本教材是“十二五”职业教育国家规划教材.本教材主要内容包括：函数、极限与连续，导数、微分及其应用，积分及其应用，微分方程，向量与空间解析几何，二元函数微积分，级数与拉普拉斯变换.本教材是新形态一体化教材，配套有同步的习题集与相关教学资源.教学资源包含PPT课件、实验录屏、教材练习和习题集参考答案等.其中部分资源以二维码形式在书中呈现.本教材教学课时数为94~122，适合作为高等职业教育各专业数学课程教学用书，也可作为广大数学学习者的自学参考用书.

本册教材的主要内容包括向量代数与空间解析几何、多元函数微分法及其应用、多元函数积分学、无穷级数、微分方程与差分方程初步等，每一小节均配套有习题，每章配以复习题，并后附答案，既方便上课使用，也可供学生自学。本书针对本科学生的知识结构和学习所需编写，对准备从事相关专业及准备考研的学生都有较大帮助。

本册教材的主要内容包括函数与极限、导数与微分、微分中值定理与导数的应用、不定积分、定积分及其应用等，每一小节均配套有习题，每章配以复习题，并后附答案，既方便上课使用，也可供学生自学。本书针对本科学生的知识结构和学习所需编写，对准备从事相关专业及准备考研的学生都有较大帮助。

In 1736， Euler founded Graph Theory by solving the Konigsberg seven-bridge problem. It has been more than two hundred years till now. Graph Theory is the core content of Discrete Mathematics， and Discrete Mathematics is the theoretical basis of Computer Science and Network Information Science. This book vulgarly introduces in an elementary way some basic knowledge and the primary methods in Graph Theory. Through some interesting mathematic problems and games the authors expand the knowledge of Middle School Students and improve their skills in analyzing problems and solving problems.

《世界数学奥林匹克经典》由数学竞赛命题委员会主席和数学邀请赛命题委员会主席等专家共同编著。《世界数学奥林匹克经典》自出版后就深受广大使用者的好评。《世界数学奥林匹克经典》为英文版本。

Probability theory is an important branch of mathematics， with wide applications in many fields. It is not only a required course for students of science and technology at universities， but also has entered into Chinese high school textbooks now.This little book will， in an interesting problem-solving way， explain what probability theory is： its concepts， methods and meanings; particularly， two important concepts-probability and mathematical expectation （briefly expectation）-are emphasized. It consists of 65 problems， appended by 107 exercises and their answers.As an extracurricular book providing supplement materials to and advanced knowledge beyond high school textbooks， its aim is to stimulate study interests of students and broaden their knowledge horizons. Some problems were given a little deeper treatment， which can be used as topics for explorative study; and they can also be skipped temporarily if a reader feels difficult to understand them at the beginning.It is presupposed that our readers possess a knowledge of permutations and combinations， and it would be better if they have already learned basic probability theory from their textbooks. However， in order to avoid repetition， we mention as little as possible the contents of textbooks.It is a random event that this little book reaches you. I do not know how much the probability that this event occurs is. However， it is my expectation that this book could reach you， which means that you have a special affinity with it.

《世界数学奥林匹克经典》由数学竞赛命题委员会主席和数学邀请赛命题委员会主席等专家共同编著。《世界数学奥林匹克经典》自出版后就深受广大使用者的好评。《世界数学奥林匹克经典》为英文版本。

This book consists of three parts： fundamental knowledge， basic methods and typical problems. These three parts introduce the fundamental knowledge of solving combinatorial problems， the important solutions to combinatorial problems and some typical problems with often-used solutions in the high school mathematical competition respectively.In each chapter there are necessary examples and exercises with solutions. These examples and exercises are of the same level of difficulty as the China Mathematical League Competitions which are selected from mathematical competitions at home and abroad in recent years. Some test questions are created by the author himself and a few easy questions in China Mathematical Olympiad （CMO） and IMO are also included. In this book， the author pay attention to leading readers to explore， analyze and summarize the ideas and methods of solving combinatorial problems. The readers' mathematical concepts and abilities will be improved remarkably after acquiring knowledge from this book.

Number theory is an important research field in mathematics. In mathematical competition， problems of elementary number theoryoccur frequently. This kind of problems uses little knowledge and has lots of variations. They are flexible and diverse.In the book we introduce some basic concepts and methods in elementary number theory via problems in mathematics competition.We hope that readers read the book with paper and pencil， and try to solve them by themselves before they read the solutions of examples.Only in this way can they really appreciate the tricks of problem solving.

Mathematical induction is an important method used to prove particular math statements and is widely applicable in different branches of mathematics， among which it is most frequently used in sequences.This book is rewritten on the basis of the book Methods and Techniques for Proving by Mathematical Induction ， and is written with an understanding that sequences and mathematical induction overlap and share similar ideas in the realm of mathematics knowledge. Since there are a lot of theses and books related to this topic already， the author spent quite a lot of time reviewing and refining the contents in order to avoid regurgitating information. For example， this book refers to some of the most updated Math Olympiad problems from different countries， places emphasis on the methods and techniques for dealing with problems， and discusses the connotations and the essence of mathematical induction in different contexts.The author attempts to use some common characteristics of sequences and mathematical induction to fundamentally connect Math Olympiad problems to particular branches of mathematics. In doing so. the author hopes to reveal the beauty and joy involved with math exploration and at the same time， attempts to arouse readers' interest of learning math and invigorate their courage to challenge themselves with difficult problems.