Textbook

# Visual Linear Algebra

• Overview
Visual Linear Algebra is a new kind of textbook—a blend of interactive computer tutorials and traditional text. The computer tutorials provide a lively learning environment in which students are introduced to concepts and methods and where they develop their intuition. The traditional sections provide the backbone whose core is the development of theory and where students’ understanding is solidified. Although the design of Visual Linear Algebra is novel, the goals for the book are quite traditional. Foremost among these is to provide a rich set of materials that help students achieve a thorough understanding of the core topics of linear algebra and genuine competence in using them.
Chapter 1. Systems of Linear Equations.

Chapter 2. Vectors.

Chapter 3. Matrix Algebra.

Chapter 4. Linear Transformations.

Chapter 5. Vectors Spaces.

Chapter 6. Determinants.

Chapter 7. Eigenvalues and Eigenvectors.

Chapter 8. Orthogonality.

Appendix A: Glossary of Linear Algebra Definitions.

Appendix B: Linear Algebra Theorems.

Appendix C: Advice for Using Maple with Visual Linear Algebra.

Appendix D: Commands Used in Maple Tutorials.

Appendix E: Appendix with Visual Linear Algebra.

Appendix F: Commands Used in Mathematic Tutorials.

Appendix G: Answers and Hints for Selected Pencil and Paper Problems.

Index.

Hallmark Features
• Tutorials and traditional text.  Visual Linear Algebra covers the topics in a standard one-semester introductory linear algebra course in forty-seven sections arranged in eight chapters. In each chapter, some sections are written in a traditional textbook style and some are tutorials designed to be worked through using either Maple or Mathematica.
• About the tutorials.    Each tutorial is a self-contained treatment of a core topic or application of linear algebra that a student can work through with minimal assistance from an instructor.  The thirty tutorials are provided on the accompanying CD both as Maple worksheets and as Mathematica notebooks. They also appear in print as sections of the textbook.
• Geometry is used extensively to help students develop their intuition about the concepts of linear algebra.
• Applications.  Students benefit greatly from working through an application, if the application captures their interest and the materials give them substantial activities that yield worthwhile results. Ten carefully selected applications have been developed and an entire tutorial is devoted to each of them.
• Active Learning. To encourage students to be active learners, the tutorials have been designed to engage and retain their interest. The exercises, demonstrations, explorations, visualizations, and animations are designed to stimulate students’ interest, encourage them to think clearly about the mathematics they are working through, and help them check their comprehension.

Professor Reviews
I like the book a lot and in fact have been watching for it ever since I participated in a visual linear algebra workshop. The geometric material and the computer images are very worthwhile. This text raises the bar extremely high for visual treatments.
You can tell that it has profited from lots of pedagocial thinking and discussion by the way topics are introduced and sequenced--very "clean" and  appealing.

Frederick Gass, Miami University

This is indeed a new kind of textbook, and it tackles with the difficult task of naturally incorporating computers into the standard linear algebra course in order to enhance student participation and understanding.   This reviewer believes that this job has been done very well.

Gizem Karaali, University of California in Santa Barbara

## Available Versions

Visual Linear Algebra
by Eugene A. Herman, Michael D. Pepe
ISBN 978-0-471-68299-8