A Study Of Van Der Waerden 's Modern Algebra

In the nineteenth century, the system of algebraic knowledge is enormous, which contains the permutation group, matrix, algebraic number theory, algebraic geometry and other branches. By the late nineteenth century, mathematicians began to conduct axiomatic study through abstracting the common features of a number of different concrete objects. Thus, by efforts of Steinitz, Emmy Noether and other mathematicians, abstract algebra was born. It is precisely van der Waerden's"Modern Algebra"that widely spread the content and ideas of abstract algebra.This book was published in 1930-1931. Once appearance, it was loved by general mathematical scholars, for its structural arrangement is so clear and the drafting style is so orderly. Since then, this book revised for several times and translated into many languages. With regard to the content, this book organized a huge body of knowledge of algebra produced in the nineteenth century. In the mathematical thinking point of view, it inherited Hilbert's idea of axiomatic and constructed the knowledge of algebra based on set theory, this approach has been accepted by Bourbakian and carried forward to form the mathematical structure of the twentieth century, which is an important mathematical ideas.Base on a number of related literatures and the method of literature comparison and analysis, this paper studies on van der Waerden's book in detail. The main results are as follows:1. In the early twentieth century, this book was completed in Germany which had an atmosphere of algebraic research. This dissertation describes the circumstances of that time as well as van der Waerden's mathematical work.2. This book contains amount of algebra knowledge created in the middle and late nineteenth century. This dissertation investigates the content of the book and studies the development of the content and their relations.3. This book revised for several times and widely spread. This dissertation has a collects and summarizes the information of several different versions, and analyzes the change in each revision further. 4. In the beginning of the twentieth century, a great debate on the foundations of mathematics among mathematicians led to three different mathematical points. This dissertation analyzes the reason why van der Waerden chose Hilbert's formalism and inherited his idea of axiomatic.5. In the late nineteenth and early twentieth century, there were several of algebraic textbooks, written by contemporary mathematician. This dissertation compares them to van der Waerden's book, and reflects the success of his book.