Visual Linear Algebra
March 2005, ©2005
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.
- 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.
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.