jupiter.math.nctu.edu.tw~smchangnewst981228

1、Pure Mathematics from Practical perspective(從應(yīng)用角度看純粹數(shù)學(xué)),華中科技大學(xué)楊曉松教授,猩猩與人類,猩猩的智力成就以及它們是怎樣學(xué)習(xí)的？人類的智力成就以及人類是怎樣學(xué)習(xí)的？希望大家保持人類尊嚴(yán)，不要按猩猩方式學(xué)習(xí)！,Applied mathematics(應(yīng)用數(shù)學(xué)),Statistics, probability, operation research, differential

2、 equation, linear algebra, control theory， applied dynamical systems, optimization，(國人見解：統(tǒng)計學(xué),概率論,運(yùn)籌學(xué),微分方程, 線性代數(shù)、控制論、(應(yīng)用）動力系統(tǒng)、最優(yōu)化理論等）一般說法：系統(tǒng)運(yùn)用數(shù)學(xué)手段進(jìn)行研究的各種科學(xué)理論都是應(yīng)用數(shù)學(xué)！i.e.,廣義相對論、流體力學(xué)、幾何力學(xué)等。最偉大的應(yīng)用數(shù)學(xué)家：牛頓,Pure mathematics(1)

3、,Why pure mathematics?丘成桐：很難找到40歲以下真正的一流應(yīng)用數(shù)學(xué)家，原因是應(yīng)用數(shù)學(xué)家在純數(shù)學(xué)的基本技巧方面沒有得到很好的訓(xùn)練！,Pure mathematics(1),Algebraic geometry, algebraic topology, Differential geometry, differential topologyNumber theory ,algebra, group, comple

4、x analysis, functional analysis, ( complex, differentiable) dynamical systems（代數(shù)幾何、代數(shù)拓?fù)?、微分幾何、微分拓?fù)?、?shù)論、代數(shù)、群論、復(fù)分析、泛函分析、（復(fù)或微分）動力系統(tǒng)等。,What can pure mathematics do?,Many things!1 Algebraic geometry, Bezout’s theorem to comp

5、utation of load flow equation of power systems.Robotics2 Differential topology:Morse theory Algebraic geometry, to estimation of load flow equation of power systems.3EconomicsIn addition to theoretical physics,What

6、can pure mathematics do?,3 Topology and data processing One important goal of data analysis is to allow the user to obtain knowledge about the data, i.e. to understand how it is organized on a large scale.,Pure mathem

7、atics for control theory,What is control theory? Control theory is the study of the manipulation of dynamical processes to achieve desired objectives.Examples:,Control theory for Snakeboard,,Mathematics for control the

8、ory for Snakeboard,Ordinary differential equationsDifferential geometryLie group and Lie algebraMechanics,Linear control theory,,Nonlinear control theory,Geometric control theory,,結(jié)束語,1 純粹（基礎(chǔ)）數(shù)學(xué)和應(yīng)用數(shù)學(xué)沒有涇渭分明的界線！2 要做好應(yīng)用