MAT 247 – Elements of Linear Algebra

Purpose: to help other instructors teaching the same course

Common Course ID:  MAT 247 – Elements of Linear Algebra
CSU Instructor Open Textbook Adoption Portrait

Abstract: This open textbook is being utilized in a linear algebra course for undergraduate students by Alex Chen at California State University, Dominguez Hills. The open textbook consists of the online text along with interactive demonstrations of linear algebra concepts in an easy-to-understand and intuitive manner. The main motivation to adopt an open textbook was the convenience, cost, and excellent presentation of the textbook. Most students access the open textbook online.

Course Title and Number:  MAT 247 – Elements of Linear Algebra
Brief Description of course highlights:  Matrix algebra emphasizing small (2x2 and 3x3) matrices and vectors over the real numbers, solutions of systems of equations, determinants, inner product spaces, and linear transformations, with applications to other subjects, e.g. physical and computer science, economics, and operations research. https://catalog.csudh.edu/academics/mathematics/#coursestext

Student population: Students are typically math majors. The prerequisite for the course is MAT 153 – Precalculus. 

Learning or student outcomes:  Upon completing MAT 247 the student will:
• Have a solid foundation in working with scalars, vectors, and vector spaces,
• Understand matrices, basic operations, and their uses,
• Be able to solve linear systems by hand and through the Sage computer algebra system.
• Be able to apply linear algebra to other fields.

Key challenges faced and how resolved: There are two key challenges in this class. First, the study of linear algebra itself is extremely varied: from a completely algebraic approach filled with equations to a more intuitive, geometric approach. For students starting out in linear algebra, learning the geometric intuition is especially important. The textbook for the course is especially strong in its relation of linear algebra concepts to geometry and to practical applications. The second challenge is that there is a wide variation in the preparation of enrolled students. This leads to challenges in presenting the material to the class. By teaching the class in a more geometric manner, students with weaker backgrounds can understand why linear algebra is useful. At the same time, stronger students will not feel bored with the class.

Textbook or OER/Low cost Title: Immersive Linear Algebra

Brief Description:  The textbook presents material in a logical manner, emphasizing geometric intuition and applications whenever possible. Its greatest strength is a large number of interactive demonstrations, where readers can manipulate objects such as vectors in a web interface. It presents some material in a non-traditional order but does so in order to enhance intuitive understanding by the student rather than a calculation approach adopted by many textbooks. 

Please provide a link to the resource  http://immersivemath.com/ila/index.html

Authors: J. Ström, K. Åström, and T. Akenine-Möller:

Student access:  Students can access material from the immersive linear algebra website and posted assignments in Canvas. 

Supplemental resources: Homework assignments, lecture notes, links to class videos, and solutions to homework, quizzes, and exams are available on Canvas.

Provide the cost savings from that of a traditional textbook.  Typical introductory textbooks in linear algebra are about $100. For example, an excellent textbook is Linear Algebra by Fraleigh and Beauregard ($114.30): https://www.amazon.com/Linear-Algebra-Third-John-Fraleigh/dp/0201526751/ref=sr_1_1?crid=1QOZ4I6SNYRT5&keywords=fraleigh+linear+algebra&qid=1684137664&sprefix=fraleigh+linear+algebr%2Caps%2C143&sr=8-1&ufe=app_do%3Aamzn1.fos.f5122f16-c3e8-4386-bf32-63e904010ad0

License: Available online (I can’t tell what the license is.).   ISBN: 978-91-637-9354-7

OER/Low Cost Adoption Process

Provide an explanation or what motivated you to use this textbook or OER/Low Cost option. I wanted to find a free or inexpensive textbook for students that would be available online. From previous experience in the fundamental field of linear algebra, I also knew that the subject could be presented in a multitude of ways, not all of which would be friendly to students starting in the subject. When I found “immersive linear algebra,” I knew that this would be the perfect textbook for students learning the subject for the first time. Many mathematics students are used to calculation-oriented problems and thus struggle at first to adapt to the geometric approach presented by this book. However, in the end, I believe that students will be rewarded by the study of linear algebra in this manner. Indeed, by learning mathematics in a more conceptual rather than calculation-based approach, students will come to understand that mathematics can solve many important problems.

How did you find and select the open textbook for this course? I searched online for open and freely available textbooks.

Sharing Best Practices: :  Take your time in choosing a good book. There are many great, open textbooks on a variety of subjects. Just because it’s free does not mean it’s an inferior book!

Describe any challenges you experienced, and lessons learned. 

The greatest challenge with the use of “immersive linear algebra” is the lack of homework problems. While this drawback is important, it is more than compensated for by the strengths of the book. I had to write many homework problems on my own, but this also gave me the chance to design the problems in a way that would supplement the textbook.

Instructor Name: Alex Chen
I am an assistant professor in Mathematics at California State University, Dominguez Hills. I teach MAT 134, 193, 241, 247, 281, 403, 421, 495.

Please provide a link to your university page.  https://www.csudh.edu/math/faculty/

Please describe the courses you teach.The courses I teach are mostly math major courses in both pure and applied mathematics.

Describe your teaching philosophy and any research interests related to your discipline or teaching.  In my classes, I try to emphasize intuitive understanding rather than calculation. With computers getting more powerful, students who understand mathematical concepts and can apply them will be able to succeed in the workplace rather than students who can only calculate. This kind of understanding is also often harder for students, who in early education often received a great deal of practice with computational exercises but less so with conceptual exercises.

Lastly, while students can often practice computational exercises with homework, it is often more difficult to check their understanding of the concepts without the aid of an instructor. Thus, in my classes, I try to spend as much time as possible on the most important ideas of a subject.

In my research in applied mathematics, I take a similar approach. My main research project is on modeling virus transmission and replication within the human body. While my work is usually not complicated in a theoretical mathematics sense, an intuitive understanding of both mathematics and the domain science is needed. The most important skills needed are the understanding of the important processes at play, what processes are relatively minor, and how to design a model to capture the essence of the system.