本书的主要内容为函数、极限、连续，导数与微分，导数的应用，不定积分，定积分及其应用，多元函数微积分，常微分方程，级数等。为了精简教学内容，提高教学效率，并考虑到高等职业教育的实际情况，将内容分模块编排。全书共分为8大模块，各大模块内约2课时的内容为一小模块，各小模块又分为“案例研究”、“抽象归纳”、“能力训练”三个模块。按照项目教学法模式编写，以学生的实际应用过程为导向，以能力培养为目标，以实际问题为载体，以学生为中心，力求实现教学做一体化。 本书具有简易化、形象化、模式化、信息化、现代化、立体化等特色，是一本新颖又易教乐学的教材，是高职高专各类专业应用数学课程的通用教材，也可作为专科学校、职业和成人大学的选用教材或教学参考书。

本书内容分为四个模块：第1个模块是初赛备考知识点专项的基础知识及对应赛题训练；第二个模块是历年高频初赛选择题精选；第三个模块是2020年入门组和提高组的真题卷；第四个模块是阅读程序和完善程序的模拟题。

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.

Nonlinear eigenvalue problems arise in many fields of natural and engineering sciences. Theoretical and practical results are scattered in the literature and in most cases they have been developed for a certain type of problem. In this book we consider the most general nonlinear eigenvalue problem without assumptions on the struct.ure or spectrum. We start by providing basic facts on the conditioning of a simple eigenvalue and an inverse operator representation in terms of the singular value decomposition. The main part of this work connects Newton-type methods for nonlinear eigenvalue problems and nonlinear Rayleigh functionals.

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.

本书汇编以往环球城市数学竞赛中的组合问题，精选其中典例，运用不同的方法和角度进行讲解，深刻分析其中蕴含的组合原理，书中按难易程度进行分类，层次明晰，划分科学。他山之石可以攻玉。借鉴、学习环球竞赛题目，对我国大中学教师、学生、数学爱好者的教学和学习都有很大的启发意义。全书体例清晰，模块分明，从知识介绍至例题讲解，再到例题评析，习题演练，语言表达合理，讲解由浅入深，由易至难，对读者有较高使用价值，具有良好的市场预期。

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