《抽象和线性代数的元素》
《Elements of Abstract and Linear Algebra》
简介：
抽象和线性代数的元素是对抽象代数的调查，重点是线性代数。它适用于数学，计算机科学和物理科学的学生。前三或四章可以独立作为一个学期的抽象代数课程，但它们的结构是为线性代数章节提供背景。这本书最困难的部分是关于组的，它们是用加法和乘法符号写的，还有陪集的概念，起初令人困惑。然而，在前第四章之后，这本书变得更容易，因为线性代数很容易遵循。完成线性代数的章节给出了抽象代数的基础一年本科课程。其余的材料完成课程。没什么背景的可以第一学期做前三章，第二学期做第4、5章。
演讲紧凑，组织严密，但仍然有些非正式。省略了许多基本定理的证明。这些证明由教授在课堂上提供或作为家庭作业练习分配。
本文的写作信念是，将抽象和线性代数作为一个连贯的学科而不是作为两个独立的学科来教授更为有效。同样，对于此文本，教授不会从文本中提取课程，而是在此基础上构建课程。从基础构建课程比从大书中提取课程更容易。因为在学生提取它之后，他仍然必须构建它。这本书的基本性质增加了它的灵活性，因为学生可以围绕它建立任何他想要的课程。
英文简介：
Elements of Abstract and Linear Algebra is a survey of abstract algebra with emphasis on linear algebra. It is intended for students in mathematics, computer science, and the physical sciences. The first three or four chapters can stand alone as a one semester course in abstract algebra, yet they are structured to provide the background for the chapter on linear algebra. The most difficult part of the book is about groups, which are written in additive and multiplicative notation, and the concept of coset, which is confusing at first. Yet, after the first fourth chapters the book gets easier as the linear algebra follows easily. Finishing the chapters on linear algebra gives a basic one year undergraduate course in abstract algebra. The rest of the material completes the course. Those with little background can do the first three chapters in the first semester, and chapters 4 and 5 in the second semester.
The presentation is compact and tightly organized, but still somewhat informal. The proofs of many of the elementary theorems are omitted. These proofs are to be provided by the professor in class or assigned as homework exercises.
This text is written with the conviction that it is more effective to teach abstract and linear algebra as one coherent discipline rather than as two separate ones. Also with this text the professor does not extract the course from the text, but rather builds the course upon it. It is easier to build a course from a base than to extract it from a big book. Because after the student extract it, he still have to build it. The bare bones nature of this book adds to its flexibility, because the student can build whatever course he want around it.
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最后更新：2025-03-15 16:46:56