您知道鲁班、塞乐斯、阿基米德、欧拉、高斯、瓦特、富兰克林、哈雷、费雪……吗？您会观察、实验、类比、联想、归纳、猜想……吗？您掌握怎样学、怎样教、怎样有灵感的诀窍吗？您想发明、发现、创新吗？ 本书将与您一起邀游美丽的数学天地，探索思维的奥秘。打开她吧，她将给您一个“词句华美而不空洞，内容精彩而不落俗”的印象，给您一个“由浅入深，老少皆宜”的全新感觉。

This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones.

您知道鲁班、塞乐斯、阿基米德、欧拉、高斯、瓦特、富兰克林、哈雷、费雪……吗？您会观察、实验、类比、联想、归纳、猜想……吗？您掌握怎样学、怎样教、怎样有灵感的诀窍吗？您想发明、发现、创新吗？ 本书将与您一起邀游美丽的数学天地，探索思维的奥秘。打开她吧，她将给您一个“词句华美而不空洞，内容精彩而不落俗”的印象，给您一个“由浅入深，老少皆宜”的全新感觉。

In spirit, thiook is closer to Elements de Geometrie Algebrique (EGA) than the existing textbooks on algebraic geometry. It prvides an introduction to schemes, formal schemesc coherent sheaves, and their cohomologies. The prerequisites for reading thiook is the knowledge of mutative algebra up to the level of Ateyah-Macdonald'ook. The material on algebraic geometry covered in thiook provides adequate preparation for reading more advanced books such as Seminaire de Geometrie Algebrique （SGA）.

本书内容包括概论、数理统计两部分，涉及条件概率、变量及其分布、数学期望、特殊分布、估计、估计量的抽样分布、假设检验、分类数据与非参数和方法、线性统计模型、模拟等。本书知识体系结构与主流的概率论与数理统计教材基本一致，但内容取材及例题的安排上都比较新颖，尤其是新增加了一些非常实用而且比较先进的模拟方法，书中最后提供了奇数号习题的解答以及索引。 本书作为概率论与数理统计的教材，适合大学本科高年级学生和研究生用作教材或参考书，也可供统计工作人员用作参考书。

作为数学工具书，这部巨型手册要求具备哪些特呢？在编写过程中，出版社负责人和我们达成了一项共识，即手册应具科学性、先进性、实用性、规范性与简明性。200余位撰稿人与审稿人按照这些特点和要求会出了艰辛的劳动，我们要感谢他们的通力合作与努力，使手册基本上体现了上述所希冀的特点或特色。 本丛书为国家“九五”重点出版项目。为了读者选购和使用方便，本手册分5卷出版，分别名为“经典数学卷”、“近代数学卷”、“计算机数学卷”、“数学卷”和“经济数学卷”。需要指出的是，各个分支(篇目)的归属是相对的，这里考虑了各分卷篇幅大小的平衡问题。例如，“蒙特卡罗法”这一篇也可归入“计算机数学卷”。

Number theory with applicationy W.C Winnie Li Copyright 1996 by World Scientific Co.Pte.Ltd.All rights reserved.This book，or parts thereof，may not be reproduced in any form or by any means，electronic or mechanical，including photocopying，recording or any information storage and retrieval system now know or to be invented，without written permission form the Publisher。

Number theory with applicationy W.C Winnie Li Copyright 1996 by World Scientific Co.Pte.Ltd.All rights reserved.This book，or parts thereof，may not be reproduced in any form or by any means，electronic or mechanical，including photocopying，recording or any information storage and retrieval system now know or to be invented，without written permission form the Publisher。

作为数学工具书，这部巨型手册要求具备哪些特呢？在编写过程中，出版社负责人和我们达成了一项共识，即手册应具科学性、先进性、实用性、规范性与简明性。200余位撰稿人与审稿人按照这些特点和要求会出了艰辛的劳动，我们要感谢他们的通力合作与努力，使手册基本上体现了上述所希冀的特点或特色。 本丛书为国家“九五”重点出版项目。为了读者选购和使用方便，本手册分5卷出版，分别名为“经典数学卷”、“近代数学卷”、“计算机数学卷”、“数学卷”和“经济数学卷”。需要指出的是，各个分支(篇目)的归属是相对的，这里考虑了各分卷篇幅大小的平衡问题。例如，“蒙特卡罗法”这一篇也可归入“计算机数学卷”。

Number theory with applicationy W.C Winnie Li Copyright 1996 by World Scientific Co.Pte.Ltd.All rights reserved.This book，or parts thereof，may not be reproduced in any form or by any means，electronic or mechanical，including photocopying，recording or any information storage and retrieval system now know or to be invented，without written permission form the Publisher。

out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations.

本书系统地总结了各种类型的奇异值分解，并研究了奇异值分解在广义逆理论中的应用，包括各种类型广义逆的反序律，加边矩阵的广义逆和性质，分块矩阵关于广义逆的块独立性，三种加权广义逆的定义和结构、性、等价格以及矩阵方程的范数解等。 本书适合数学专业研究和从事数值代数研究的科技工作者阅读参考。

as the the title suggests, the goal of thiook is to give the reader a taste of the "unreasonable effectiveness" of morse theory. the main idea behind thistechnique can be easily visualized. suppose m is a smooth, pact manifold, which for simplicity we assume is embedded in a euclidean space e. we would like to understand basictopological invariants of m such as its homology, and we attempt a "slicing" technique.

This volume of the Encyclopaedia contains two contributions．In the first Yu.V.Egorov gives an at of microlocal analysis as a tool for investigating partial differemial equations．This 113ethod haee increasingly important in the theory．of Hamiltonian systems in recent years． The second survey written by V.Ya．1vrii treats linear hyperbolic equations and systems．The author states necessary and sufficiient conditions for C∞-and L2-well-posedness and he studies the analogous pmhlem in the ext ofGevrey classes．He also describes,the latest results in，the theory of mixed problems for hyperbolic operators and concludes with a list of unsolved problems． Both parts coyer recent research in two important fields,which before was scattered in numerous joumals．The book will hence be of immense value to graduate students and researchers in partial differential equationS and theoretical physics。