二元二次型理论的发展演化

【作者】 胡俊美；

【导师】 邓明立；

【作者基本信息】 河北师范大学 ， 基础数学， 2006， 硕士

【摘要】 作为数论的一个分支,二元二次型理论有着悠久的历史。从对平方数的注意到对特殊二元二次型的研究,再到对一般二元二次型的探索与发展,中间经历了一个漫长曲折的历史过程。 本文在详尽占有资料的基础上,对二元二次型理论的发展演化做了系统的分析与总结。以二元二次型的发展为中心,阐明了它与后来许多重要数学思想的关系,强调了从特殊到一般、化无穷为有穷、从具体到抽象的重大作用,以期给现代数学研究提供借鉴意义。更多还原

【Abstract】 As a branch of number theory, the theory of binary quadratic forms has a long history. From noticing square numbers to studying special binary quadratic forms, and to exploring the general binary quadratic forms, it was a long and hard process.On the basis of abundant material, the present paper tries to summarize and analyze the evolution of the theory of binary quadratic forms;Centering on the development of binary quadratic forms, this paper illuminate its relationship to much important ideas in mathematics;It emphasizes the great significance of the development from specification to generalization, from infinity to finitude, and from concretion to abstraction. I hope that it is useful to the research of modern mathematics.更多还原