Mission Statement

Teaching is a divine art. The beauty and value of any art lie in its degree of variation and deviation from convention. Teaching, therefore, must evolve and make adaption, to allow its holy customers -- the students, to be able to feel the exciting pulses of contemporary science and technology. This philosophy serves as the solid bedrock of this year's Modeling course (or experiment). It is purely personal, and therefore could be heavily biased. Keep my warning signal tight in mind throughout your reading.

The road of Mathematical Modeling is two-way: one direction from tools to applications, and the other,  from applications to tools.

The traditional way is to first equip you with  many tools, and then show you how they could possibly be applied in real problems.  It certainly follows the more global trend of the entire western education system, namely, preparing each young adult  for being a skilled worker,  a professional scholar,  and a knowledgable manager, etc.  When you have no definite clue on which profession you are most likely to step into in the future, you learn all the skills that the gossips of other people confirm to be useful. Here you are - you sacrifice all your movie and party time to take Calculus I, II, III;  Linear Algebra Introduction, Applied, and Advanced; Chemistry A, B, and C... Gradually you feel lost, in the vast ocean of knowledge.

So, before you fall on your knees as a knowledge slave, you start to question the whole system: W---H---Y---,  WHY? Why Calculus,? Why Linear Algebra? Why Inorganic, Organic, Analytical, and Bio-Chemistry? That is, you demand THE meaning of LEARNING, as human beings have turned to God for the ultimate meaning of living.

Do we need a God to justify all our learning efforts? Yes, absolutely! Who is the Learning God? His last name is Curiosity, not Christ this time probably. And his first name is Enlightening. Learning must follow the will of Enlightening Curiosity.

What is the biggest curiosity of contemporary science and technology? It is LIFE! --- its ingredients, evolution, dynamics, balance, self-assembly, self-correction, information communication and processing, its complexity and stability, intelligence, and eventually, the meaning of human soul and spirit.   

After spending hundreds of years on machines since the starting of  the Industrial Revolution ---  steam engines,  automobiles, ships, airplanes, and computers, we human being finally turn to ourselves, the wonderful and unique creature of God, and to our friends: all lives in the biological world.

From the nanotechnology, information and digital technology, artificial intelligence,  to the genetic project, we are ready to enlighten this biggest curiosity. It is our privileged mission, as well as of the many generations to come. But we have to start to beat the drum first, or silence and darkness will prolong.

Therefore,  it is not that we go visit Mathematical Biology, but that Mathematical Biology is eagerly knocking on our door.

My exciting view extends much further!  The diversity of the life phenomenon covers almost every corner of the human knowledge world. As a result, almost all tools from the civilized world can be potentially useful for enlightening  the life phenomenon: physics, chemistry, chemical engineering, mechanical engineering, computer science, medical science, biology, ecology, computer vision, artificial intelligence, and of course, mathematics. It terms of mathematics and mathematical modeling, it simply means that all the major tools,  such as deterministic or stochastic modeling,  linear and nonlinear optimizations, static or dynamic modeling, can be our powerful weapons to remove the blind spots of human knowledge.

Now, you see the heart of my trick: we choose a good application: biology, standing from which,  we discuss and develop all the major modeling tools that a classical  modeling course usually teaches. The difference? We are able to feel the actual pulses of our era and this generation. The risk? It is risk free, since we still cover all the topics, and teach them in a way that they are equally applicable to other fields, such as computer science, information technology, chemistry, electrical engineering, dot, dot, dot. After all, the life phenomenon is where all science and technology converge.

Intended Book: Modeling Differential Equations in Biology , by Professor Clifford H. Taubes, Mathematics Department, Harvard University, published by Prentice Hall, 2001. It is a unique book in the many years to come, in that it includes (without any distortion) carefully chosen research papers from Nature and Science, the unquestionably No. 1 and 2 journals in all today's sciences and technologies.

Depending on our pace, I will also possibly develop some new tools and problems beyond the book, such as computational neuron science and human/machine vision.

Prerequisites : Math-2243 (Linear Algebra and Differential Equations) or equivalent (IT-2373 for example), and some elementary probability (such as mean, variance, and normal distribution). Math-2263 (Multivariable Calculus) is recommended.

So, are you ready for the challenge, and fun?

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