My personal statement for applying the BISP

Dear admission officer,

I come from China. I have research interests on mathematics, physics or AI, but I dropped out of college five years ago due to the bad teaching, while I still keep studying alone, I am seeking an opportunity to achieve my dream. I write to tell my case and want to know if I am qualified to apply the BISP. This mail is almost a personal statement, and I know one requirement for the personal statement is “no more than one page”, but I think my situation is special, so I apologize for the following content is a little longer.

While I have not finished my calculus learning, I have spent a lot of effort investigating the foundation of mathematics, how mathematics works (based on axioms), where mathematical theories originated, how mathematical theories evolve, etc. Besides mathematics, I am also experienced at Python programming and interaction design, the latter is helpful for me to write readable and easy-understanding expository calculus essays, I would talk it a bit more in the following.

I think there are few good textbooks on Calculus written in Chinese for beginning students, most of the textbooks put too much emphasis on rigor, while the rigorous presentation is difficult to grasp and obscures the understanding, so many students struggled with the course. I suffered the same difficulty when I started learning Calculus on my own. Fortunately, I finally found a very good book suitable for self-study - “Calculus: An Intuitive and Physical Approach” by Morris Kline. Although I have found my way to go on my Calculus learning, many students still struggle with the course, thus I feel a sense of mission to help ease the learning of Calculus for our country’s students, so I started to write expository essays on hard topics of Calculus or Real Analysis, and also created a WeChat "public account"（named 高数变简单） to push my new expository essay to the subscribers, up to now, there are 3074 subscribers, below are part of the user analysis statistical charts(translated into English by Google). 

I have written 14 essays(all written in Chinese). A Calculus learning guide essay written by myself was viewed 50287 times, an video tutorial on explaining the notation dx, dy, differentials and derivatives was played 5.8 thousand times, an essay on constructing the number continuum in an intuitive but still rigorous approach was viewed 8125 times. Another worthwhile mentioning essay is about proving the L’Hospital’s Rule, which was viewed 11821 times, it was because I am not satisfied with proofs presented on three commonly used chinese Real Analysis textbooks(they all used hard devised special tricks to help the proof, while I think they should give constructible and informative proofs) so that after spending a lot of effort, I figured out my satisfactory proofs.

Besides my expository essays, you can also assess my academic potential according to the questions I asked during my Calculus learning process, you can view them on my Math Stack Exchange page, a recent review of them makes me more confident on my academic potential. I think I am good at asking deep questions, so sometimes one can say I am learning Real analysis instead of Calculus, although I am actually learning Calculus. These days I am revising my essay(mentioned above) on constructing the number continuum because I have learned more and realized the drawbacks of the essay. Two famous construction of the number continuum was historically done by Georg Cantor and Richard Dedekind respectively, but their constructions are independent of geometric magnitude, and the definition of irrational numbers are not a single symbol or a pair of symbols, such as a ratio of two integers, but an infinite collection, so their theories are difficult to understand, as mathematician Hermann Hankel(1839 - 1873) criticized: “Every attempt to treat the irrational numbers formally and without the concept of (geometric) magnitude must lead to the most abstruse and troublesome artificialities, which, even if they can be carried through with complete rigor, as we have every right to doubt, do not have a higher scientific value.” Therefore I decided to try to put forward an intuitive but still rigorous construction of the number continuum(the work has not been done right now). Another question I am about to investigate is “why Leibniz’s indefinite integral notation is superior?”, the question originated from another question “why dx is necessary in ∫f(x)dx?” I have considered. 

Although I received many thanks from my readers, sometimes I feel upset - I am able to help students with my essays, but I cannot find one who can help me achieve my academic dream. There seems no other ways to achieve my dream in China except entering colleges again, but I am not satisfied with the teaching methodology and the course arrangement of most universities in China. As mathematician Paul Halmos said :“The only way to learn mathematics is to do mathematics.” I like learning by researching or doing. However, there is not enough time to take this approach if you are a Chinese college student, one reason is that you have to cope with plenty of subjects. I also don’t like the way a teacher teaches you everything even the simple ones during his lecture and rather doesn’t trust our self-study ability. One ideal learning scenario I am eager for is that we first study by ourselves, then the teacher comes to check our grasp of the knowledge, offer guidance if necessary. We should also have the opportunity to communicate with our classmates and teachers. I wonder whether Berkeley could offer such a learning environment.

I had written an application letter to Brown University about seven years ago (following is the screenshot of the email with Brown University). 

They kindly offered me an opportunity to learn there, but unfortunately I was unable to go in the end, there were mainly three reasons: (1) I didn’t talk the opportunity with my parents, relatives or teachers, and neither did I seek help from them, because I found it was hard to tell that I got the chance due to disappointment with my college education at that time. (2) As a student grew up in the countryside, I had never traveled alone before, so I was not brave enough to go to America. (3) Compared with the high living cost in America, I think my family was unable to afford the fees needed in America.

I feel pity on failing to seize the precious opportunity to pursue my dream. After years of struggle with my academic dream, I am now brave enough to go for achieving my dream if a similar opportunity presented again. Please give me a consideration on joining the BISP, I am confident on my academic potential. I will go on my math study for at least three years even if I was rejected this time.

Sincerely,

Zhao Lee