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Books > Science & Mathematics > Mathematics > Algebra
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The Linear Algebra a Beginning Graduate Student Ought to Know (Paperback, 3rd ed. 2012)
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The Linear Algebra a Beginning Graduate Student Ought to Know (Paperback, 3rd ed. 2012)
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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.
General
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