The first three chapters cover the standard material on sets, relations, and functions and algorithms. Next come chapters on logic, counting, and probability. We then have three chapters on graph theory: graphs, directed graphs, and binary trees. Finally there are individual chapters on properties of the integers, languages, machines, ordered sets and lattices, and Boolean algebra, and appendices on vectors and matrices, and algebraic systems. The chapter on functions and algorithms includes a discussion of cardinality and countable sets, and complexity. The chapters on graph theory include discussions on planarity, traversability, minimal paths, and Warshall’s and Huffman’s algorithms. We emphasize that the chapters have been written so that the order can be changed without difficulty and without loss of continuity

1 Preliminaries The Integers 3 Groups 4 Cyclic Groups 5 Permutation Groups 6.1 Cosets 7 Introduction to Cryptography 8 Algebraic Coding Theory 9 Isomorphisms 10 Normal Subgroups and Factor Groups 11 Homomorphisms 12 Matrix Groups and Symmetry 13 The Structure of Groups 14 Group Actions 15 The Sylow Theorems 16 Rings 17 Polynomials 18 Integral Domains 19 Lattices and Boolean Algebras 20 Vector Spaces 21 Fields 22 Finite Fields 23 Galois Theory

了解人工神经网络的有关研究思想,从中 学习开拓者们的部分问题求解方法。 通过实验进一步体会有关模型的用法和性 能,获取一些初步的经验。 查阅适当的参考文献,将所学的知识与自 己未来研究课题(包括研究生论文阶段的 研究课题)相结合起来,达到既丰富学习 内容,又有一定的研究和应用的目的

1 The How, When, and Why of Mathematics Spotlight: George Polya Tips on Doing Homework 2 Logically Speaking 3 Introducing the Contrapositive and Converse 4 Set Notation and Quantifiers Tips on Quantification 5 Proof Techniques Tips on Definitions …… 10 Relations Tips on Reading Mathematics 11 Partitions Tips on Putting It All Together 12 Order in the Reals 13 Consequences of the Completeness of R Tips: You Solved ItNow What? 14 Functions, Domain, and Range Spotlight: The Definition of Function 15 Functions, One-to-One, and Onto 16 Inverses 17 Images and Inverse Images Spotlight: Minimum or Infimum? 18 Mathematical Induction 19 Sequences 20 Convergence of Sequences of Real Numbers 21 Equivalent Sets 22 Finite Sets and an Infinite Set 23 Countable and Uncountable Sets 24 The Cantor–Schroder–Bernstein Theorem Spotlight: The Continuum Hypothesis ……

§2.1 真空中静电场的基本定律 §2.2 静电场的电位 §2.3 静电场问题求解方法概述 §2.4 电位的多极展开 §2.5 存在介质时静电场的基本定律 §2.6 静电场中的导体 §2.7 静电场的能量

Preface Part I: Preliminaries Column 1: Cracking the Oyster Column 2: Aha! Algorithms [Sketch] Column 4: Writing Correct Programs [Sketch] Column 5: A Small Matter of Programming [Sketch] Part II: Performance Column 7: The Back of the Envelope Column 8: Algorithm Design Techniques [Sketch] Part III: The Product Column 14: Heaps [Sketch] Column 15: Strings of Pearls Epilog to the First Edition Epilog to the Second Edition Appendix 2: An Estimation Quiz Appendix 3: Cost Models for Time and Space Appendix 4: Rules for Code Tuning Solutions for Column 1 Column 5 Column 7 Column 15 Index About The Book Why a Second Edition? To Readers of the First Edition About the First Edition Errata Supporting Material Source Code Web Sites Relevant to the Book Animation of Sorting Algorithms Tricks of the Trade Teaching Material

一、发展历史 ALGOL(Algorithmic Language)1962年开发,面向问题求解过程、适合数值计算、结构严谨的算法语言。不能直接操作硬件,不适合写系统软件

MATLAB基础 矩阵与数组运算 常用数学函数 符号运算 MATLAB编程 二维与三维绘图 最优化问题求解 线性规划 整数规划 二次规划

对银行的三种营业模型进行分析后指出,现代“机—机”模型是未来银行的必然经营方式,而其关键技术是储户的身份甄别和确保交互信息在网路中的安全。提出了两种安全性控制策略,即双密钥(伴随密钥)与语音智能识别,前者绕过了身份直接甄别,后者则是用动态语音代替动态图像来甄别身份。最后对问题求解策略及算法给出了框架性描述

1.1 计算电磁学的产生背景 1.2 电磁场问题求解方法分类 1.3 计算电磁学中的三种重要方法 1.4 电磁场工程专家系统