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

用改进的SUMT方法编写的FORTRON程序,对等式约束的化学平衡的最小自由能问题求解,精度优于同类程序,并可用于普通微机。改进的主要部分是强迫等式约束达到一定的精度后,主程序进入收敛判断

1 The Role of Algorithms in Computing 2 Getting Started 3 Growth of Functions 4 Divide-and-Conquer 5 Probabilistic Analysis and Randomized Algorithms 6 Heapsort 7 Quicksort 8 Sorting in Linear Time 9 Medians and Order Statistics 10 Elementary Data Structures 11 Hash Tables 12 Binary Search Trees 13 Red-Black Trees 14 Augmenting Data Structures 15 Dynamic Programming 16 Greedy Algorithms 17 Amortized Analysis 18 B-Trees 19 Fibonacci Heaps 20 van Emde Boas Trees 21 Data Structures for Disjoint Sets 22 Elementary Graph Algorithms 23 Minimum Spanning Trees 24 Single-Source Shortest Paths 25 All-Pairs Shortest Paths 26 Maximum Flow 27 Multithreaded Algorithms 28 Matrix Operations 29 Linear Programming 30 Polynomials and the FFT 31 Number-Theoretic Algorithms 32 String Matching 33 Computational Geometry 34 NP-Completeness 35 Approximation Algorithms

Chapter 1 Introduction to Computers and C++ Programming Chapter 2 C++ Basics Chapter 3 More Flow of Control Chapter 4 Procedural Abstraction and Functions That Return a Value Chapter 5 Functions for All Subtasks Chapter 6 I/O Streams as an Introduction to Objects and Classes Chapter 7 Arrays Chapter 8 Strings and Vectors Chapter 9 Pointers and Dynamic Arrays Chapter 10 Defining Classes Chapter 11 Friends, Overloaded Operators, and Arrays in Classes Chapter 12 Separate Compilation and Namespaces Chapter 13 Pointers and Linked Lists Chapter 14 Recursion Chapter 15 Inheritance Chapter 16 Exception Handling Chapter 17 Templates Chapter 18 Standard Template Library Appendices 1 C++ Keywords 2 Precedence of Operators 3 The ASCII Character Set 4 Some Library Functions 5 Inline Functions 6 Overloading the Array Index Square Brackets 7 The this Pointer 8 Overloading Operators as Member

Ｃ语言定义的几种基本数据类型，它们有规定 的类型说明符、数据长度及数据组织和存储形式， 程序设计时可直接用它们来定义数据对象。 在实际应用中仅有这些基本数据类型是不够的, 为了增强数据的表示能力,能够使用各种数据,常需 要各种新的数据类型来满足问题求解的需要。 例如,一个传统的例子:

一、计算机软件工程和硬件工程可以看作是一门更 广义的学科“计算机系统工程”内的活动。 它们所要做的都是按一定的次序开发基于计算 机的系统。 二、计算机系统工程是指与构造基于计算机系统有 关的过程、方法和技术。它是一种问题求解活 动。计算机系统工程的任务是:组织并指导系 统工程师定义全系统各层次中的所有基于计算 机系统的要素

一、齐次演化问题的求解 二、齐次稳定场问题的求解 三、非齐次问题的求解 四、多变量推广 五、本章小结

Number Theory 1. Six proofs of the infinity of primes …… 3. Binomial coefficients are (almost) never powers 4. Representing numbers as sums of two squares …… 8. Some irrational numbers 9. Three times π2/6 Geometry 10. Hilbert’s third problem: decomposing polyhedra63 11. Lines in the plane and decompositions of graphs …… 15. The Borromean rings don’t exist …… 17. Every large point set has an obtuse angle 18. Borsuk’s conjecture Analysis …… 21. The fundamental theorem of algebra …… 25. Cotangent and the Herglotz trick 26. Buffon’s needle problem Combinatorics 27. Pigeon-hole and double counting …… 32. Cayley’s formula for the number of trees 33. Identities versus bijections …… 36. The Dinitz problem247 37. Permanents and the power of entropy253 …… 41. Communicating without errors 42. The chromatic number of Kneser graphs …… 44. Probability makes counting (sometimes) easy

一、最小二乘问题的概念 二、线性最小二乘法 三、非线性最小二乘法 四、最小二乘问题的Matlab求解