Understanding Linear Algebra by David Austin
Understanding Linear Algebra - Table of Contents
1. Systems of Equations
2. Vectors, Matrices, and Linear Combinations
3. Invertibility, Bases, and Coordinate Systems
4. Eigenvalues and Eigenvectors
5. Linear Algebra and Computing
6. Orthogonality and Least Squares
7. Singular Value Decompositions
What You Will Learn in Understanding Linear Algebra
This book focuses on helping learners grasp the core concepts of linear algebra without requiring prior knowledge of calculus. The book emphasizes active learning through interactive activities and exercises, encouraging students to develop their mathematical reasoning skills. It also integrates computational tools like Sage Math, allowing students to perform calculations directly within the text. Real-world applications, such as image compression and Google's Page Rank algorithm, are included to demonstrate the practical relevance of linear algebra.
Understanding Linear Algebra is an open textbook designed to support a two-course undergraduate linear algebra sequence. Topics include systems of equations, vector and matrix algebra, span, linear independence, bases, eigenvectors and eigenvalues, orthogonality, least squares, and singular value decompositions.
Until recently, linear algebra has mainly lived in the long shadow of calculus with many university linear algebra courses requiring several semesters of calculus as a prerequisite. Given the increasing prominence of linear algebra, Understanding Linear Algebra assumes no familiarity with calculus and, as such, can provide an alternative introduction into university-level mathematics. This book arises from my belief that linear algebra, as presented in a traditional undergraduate curriculum, has for too long lived in the shadow of calculus. Many mathematics programs currently require their students to complete at least three semesters of calculus, but only one semester of linear algebra, which often has two semesters of calculus as a prerequisite.
Book Details & Specifications
Title:
Understanding Linear Algebra by David Austin
Publisher:
Wreath
Year:
2023
Pages:
517
Type:
PDF
Language:
English
ISBN-10 #:
1958469165
ISBN-13 #:
978-1958469163
License:
CC BY 4.0
Amazon:
Amazon
About the Author: David Austin
The author
David Austin
is a Professor of Mathematics at Grand Valley State University. He is well know for his work on Linear Algebra. In his work, he explains difficult ideas step by step, making them easier to understand.
Read or Downloadable Understanding Linear Algebra
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