复杂性理论主要研究决定解决算法问题的必要资源，以及利用可用资源可能得到的结果的界，而对这些界的深入理解可以防止寻求不存在的所谓有效算法。复杂性理论的新分支随着新的算法概念而不断涌现，其产物——如NP一完备性理论——已经影响到计算机科学的所有领域的发展。本书视随机化为一个关键概念，强调理论与实际应用的相互作用。本书论题始终强调复杂性理论对于当今计算机科学的重要意义，包含各种具体应用。

Except for minor modifications, this monograph represents the lecture notes of a course I gave at UCLA during the winter and spring quarters of 1991. My purpose in the course was to present the necessary background material and to show how ideas from the theory of Fourier integral operators can be useful for studying basic topics in classical analysis, such as oscillatory integrals and maximal functions. The link between the theory of Fourier integral operators and classical analysis is of course not new, since one of the early goals of microlocal analysis was to provide variable coefficient versions of the Fourier transform. However, the primary goal of this subject was to develop tools for the study of partial differential equations and, to some extent, only recently have many classical analysts realized its utility in their subject.

This is primarily a textbook on mathematical analysis forgraduate students in economics. While there are a large number ofexcellent textbooks on thiroad topic in the mathematicsliterature， most ofthese texts are overly advanced relative to theneeds of the vast majority of economics students and concentrate onvarious topics that are not readily helpful for studying economictheory. Moreover， it seems that most economics students lack thetime or courage to enroll in a math course at the graduatelevel. Sometimes this is not even for bad reasons， for only fewmath departments offer classes that are designed for the parhcularneeds of economists. Unfortunately，more often than not， theconsequent lack ofmathematical background cre-ates problems for thestudents at a later stage of their education， since an exceedinglylarge fraction ofeconomic theory is imperable without somerigorouackground in real analysis. The present text aims atproviding a remedy for this inconvenient situation.

《希尔伯特空间及其应用导论(第3版)(英文版)》无论是学生还是科研人员，都将从《希尔伯特空间及其应用导论(第3版)(英文版)》的特别表达中受益。《希尔伯特空间及其应用导论(第3版)(英文版)》在原来版本的基础上做了不少改动，新增加了一部分讲述Sobolev空间，展开讲述了有限维赋范空间，有关小波的一章做了全面更新。并且包括了积分和微分方程、量子力学、化、变分和控制问题、逼近理论问题、非线性不稳定性和分岔理论的多种应用。在众多希尔伯特空间的书中，《希尔伯特空间及其应用导论(第3版)(英文版)》在讲述勒贝格积分方面独具特色。学习泛函分析和希尔伯特理论的老师和学生都十分推崇这本书作为教材或者参考书。

《数学物理方程及其matlab解算》包括数理方程研究的对象与基本方法、三类典型方程、数理方程的定解问题等基础概论，以及特殊函数和求解数理方程的行波法、积分变换法、分离变量法及格林函数法等基本内容。 《数学物理方程及其matlab解算》有两大特色：一是对数理方程的传统架构进行了适当的调整：先讲微分方程，再讲偏微分方程。二是引进了易学好用的matlab软件。书中所有的计算几乎全用这个软件进行，使读者从费时易错的繁杂数学推导、变换和演算中解放出来。 《数学物理方程及其matlab解算》可作为高等学校非数学专业的教材，亦可供科技人员参考。