jupiter.math.nctu.edu.tw~smchangnewst981228

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

2、 equation, linear algebra, control theory， applied dynamical systems, optimization，(國人見解：統(tǒng)計學,概率論,運籌學,微分方程, 線性代數(shù)、控制論、(應用）動力系統(tǒng)、最優(yōu)化理論等）一般說法：系統(tǒng)運用數(shù)學手段進行研究的各種科學理論都是應用數(shù)學！i.e.,廣義相對論、流體力學、幾何力學等。最偉大的應用數(shù)學家：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用數(shù)學家，原因是應用數(shù)學家在純數(shù)學的基本技巧方面沒有得到很好的訓練！,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)拓撲、微分幾何、微分拓撲、數(shù)論、代數(shù)、群論、復分析、泛函分析、（復或微分）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）數(shù)學和應用數(shù)學沒有涇渭分明的界線！2 要做好應用