Linear Algebra by Jason Siefken
Linear Algebra - Table of Contents
1. Sets, Vectors, and Notation
2. Sets of Vectors, Lines and Planes
3. Spans, Translated Spans and Linear Independence/Dependence
4. Dot Prudcts and Normal Forms
5. Projections and Vector Components
6. Subspaces and Bases
7. Matrix Representations of Systems of Linear Equations
8. Coordinates and Change of Basis
9. Linear Transformations
10. The Composition of Linear Transformations
11. Range and Nullspace of a Linear Transformation
12. Inverse Functions and Inverse Matrices
13. Change of Basis II
14. Determinants
15. Eigenvalues and Eigenvectors
16. Diagonalization
What You Will Learn in Linear Algebra
"Linear Algebra" by Jason Siefken is a modern introductory textbook designed to help students truly understand the foundations of "Linear Algebra" through active participation. Rather than presenting long lectures of theory, the book encourages learners to think, explore, and discover ideas on their own. Its clear structure and student-friendly tone make it well suited for first-year university courses.
The book is organized into short modules that blend explanations with carefully designed questions and exercises. Topics such as vectors, matrices, systems of equations, and linear transformations are introduced gradually, allowing students to build intuition step by step. This "Inquiry-Based Learning" approach shifts the focus from memorizing formulas to developing reasoning skills and mathematical confidence through guided problem solving.
Widely used as a classroom workbook and self-study resource, the book supports interactive teaching methods and collaborative learning. Its emphasis on "Conceptual Understanding" and "Mathematics Education" makes it especially helpful for students who find traditional textbooks overwhelming. Overall, Jason Siefken’s book offers a thoughtful, engaging, and accessible pathway into "Abstract Algebra" ideas at the introductory level.
Book Details & Specifications
Title:
Linear Algebra by Jason Siefken
Publisher:
Jason Siefken
Year:
2020
Pages:
219
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
CC BY-SA 4.0
Amazon:
Amazon
About the Author: Jason Siefken
The author
Jason Siefken
is a mathematician and university educator known for his strong focus on "Mathematics Education" and student-centered teaching. He teaches at the "University of Toronto", where he works closely with undergraduate students in courses such as "Linear Algebra" and differential equations. As the author of "Linear Algebra", he emphasizes "Inquiry-Based Learning", encouraging students to explore ideas through guided problems and discussion. His teaching philosophy prioritizes "Conceptual Understanding" over memorization, helping learners develop intuition about vectors, matrices, and linear systems through active engagement and clear mathematical thinking.
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