本书为《数学及其应用的进展》的英文版。全书涉及了数学的各个领域。包括代数几何、应用数学、几何分析、图论、数学规划、数值分析和科学计算、运筹学和数学经济、算子代数、常微分和偏微分方程以及黎曼几何。

本书是由一些综述性或原始研究论文组成的，涉及了数学的各个领域。包括代数几何、应用数学、几何分析、图论、数学规划、数值分析和科学计算、运筹学和数学经济、算子代数、常微分和偏微分方程以及黎曼几何。并且，每篇论文的作者至少有一位是中国科学技术大学数学系1977级学生。

本书适合数学研究者和研究生使用。

Preface to the USTC Alumni's Series

Preface I

Preface II

Preface III

Preface IV

Image Methods for Electrostatic Potentials

The Inverse Problems of Some Mathematical Programming Problem

Cyclic Cohomology for Discrete Groups and its Applications

Recent Results for Some Higher Order Abstract Differential Equations

Diracs Theorem and Its Generalization in Hamiltonian Graph Theory

Curvature and Topology in Riemannian Geometry

Hodge Theory and Its Applications to Geometry

High Order Accurate Numerical Methods for Convection Dominated

PDEs

Inverse Boundary Value Problems for Elliptic Equations

Entropy Functionals, Sobolev Inequalities and a-Noncollapsing

Estimates Along the Ricci Flow

k-Solutions of the Ricci Flow

Recent Advances in Mathematical Modeling of Supply Chain

Network Equilibrium

Some Divergence-free Finite Elements for the Stationary Stokes

Equations

Gradient Recovery and A Posteriori Error Estimates