General Theory of Mathematics History (translated version) is divided into four parts: mathematics before the 6th century; Medieval mathematics (500-1000); Early modern mathematics (1400-1700); Modern Mathematics (1700-2000). The main features of General Theory of Mathematical History are as follows: 1. Flexible arrangement: Although the General Theory of Mathematical History is mainly arranged in chronological order, each period revolves around a special topic. Readers can trace the whole history of this period by consulting the detailed title of the book. 2. Important textbooks in different periods: Each chapter of General History of Mathematics will discuss one or several important textbooks in that period. Through them, we can not only learn the thoughts of those great mathematicians, but also today's students can see how some problems were handled in the past. 3. Non-Western Mathematics: A lot of materials in the general history of mathematics are about mathematics in China, Indian and Islamic world; In the inserted chapter, we also compare the mathematics of major civilizations around14th century. 4. Biography and comments: The General Theory of Mathematical History is equipped with more than 100 stamps and pictures commemorating mathematicians and their work in past dynasties, and the biographies of mathematicians are mainly equipped with block diagrams.
In addition, The General Theory of Mathematical History also has many characteristics in exercise configuration, topic discussion, content coherence and so on. General Theory of Mathematics History can be used as a teaching material for students majoring in science and engineering in comprehensive universities, normal universities, and as a reference for mathematicians and science lovers. I believe that middle school teachers and students will also benefit from the general theory of mathematics history.
The discovery of mathematics
The Discovery of Mathematics: Understanding, Research and Teaching of Solving Problems is the representative work of George Polya, a famous American mathematician. In the book, the author makes a detailed analysis of various vivid and interesting typical problems (some of which are non-mathematical), puts forward their essential characteristics, and summarizes various mathematical models. The author tells the principle with high mathematical generality in easy-to-understand language and heuristic narrative method, which has benefited readers at all levels. This simple, simple and vivid teaching fully embodies the style characteristics of an education master. The exercises and notes at the end of each chapter of this book are the continuation of the main text, which is closely related to the main text after careful selection and arrangement by the author. These exercises provide readers with an excellent opportunity to do creative work, which will stimulate your competitiveness and initiative and let you enjoy the fun of math work.
Mathematics and art
Some people have stereotypes about mathematics and art, thinking that mathematics works through the right brain and art works through the left brain. Mathematicians are rational and rigorous, and artists are emotional and romantic. They are two completely different types of people. This book aims to overthrow this prejudice. In this book, readers will see how some mathematicians work tirelessly for art and how some artists are keen on the latest discoveries of mathematics. Actually. Now there are some modern mathematicians, who are not only pioneers of modern mathematics, but also accomplished artists and some artists. They use mathematical principles to create unexpected excellent works, where mathematics and art are completely communicated.
The influence of mathematics on art has a long history. During the Renaissance, artists used the perspective principle to create immortal masterpieces. In the 20th century, the Dutch artist escher's exploration of infinite puzzles inspired people, and Salvador Dali used the four-dimensional cube to unfold the picture to create shocking works. Artists get inspiration from Fibonacci sequence, minimal surface and Mobius belt, and mathematicians publicize mathematical achievements with plastic sculptures.
Looking at Elementary Mathematics from a High Angle
Felix Klein was the founder of the Gottingen School, the most influential mathematics school in the world at the end of 19 and the beginning of the 20th century. He is not only a great mathematician, but also the founder of modern international mathematics education, an outstanding mathematical historian and educator, and enjoys a high reputation and great influence in the field of mathematics.
This book is a popular reading of basic mathematics written by Klein based on the lectures he gave to German middle school mathematics teachers and students at the University of G? ttingen for many years. This book reflects many of his views on mathematics and vividly shows people the legacy of first-class masters. After publication, it was translated into many languages, which is an immortal masterpiece of mathematics education, and its influence has never weakened. This book is divided into three volumes. Book 1: Arithmetic, Algebra and Analysis; Volume II: Geometry; Volume III: Exact Mathematics and Approximate Mathematics.
Klein thinks that function is the "soul" of mathematics. It should be the "cornerstone" of middle school mathematics, and the contents of arithmetic, algebra and geometry should be integrated with the concept of function-centered through geometric forms; It emphasizes the need to transform the traditional middle school mathematics content with the viewpoint of modern mathematics, advocates strengthening the teaching of function and calculus, reforming and enriching the content of algebra, and advocates the consciousness of "thinking highly of elementary mathematics". In Klein's view, the duty of a math teacher is to "make students understand that mathematics is not an isolated subject, but an organic whole"; Teachers of basic mathematics should look at it from a higher angle (advanced mathematics). To understand elementary mathematics problems, only when the viewpoint is high can things be clear and simple; A qualified teacher should master or understand the concepts and methods of mathematics, the process of its development and perfection, and the evolution of mathematics education. He believes that "every branch concerned should be regarded as the representative of the whole mathematics in principle" and that "many phenomena in elementary mathematics can only be deeply understood within the non-elementary theoretical structure".
This book has a good enlightening effect on readers engaged in mathematics learning and education in China. In the words of Mr. Wu Daren, a mathematician and educator in China, one of the translators of this book, "Anyone who has a certain understanding of mathematics can get lessons and inspiration from it", this book still feels very cordial to read. This is because its content is mainly basic mathematics, and its viewpoint contains truth ... "。
History of Mathematics in Middle School
This book is compiled according to China's "Mathematics Education Standards for Middle Schools". The book introduces the knowledge of the history of mathematics, such as the history of sphere volume formula, binomial theorem, sine and cosine formula of n times angle, the birth of analytic geometry, the invention of logarithm, the game between chance and probability, etc. It also discusses the relationship between mathematics history and mathematics education in theory, expounds the role of mathematics history in mathematics teaching and how to integrate it into mathematics education, which is a reference book for students of mathematics department in normal universities, teachers of mathematics history and middle school mathematics teachers.
I hope it works ~ ~ ~