about mathematcis

It is an old topic, but I think I have some newer understandings.

One year ago, when I first moved to the east campus for my second degree of statistics, I cherished a notion that was quite distinct from my present one. I was naive then, having a somewhat religious and pious belief on the strength of mathematics. I thought, then, that mathematics might hold the key for the ultimate truth of nature.

However, as I know more and more about the application of mathematics in biology, I become more and more realistic. As a part of nature, biology has its innate properties and complexities that are intractable to math. Actually, it seems that, besides biology, most of our nature is intractable to math, such as meteorology. Physics has much math because it starts from very simplifying and ideal systems. Therefore, my previous conviction seems quite untenable.

What role does theoretical biology play in the filed? As I become more realistic, my answer becomes more conservative. I think it is helpful to integrating and systemizing what we know experimentally, and contributes conceptually. However, this role is limited, as can be seen from the fact that most of the cornerstones in biology are experimental discoveries.

I choose to study theoretical aspects simply because I like it. Of course, as biology becomes more and more quantitative, the role theoretical biology plays will become more and more significant. I hope to make some contributi0ns to this change.

Based on my current knowledge, the following branches of math are close to biology:
statistics (abundant branches)
probability (including stochastic process)
calculus (notably ODE & PDE)
linear algebra
Some other not-so-intimate branches include dynamic programming, game theory(behavioral study), etc. Hence, it is better to focus on and master these subjects than to study much math without grasping firmly these core branches.

In the following I'd like to talk about another aspect. I gradually realize the great distinction between applied math and mathematical theory. For those who mainly apply math, math is a tool and little theory is required. A very convincing example is the success of Newton in deriving the law of general gravity based on the Kepler's three observational principles. By his time the rigorous basis of mathematical analysis (calculus) had not been set up, which did no harm at all to its utility. Therefore, I think I don't have to waver at whether I should study those theoretical aspects of math any more. For example, for applying calculus, I think what I need to master includes how to develop a continuous model (involving instantaneous rate), calculating integration and most importantly, how to solve DEs. For theoretical aspects like epsilon-delta language, mid-value theorem of differential, I don't think they are necessary. I won't study course like real analysis until I later find it useful.

For those who wish to study more math, I suggest that taking courses may not be as helpful as they expect. In fact, as our academic careers go on, we will find that most of what we know are got from self-study. I think self-study has some advantages over taking courses, such as more flexible, less homework-oriented, less requirement-oriented (that is, you can study to the extent your think it is enough, rather than what teachers tell you are enough. In my probability course, my teacher told us that CLT, large number theorem, convergence in probability/distribution, characteristic function, moment function, etc., were beyond the scope of the course, which, however, turned out to be very important), etc.

In the coming semester, I will audit, not take, two courses: stochastic process and PDE (perhaps plus nonparametric statistics). I believe they will be useful and I hope I can master them relatively well.

My summer vacation

7.2-7.6 Graduation
ceremony, taking pictures, dinner, seeing classmates off, etc.
It feels bad.

7.7-8.6 lab (miRNA project)
A dull month. Wu Laoshi came during the month.

8.7-8.23 WH
A very pleasant fortnight. Hometown, 14th floor, icecream, self-study, soothing weather, movies, grand parents, spicy food... The boredom I underwent during the lab month was compensated.

8.24-8.25 JM
A brief stay at home.

8.26-9.2 GZ
preparing for the coming semester by studying some math and population genetics.

In sum, it is a satisfying summer vacation. I spare no effort.