A First Course in Linear Algebra by Robert Beezer
A First Course in Linear Algebra - Table of Contents
1. Systems of Linear Equations
2. Vectors
3. Matrices
4. Vector Spaces
5. Determinants
6. Eigenvalues
7. Linear Transformations
8. Representations
9. Preliminaries
What You Will Learn in A First Course in Linear Algebra
This book is an introductory textbook aimed at college-level sophomores and juniors. It has numerous worked examples and exercises, along with precise statements of definitions and complete proofs of every theorem, making it ideal for independent study. The text has two goals: to teach the fundamental concepts and techniques of matrix algebra and abstract vector spaces, and to teach the techniques associated with understanding the definitions and theorems forming a coherent area of mathematics. So there is an emphasis on worked examples of nontrivial size and on proving theorems carefully. Typically such a student will have taken calculus, but this is not a prerequisite.
This book begins with solving systems of linear equations, then builds up through topics like matrix algebra, abstract vector spaces, determinants, and eigenvalues, culminating in advanced ideas such as linear transformations, diagonalization, change of basis, and Jordan canonical form. Beezer also integrates SageMath into the learning experience, offering a video tutorial and optional computation notes to use with Mathematica or Sage, encouraging interactive exploration. Reviewers praise its clarity, completeness, and the significant value.
Book Details & Specifications
Title:
A First Course in Linear Algebra by Robert Beezer
Publisher:
University of Puget Sound
Year:
2010
Pages:
1035
Type:
PDF
Language:
English
ISBN-10 #:
0984417559, B00262XN6S
ISBN-13 #:
978-0984417551
License:
GNU
Amazon:
Amazon
About the Author: Robert A. Beezer
The author
Robert A. Beezer
is a Professor of Mathematics at the University of Puget Sound. In addition to his teaching at the University of Puget Sound, he has made sabbatical visits to the University of the West Indies (Trinidad campus) and the University of Western Australia. He has also given several courses in the Master’s program at the African Institute for Mathematical Sciences, South Africa.
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