is not always effective. Sometimes we even can not decide the authenticity of a proposition in our predefined logical system. We have to find answers outside the existed system.
The department of mathematics at z University has many creative faculty members. They are the most precious resources for a graduate student. That’s the most important reason of my application. It is a long way for me to go. At Newton’s time, a genius can master mathematics, Physics, and Astronomy together. But today, only a few people can keep up with the rapidly advancing frontier of knowledge, and they have to devote their whole time to it and specialize in a small area. I am just a beginner at this time, and do not have a fixed direction yet. I also know that my academic background is not the best. But I believe my determination, persistence, and intelligence can help me achieve my goal – discovering more mysteries on mathematics. Yes, I can. I wish sincerely I could study and perform research here, and gain a broad vision of mathematics.
P.S. A writing sample is attached with this statement. It is very simple. But you may take a look at it if you wish.

 

[Vanadium 50]

You should start with asking yourself what three ideas you want to get across. The three I gathered from your essays are:

(1) Isn't sure what he wants to study.

(2) Isn't sure of why he wants to come here. "Many creative faculty members" is very, very vague. Might not want to come here at all - but it's the only place he thinks he can get in.

(3) Good at making excuses.

Those are probably not the ideas you want to put forward. So I would start with writing down the three ideas that you do want to put forward, and write an essay around them.

 

[xunoname]

New version. Please strike me down!

It is complex for me to explain why I like mathematics. The internal causes maybe are: A. I like the feeling of discovery and imagination. B. I realize that mathematical principles govern the universe. The external causes come from many resources: good books such as The Emperor's New Mind, by Roger Penrose, Mathematics’s past, present, and future, by Jincai Zhou and Xi Liang, as well as the prizes I won from various mathematical contests.
In my senior year, I planned to go to the U.S. for graduate study, and I got an offer from A University, but my visa application was refused. Furthermore, due to financial pressure I was unable to seek graduate study in China, instead I found a job at the National Science Park of B University, where I linked to researchers who had inventions or projects which showed commercial and technological promise, and provided (R&D) proposal writing assistance.
Years past, I had got a lot from my job: working experience, decent pay, promotion. Unfortunately, they were far from what I really wanted. I missed the intellectual stimulation of mathematics, so I began preparing for further study.
My action was not very easy, since my job duties took up much time. Nevertheless, I developed a good independent-thinking ability and got a fair score on GRE subject finally. Most importantly, I began to look at mathematics from a totally new angle. To name a few, I noticed that Bolzano-Weierstrass Theorem and Nested Interval Theorem basically refer to one thing in different ways; the essential contents of Linear Algebra are vector spaces and linear maps, rather than linear equations and matrices. Therefore, I began to pay more attention to the meaning of basic concepts and ideas, instead of methods and proofs. Also, I started to seek connections between different mathematics branches, rather than study a specialized field in itself.
A graduate student in Philosophy once said to me” Mathematics is totally different from other natural sciences, because it is absolute truth, precise and flawless. ” I partly agree with him. Yes, mathematics is a precise science, and it maps to the real world very well. But it is not perfect at this time. We derive theorems from axioms or self-evident truths by logic reasoning. But this method is not always effective. Sometimes we even can not decide the truthfulness of an arithmetic proposition in our predefined logical system. We have to find answers outside the existed system. This uniqueness of mathematics makes me eager to know the essential beauty of mathematics, and it is the most important motivation for my further study.
Although nearly every branch of mathematics attracts me, I find the following areas especially interesting: discrete mathematics, combinatorics, and statistics. There are a lot of funny questions unsolved. For instance, is there a general way to quickly determine whether 4-realizable graph with specified edge lengths can be realized in R3?
C University' s Mathematics program offers a wide spectrum of training and research topics related to my field of interest. Xinyu’s work on Goncarov-Type Polynomials and Maria’s work on really Realizability of Graphs left a deep impression on me. The opportunity to learn from them directly would be invaluable indeed. Therefore I wish sincerely I could study and perform research here.
I haven’t got any graduate research experience at this time and I realize that I still have a lot to learn. In the next few months, I will substantiate my knowledge on function analysis and topology, and then read some classical literature on discrete mathematics. I believe I will gradually find a right path.
P.S. A simple writing sample about Combinatorics is attached with this statement.

 

[Vanadium 50]

Let's start with the good. You are very specific in what area you're interested in. Yes, you don't know exactly what, but that's to be expected. Still, you have a direction, which is very good: I can tell that you are not interested in getting a PhD based on work in topology, or in number theory, or analysis.

Now on to areas where you might improve. I still don't really know the three points you are trying to get across. When you studied English, did you study the five paragraph essay? This is a very commonly used form. Basically, paragraph 2 covers point 1, paragraph 3 covers point 2, and paragraph 4 covers point 3. Paragraph 1 is an introduction and paragraph 5 is a summary. I would strongly encourage you to use this form, particularly as it is clear that English is not your first language. If you have never heard of such a thing before, Google it. You'll find thousands of sites.

Next, use simple, direct language. This will help get your point across. Don't be afraid of simplicity. Ernest Hemmingway wrote in simple, direct language and he got the Nobel Prize in literature.

Finally, if they did not ask for a writing sample, do not include it. If they didn't ask for it, it probably cannot help you, and it may hurt.

Good luck!

 

[xunoname]

To Vanadium 50: Thank you very much! Very useful sugggestion!