This Volume gives an account of the principal methods used in developing a theory of algebraic varieties in space of n dimensions. Applications of these methods are also given to some of the more important varieties which occur in projective geometry. It wasorigina113 our intention to include an account of the arithmetic theory of varieties， and of the foundations of birational geometry， but it has turned out to be more convenient to reserve these topics for a third volume. The theory of algebraic varieties developed in this volume is therefore mainly a theory of varieties in projective space.In writing this volume we have been faced with two problems： the difficult question of what must go in and what should be left out， and the problem of the degree of generality to be aimed at. As our objective has been to give an account of the modern algebraic methods available to geometers， we have not sought generality for its own sake. There is still enough to be done in the realm of classical geometry to give these methods all the scope that could be desired， and had it been possible to confine ourselves to the classical case of geometry over the field of complex numbers， we should have been content to do so. But in order to put the classical methods on a sound basis， using algebraic methods， it is necessary to consider geometry over more general fields than the field of complex numbers. However， if the ultimate object is to provide a sound algebraic basis for classical geometry， it is only necessary to consider fields without characteristic. Since geometry over any field without characteristic conforms to the general pattern of geometry over the field of complex numbers， we have developed the theory of algebraic varieties over any field without characteristic. Thus fields with finite characteristic are not used in this book.

《几何瑰宝：平面几何500名题暨1500条定理（上下）（第2版）》共有三角形、几何变换，三角形、圆，四边形、圆，多边形、圆，完全四边形，以及值，作图，轨迹，平面闭折线，圆的推广十个专题。对平面几何中的500余颗璀璨夺目的珍珠进行了系统地、全方位地介绍，其中也包括了近年来我国广大初等几何研究者的丰硕成果。《几何瑰宝：平面几何500名题暨1500条定理（上下）（第2版）》中的1500余条定理可以广阔地拓展读者的视野，极大地丰厚读者的几何知识，可以多途径地代领数学爱好者进行平面几何学的奇异旅游，欣赏平面几何中的精巧、深刻、迷人、有趣的历史名题及新成果，该书适合于广大数学爱好者及初、高中数学竞赛选手，初、高中数学教师和数学奥林匹克教练员使用，也可作为高等师范院校数学专业开设“竞赛数学”“中学几何研究”等课程的教学参考书。

Imagine two triangles in the three-dimensional space， such that an edge of the one pierces through the interior of the other， and vice versa. In such a geometrical situation， any continuous transformation that separates the two triangles would lead to an intersection of their boundaries at one moment， and so we call the two triangles and their boundaries linked （germ： verschlungene Dreiecke）.It is a known fact in graph theory [8] that any embedding of the complete graph with 6 vertices K6 into R3 has at least one pair of those linked triangles. Prof.Dr.U.Brehm （TU-Dresden）， who was my advisor during this diploma thesis， used the so called Gale diagrams to proof that any straight line embedding of the K6 contains either one or exactly three pairs of linked triangles. In Section 1.3.1 we will explain this technique， which leads to the proof of the corresponding Theorem 1.4， and we give visual examples for both cases in Figure 2.

The Purpose of this volume is to provide an account of the modern algebraic methods available for the investigation of the birational geometry of algebraic varieties. An account of these methods has already been published by Professor Andre Weil in his Foundations of Algebraic Geometry （New York， 1946）， and when Professor Zariski's Colloquium Lectures， delivered in 1947 to the American Mathematical Society， are published， another full account of this branch of geometry will be available. The excuse for a third work dealing with this subject is that the present volume is designed to appeal to a different class of reader. It is written to meet the needs of those geometers trained in the classical methods of algebraic geometry who are anxious to acquire the new and powerful tools provided by modern algebra， and who also want to see what they mean in terms of ideas familiar to them. Thus in this volume we are primarily concerned with methods， and not with the statement of original results or with a unified theory of varieties.Such a purpose in writing this volume has had several effects on the plan of the work. In the first place， we have confined our attention to varieties defined over a ground field without characteristic. This is partly because the geometrical significance of the algebraic methods and results is more easily comprehended by a classical geometer in this case; also， though others have shown that modern algebraic methods have enabled us to make great strides in the theory of algebraic varieties over a field of finite characteristic， many of the theorems which the classical geometer regards as fundamental have only been proved， as yet， in the restricted case.

This Volume is the first part of a work designed to provide a convenient account of the foundations and methods of modern algebraic geometry. Since nearly every topic of algebraic geometry has some claim for inclusion it has been necessary， in order to keep the size of this volume within reasonable limits， to confine ourselves strictly to general methods， and to stop short of any detailed development of geometrical properties.We have thought it de8irable to begin with a section devoted to pure algebra， since the necessary algebraic topics are not easily accessible in Engl18h texts. After a preliminary chapter on the basic notions of algebra， we develop the theory of matrices. Some novelty has been given to this work by the fact that the ground field is not assumed to be commutative. The more general results obtained are used in Chapters V and VI to analyse the concepts on which projective geometry is based. Chapters III and IV， which will be required in a later volume， are devoted to a study of algebraic equations.Book II is concerned with the definition and basic properties of projective space of n dimensions. Both the algebraic and the 8ynthetic definitions are discussed， and the theory of matrices over a non-commutative field is used to show that a space based on the propositions of incidence can be represented by coordinates， without the introduction of any assumption equivalent to Pappus' theorem. The necessity of considering a large number of special case8 has made Chapter VI rather long， but some space has been 8aved in the later parts of the chapter by merely mentioning the special cases and leaving the proofs to the reader， when they are sufficiently simple. It is hoped that this will not cause any difficulty. This Book concludes with a purely algebraic account of collineations and correlations. Certain elementary geometrical consequences are indicated， but a complete study of the geometrical problems involved would have taken us beyond our present objective.

常用不等式（第五版）

《黎友源数学创新文集》介绍黎友源教授研究创建的数学一元高次不等式解集定理（黎氏定理）等6个新定理、新公式，以及用数学方法考证“萍实是巨型灵芝”，破解“萍实”千古谜。本书详细地介绍了黎友源教授创建的每个新定理、新公式的内容、证明、应用，有的还详细地介绍了它被发现、被破解的思维全过程。本书所选主论文均为省级学术专刊正式发表的论文。本书可供中学数学教师、师范院校数学系学生、其他数学爱好者参考阅读。

本书为“可爱的数学丛书”之一，包括单位的PK赛、货币交换、绝对值、精确计数法、如意算盘、计算工具的演变、字母表示数之旅和数形结合比翼飞等内容，通过漫画故事、抢答问题、参加辩论等形式，让学生以最简单、最轻松的方式掌握数学运算知识，培养和提高青少年的数学学习能力和人文素养。

《好玩的几何/可爱的数学丛书》为“可爱的数学丛书” 之一，通过漫画故事、抢答问题、参加辩论等形式，让学生以最简单、最轻松的方式掌握数学运算知识，培养和提高青少年的数学学习能力和人文素养。

《经济数学作业集（下 套装共2册）》为适应应用型本科人才的培养要求而编写，分为A、B两册，即奇数周作业为A册，偶数周作业为B册。本册为A册，内容涉及行列式（包括二、三阶行列式，行列式的性质，行列式按行（列）展开，克莱姆法则）、线性方程组（向量组的秩和矩阵的秩，线性方程组解的一般理论）、矩阵（逆矩阵）、随机事件与概率（随机事件的概率，条件概率，乘法公式与全概率公式）、随机变量的分布和数字特征（随机变量及其分布，常用的离散型分布，随机变量的数字特征）。此外，附录中给出了练习题的参考答案，可方便学生进行自我测试。