Contemporary Linear Algebra
September 2002, ©2003
From one of the premier authors in higher education comes a new linear algebra textbook that fosters mathematical thinking, problem-solving abilities, and exposure to real-world applications. Without sacrificing mathematical precision, Anton and Busby focus on the aspects of linear algebra that are most likely to have practical value to the student while not compromising the intrinsic mathematical form of the subject. Throughout Contemporary Linear Algebra, students are encouraged to look at ideas and problems from multiple points of view.
* Systems of Linear Equations
* Matrices and Matrix Algebra
* Matrix Models
* Linear Transformations
* Dimension and Structure
* General Vector Spaces
Appendix A: How to Read Theorems
Appendix B: Complex Numbers
- Contemporary Linear Algebra meets the guidelines of the Linear Algebra Curriculum Study Group (LACSG).
- The authors believe that a working knowledge of vectors in Rn and some experience with viewing functions as vectors is the right focus for this course. Material on Axiomatic vector spaces appears toward the end so as to avoid the wall of abstraction so many students encounter.
- All major concepts are introduced early and revisited in more depth later on. This spiral approach to concept development ensures that all key topics can be covered in the course.
- The text provides students with a strong geometric foundation upon which to build. In keeping with this goal, the text covers vectors first then proceeds to linear systems, which allows the authors to interpret parametric solutions of linear systems as geometric objects.
- Looking Ahead features provide students with insight into the future role of the material currently being studied.
- A wide range of applications throughout gives students a sense of the broad applicability of linear algebra. The applications include very modern topics such as global positioning and internet search procedures.
- Basic Exercises progressing in difficulty from drill to challenging.
- Discussion and Discovery exercises that are more open-ended.
- Working with Proofs exercises which ask students for precise proofs.
- Technology Exercises that teach students how to use such tools as MatLab, Mathematica, Maple and Derive.
- Theorems and proofs are presented with precision, but in a style appropriate for beginning students.
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