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。

本书是清华大学附属中学针对大学自主招生开设的校本课程“不等式选讲”的教材，该校本课程面向高一学生，在高一下学期开设，共18学时，系统讲授不等式问题的思想与方法，拓宽解决数学问题特别是不等式问题的思路.全书共14讲，分为基础知识篇、思想进阶篇和试题赏析篇，每讲精选例题，并配有习题，附有习题提示与解答.本书适合高中师生及数学爱好者研读.