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The Linear Algebra a Beginning Graduate Student Ought to Know, by Jonathan S. Golan
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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 to computer science, to the physical, biological, and social sciences, and to engineering. It encompasses an extensive corpus of theoretical results as well as a large and rapidly-growing body of computational techniques. Unfortunately, in the past decade, the content of 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 course is insufficient for graduate study. This book is intended to fill the gap which has developed by providing enough theoretical and computational material to allow the advanced undergraduate or beginning graduate student to overcome this deficiency and be able to work independently or in advanced courses. The book is intended to be used either as a self-study guide, a textbook for a course in advanced linear algebra, or 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 of the basic ideas and techniques, such as manipulation of small matrices and the solution of small systems of linear equations over the real numbers. More importantly, it assumes a seriousness of purpose, considerable motivation, and a modicum of mathematical sophistication on the part of the reader. In the latest edition, new major theorems have been added, as well as many new examples. There are over 130 additional exercises and many of the previous exercises have been revised or rewritten. In addition, a large number of additional biographical notes and thumbnail portraits of mathematicians have been included.
- Sales Rank: #1284718 in Books
- Published on: 2012-03-16
- Released on: 2012-03-16
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x .95" w x 6.10" l, 1.56 pounds
- Binding: Paperback
- 420 pages
Review
From the reviews of the third edition:
“This edition is enhanced by the inclusion of further results and many new examples. There are also over 130 additional exercises and many of the earlier ones have been revised. Furthermore, many more biographical notes and thumbnail portraits of mathematicians connected in some way with linear algebra have been added. This book continues to be very successful and useful, not only as a textbook for advanced linear algebra courses, but also for self-study and reference purposes.” (Rabe von Randow, Zentralblatt MATH, Vol. 1237, 2012)
From the Back Cover
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 to computer science, to the physical, biological, and social sciences, and to engineering. It encompasses an extensive corpus of theoretical results as well as a large and rapidly-growing body of computational techniques. Unfortunately, in the past decade, the content of 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 course is insufficient for graduate study.
This book is intended to fill the gap which has developed by providing enough theoretical and computational material to allow the advanced undergraduate or beginning graduate student to overcome this deficiency and be able to work independently or in advanced courses. The book is intended to be used either as a self-study guide, a textbook for a course in advanced linear algebra, or 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 of the basic ideas and techniques, such as manipulation of small matrices and the solution of small systems of linear equations over the real numbers. More importantly, it assumes a seriousness of purpose, considerable motivation, and a modicum of mathematical sophistication on the part of the reader.
In the latest edition, new major theorems have been added, as well as many new examples. There are over 130 additional exercises and many of the previous exercises have been revised or rewritten. In addition, a large number of additional biographical notes and thumbnail portraits of mathematicians have been included.
Most helpful customer reviews
14 of 15 people found the following review helpful.
Excellent next step after introductory linear algebra
By Tyler Fara
I've worked my way through the first six chapters of this book now, which have covered all of the most fundamental elements in linear algebra--fields, vector spaces, linear transformations, and so on--and it has been phenomenal. I'm probably exactly the intended audience for this book; I have a minor in Mathematics, a background in introductory linear algebra, and I'm studying higher level math independently to prepare for graduate school. This book does a phenomenal job balancing formal proofs with exposition and examples. I've never found the exposition tedious, but rather it's just enough to motivate the proofs as they arise. And each new proof will usually be illustrated by a handful of examples. The examples are great because they get well off the beaten path of finite dimensional vector spaces over the reals. One of the primary things I was looking for in a linear algebra book was one that showed linear algebra in applications outside of finite dimensions over the reals, and so I've really enjoyed the examples. In short, if you're looking for a comprehensive, challenging, and rewarding "next step" after introductory linear algebra, this is a great book!
2 of 18 people found the following review helpful.
One Star
By Robert
This is not the 3rd Edition
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