1、Pure Mathematics from Practical perspective(从应用角度看纯粹数学),华中科技大学杨晓松教授,猩猩与人类,猩猩的智力成就以及它们是怎样学习的？人类的智力成就以及人类是怎样学习的？希望大家保持人类尊严，不要按猩猩方式学习！,Applied mathematics(应用数学),Statistics, probability, operation research, differential equation, linear algebra, control theory， applied dynamical systems, optimization，(国
2、人见解：统计学,概率论,运筹学,微分方程, 线性代数、控制论、(应用）动力系统、最优化理论等）一般说法：系统运用数学手段进行研究的各种科学理论都是应用数学！i.e.,广义相对论、流体力学、几何力学等。最伟大的应用数学家：牛顿,Pure mathematics(1),Why pure mathematics?丘成桐：很难找到40岁以下真正的一流应用数学家，原因是应用数学家在纯数学的基本技巧方面没有得到很好的训练！,Pure mathematics(1),Algebraic geometry, algebraic topology, Differential geometry, different
3、ial topologyNumber theory ,algebra, group, complex analysis, functional analysis, ( complex, differentiable) dynamical systems（代数几何、代数拓扑、微分几何、微分拓扑、数论、代数、群论、复分析、泛函分析、（复或微分）动力系统等。,What can pure mathematics do?,Many things!1 Algebraic geometry, Bezouts theorem to computation of load flow equation of po
4、wer systems.Robotics2 Differential topology:Morse theory Algebraic geometry, to estimation of load flow equation of power systems.3EconomicsIn addition to theoretical physics,What can pure mathematics do?,3 Topology and data processing One important goal of data analysis is to allow the user to obta
5、in knowledge about the data, i.e. to understand how it is organized on a large scale.,Pure mathematics 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 theory for Snakeboard,Ordinary differential equationsDifferential geometryLie group and Lie algebraMechanics,Linear control theory,Nonlinear control theory,Geometric control theory,结束语,
