Is David C. Lay’s Linear Algebra and its Applications a Suitable Choice for Beginners?

David C. Lay’s Linear Algebra and its Applications has long been the textbook for Florida State University (FSU)’s MAS 3105 Applied Linear Algebra I course. This textbook has served us well as it allows flexibility in selecting the content for multiple courses. However, instructors often adapt the material to suit their specific course goals, leading to significant modifications. This article explores whether this textbook is a good fit for beginners in linear algebra, considering its applications and breadth.

Course Context and Key Features

When this course was first established, there already existed a proof-based linear algebra course. This proof-based course served as an introduction to mathematical proofs, while the Lay version was specifically designed for applied mathematics majors. It was also taken by students in science and engineering. Over time, the applied course delved into eigenvectors and eigenvalues, while the proof-based course did not.

Linear algebra is a vast field, and instructors often underestimate the amount of material they can cover in a semester. This is particularly true for the first introductory course, where foundational concepts are introduced.

Teaching Experience and Perspective

For many years, I have taught the follow-on course MAS 4106 Applied Linear Algebra II. In this course, I always began with a thorough study of eigenstuff on 2x2 matrices. This provided valuable review and reinforcement for the students, helping them grasp more complex concepts as the course progressed.

Is the Book Suitable for Beginners?

The answer is yes, but with certain caveats. The book excels in providing a broad range of applications, which aligns with its title, Linear Algebra and its Applications. This feature makes it particularly useful for students who want to understand the practical applications of linear algebra. However, if your immediate goal is to master the theoretical underpinnings of linear algebra, including proofs, there are other books that might be more suitable.

Alternative Books for Proof-based Learning

If your objective is to delve into the theoretical aspects of linear algebra and not just the computational methods, consider books such as Paul Halmos’ Finite-Dimensional Vector Spaces. Halmos’ book is a rigorous introduction to the subject, making it an excellent choice for students who wish to deepen their understanding through proofs and theoretical exploration.

Conclusion

The choice of textbook ultimately depends on your specific goals. If you aim to excel in computational methods and understand various applications of linear algebra, Lay’s book is a solid choice. However, if your primary objective is to study linear algebra with a focus on proofs and theoretical understanding, there are other, more appropriate texts available.

Note: This article is intended to provide guidance for students choosing a textbook for their linear algebra course. It is based on the author's experience and may vary depending on the instructor's approach and course objectives.