现在是2013年儿童节过后的第一个凌晨，可能是下午喝了绿茶，果断失眠了。犹豫了很久，还是决定坐到电脑前开始写吧。虽然不比毕业论文的Introduction, 这篇毕业感悟同样很让我伤脑筋。感悟肯定是有的，而且还不少。当然是感慨大大多于领悟。但是我这个人挺别扭的，一方面想娓娓道来自己的心路历程，另一方面又觉得这样做很矫情，无法把这些personal petty things 渲染到我心目中值得郑重写下来的程度，就这样一直很纠结.....嗯，还是写那些我认为必须要写的吧(至于什么心路历程这种单单看这四个字就让我的理智浑身不舒服的东西，如有人愿意了解和分享，请午夜时分与本人联系面谈，相信借助夜色的力量，感性的我应该可以全面压制理性的我。Girls are most welcomed!)。
I can never be too thankful. 父母，我最亲近的人，过去，现在，以及将来必定是我幸福快乐生活的根基与源泉。感谢你们！养育我长大，谢谢！这份恩情，无以为报！哎呀，略激动啊，平复一下...这四年我一直是抱着感恩的心在学习与生活的。能进入交大理科班，真心觉得自己很幸运。我很喜欢理科班的课程设置，课程不多但是内容比较深入。若是你对某些内容很感兴趣，你完全有时间去自学得更加深入完善并触类旁通而不用忙着去上过多的课，赶作业，以及复习考试。这并不是说理科班的学习任务轻，压力小，相反，在这个高标准严要求的集体中，若你不是发自内心的热爱你需要去做的事情，应该会感到不小的挫败感。我是很享受这四年的学习生活的。聆听众多优秀学者教诲时常能使我感受心灵的震撼。还记得教授我们抽象代数课程的章璞老师那以拍照片解释群同态的绝妙比喻以及“商群再做商群真是伤不起啊”的幽默风趣。坂内英一教授以清晰严谨而又直观易懂的方式讲解美妙的代数图论课程，还时常说几个open questions,并且以“If you solve it, you will be instantly famous”“诱惑”我们，哈哈。值得一提的是，坂内教授，这位Algebraic combinatorics 领域的创始人之一，在70岁的高龄还进行着高强度的科研工作并且亲自批改我们的作业！每当看见坂内教授与其夫人（也是一位组合领域的数学家）在交大散步时，心中总有一股油然而生的感动与敬佩。虽然我个人偏爱分析类课程，将来可能也不会做代数领域的研究，但这些课程对我的思维方式的影响无疑是重大的且益处是不可估量的。感谢所有无私奉献的老师们！学院领导和行政工作人员们也时刻默默地关心着我们，感谢你们！
1. Brief review of my 21-year-old life
I was very fortunate to be born in such a warm family. My father is a mathematics professor and my mother was a high school history teacher. They are not only the ones who love and care me most but also who know my heart best. They teach me many things which I will appreciate through all my life. Thanks to them, I live a very happy and content life.
Unlike some parents who put lots of pressure on their children due to the fierce competition into college, my parents didn't care much about my scores in school. They always ask me like:"How's your day today in school, Xiao(my pet name)? any interesting things?" They must have known better than me that I will do well in school without much pushing because I just like learning and thinking . I never take extra classes for cramming exams as so many my classmates did, however, lucky in exams or talented in learning, I was enrolled by Shanghai Jiao Tong University(SJTU), Zhiyuan College which consists of 300 selected students within SJTU and excellent scientists as faculty. After more than three years of studying in Zhiyuan College, I am convinced of having a reasonable talent in mathematics and starting to turn my early interest in mathematics into a serious pursue of a life-time career as a mathematics researcher. So, here I am.
2 Mathematics and me
According to my parents, I developed a little hobby of counting numbers on calendar or page numbers of a heavy book in my 2-3 years old. I was really into this that I could sit on bed counting numbers for hours. I vaguely remembered, about 5-year old, the biggest unit I knew was trillion and I didn't know how to count beyond it. At the same time, a question occurred in my mind: what do I get if keep counting?. Even now I clearly feel the shock and excitement of curiosity washed over me when I was told by my father that there is no biggest number and no boundary in universe. I was both feared and thrilled about the mysterious "infinity".
That may account much for my later obsession with limit theory. After studying mathematical analysis & real analysis, I am totally impressed that puzzling though "infinity" is, we can still tackle it through a well-defined system and somehow understand it! Understanding "infinity" are really fascinating that so many great philosophers and mathematicians thought about it. The definition of limit concerning ε-δ language is actually a reflection of the philosophic notion "potential infinity" and its counterpart "actual infinity" lies behind Cantor's set theory.
The more l learn the more I believe in the power of logic and mathematics. Since Kolmogorov has put the notion of probability naturally in the framework of measure theory, probability theory becomes a branch of mathematics. But the idea of random variable is not merely tautology of measurable mapping, it embodies the probability thought and provides powerful mathematic tool at the same time. Once again, how amazing is that we can even comprehend and handle randomness through mathematics!.
Talking about randomness, one must refer to the pioneering work on physics for last century--Quantum Mechanics. The violation of Bell's inequality tell us that randomness is not a makeshift for man's unable to describe precisely but essential. By the way, after I have studied functional analysis course, I think I get a deeper understanding on quantum mechanics theory. Wave function is an element in Hilbert space and dynamic variables are linear Hermit operators on it. I believe studying of spectrum theory in functional analysis will definitely help developing quantum mechanics theory
The two concepts that attract me most are actually closely related.
Limit theory is of great significance in probability and statistics. Kolmogorov once said(I paraphrased):" The meaning of probability can only be understood by taking the limit." Statistics can sort of be viewed as "inverse problem of probability" which is aimed at reconstruct the probability space of the population through estimation over samples.
On the other hand, probability and statistic method is vital in many fields concerning complex data processing such as biology ,finance, etc. I am really looking forward to cooperating with scientists in various fields in the future if my dream of becoming a mathematics researcher comes true.