The Linear Algebra a Beginning Graduate Student Ought to Know
The Linear Algebra a Beginning Graduate Student Ought to Know
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DOI：
10.5860/choice.41-6582
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发表时间：
2004-01
期刊：
影响因子：
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通讯作者：
J. Golan
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文献类型：
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作者：
J. Golan
线性代数是一个活的，活跃的数学分支，是中央几乎所有其他领域的数学，无论是纯粹的和应用，以及计算机科学，物理和社会科学，工程。它需要一个广泛的语料库的理论结果，以及大量的计算技术。不幸的是，近年来，完成数学本科学位所需的线性代数课程的内容已经耗尽，以至于它们无法提供足够的理论或计算背景。学生们不仅不太能够制定甚至遵循数学证明，他们也不太能够理解他们需要的应用程序的数值算法的数学。当然，一般本科线性代数课程中提供的材料对于研究生学习是不够的。这本书的目的是填补这一空白，提供足够的材料“理论和计算”，让学生独立工作或在先进的课程。这本书的目的是用于几种可能的方式之一：（1）作为自学指南;（2）作为教科书的课程，在高等线性代数，无论是在高年级本科水平或在第一年的研究生水平;或（3）作为参考书。它也是为了准备学生的线性代数部分的预备考试或博士资格考试。这本书是自成一体的，它没有假设任何以前的线性代数的正式知识，虽然读者被假定已经暴露，至少非正式地，一些基本的思想和技术，如解决一个小系统的线性方程组的真实的数字。更重要的是，它确实假定了读者的严肃性和一点点数学复杂性。这本书还包含了1000多个练习，其中许多都是非常具有挑战性的。
Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques. Unfortunately, in recent years the content of the linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the mathematics of the numerical algorithms they need for applications. Certainly, the material presented in the average undergraduate linear algebra course is insufficient for graduate study. This book is intended to fill this gap by providing enough material "theoretical and computational" to allow the student to work independently or in advanced courses. The book is intended to be used in one of several possible ways: (1) as a self-study guide ; (2) as a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level ; or (3) as a reference book. It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams. The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, such as the solution of a small system of linear equations over the real numbers. More importantly, it does assume a seriousness of purpose and a modicum of mathematical sophistication on the part of the reader. The book also contains over 1000 exercises, many of which are very challenging.