Jeff Anderson’s Applied Linear Algebra Fundamentals (ALAF) Textbook Project

~ Jeff Anderson Math

In this post, I describe my goals for my Applied Linear Algebra Fundamentals (ALAF) textbook. I started work on this textbook in 2013 and continue to build, refine, and improve my writing on a daily basis. I present the larger vision for this work and also provide links to my current progress on this book.

Textbook features

Here are some unique features of this textbook:

  • This textbook features a library of rich and authentic linear algebra laboratory experiences that invite learners to engage in applied mathematical modeling using linear algebraic techniques. Each laboratory experience from this library relates to students’ academic and career interests. The goal is to provide students with a large choice of options so that they can choose their own adventure in their introductory classes. If I do this well, students will be able to explore the entire introductory applied linear algebra curriculum through the lens of a sequence of applied problems they choose that are related to their major. Learners will also learn how to apply the math they learn to solve problems in their world and gain valuable experiences engaging in meaningful real-world modeling.

  • The equipment, software, and materials needed for each laboratory experience is available to students and institutions at low cost. I also create a rich support structure so that schools that operate on a constrained budget can easily access these high-quality laboratory materials. As this project grows, I plan to provide training and support so that teachers feel comfortable guiding their students to use and play with the laboratory equipment as part of their introduction to applied linear algebra.   
  • The textbook material is written to support and enrich each laboratory experiences. Throughout the textbook, I provide examples and mathematical content that support student explorations on the laboratory experiences. The goal is to make it much easier for students to work on meaningful applied modeling and for teachers to support their students work.
  • This textbook presents the rich history of applied linear algebra as it exists today. By the time students finish with this textbook, they will be ready to apply their expertise in linear algebra to solve applied problems in government, industry, and academia. A dedicated student can use this learning resource to become a creator of new mathematics and to understand linear algebra at the deepest and highest levels possible. This book represents an on-ramp to modern day linear algebra as it is used by the world’s leading experts. Moreover, I organize and develop this book based on research in cognitive science, the psychology of learning, and in the science of expertise so that my work leverages research-based models for learning to accelerate students development in meaningful ways.
  • To enhance the mathematical definitions, theorems, and techniques in this textbook, I make a concerted effort to present a wide array of interesting and relevant real-world examples that elucidate interesting features of each mathematical idea in applied contexts related to student interests. Whenever possible, I will eschew toy examples that have no grounding in the readers observed reality and instead create examples that relate to the learners lived experiences.

    Note: one of the downsides of applied learning involves added complexity. I anticipate that in rare cases, I will present a toy example to illustrate an idea in its simplest form as a starting point. However, I pledge to do everything I can to avoid this type of writing. I want to write a book that speaks to the applied nature of linear algebra in significant and meaningful ways.
  • The practice problems and exercises available in this textbook will be meaningful. I will not follow the lead of many, many authors who write a large collection of low-level problems that target theorems. In other words, the practice problems I provide are not focused on the drill-and-kill approach to learning mathematics. Instead, I guide learners to do the much harder work of meaning making, career building, and applied modeling. Of course, I will provide a small collection of procedural practice problems but only within the context of a larger collection of deeper problems that push students to develop deep understanding of the mathematical ideas, to make interconnections between their past and current learning, and to learn how to use math in applied contexts related to their own interests.

  • My current plan is to provide practice exercise at multiple levels of depth including: undergraduate-level exercises, graduate-level exercises, and post-graduate-level research projects. I also plan to provide pointers to other educators who want to develop curriculum to support the mission of this project and to inspire future generations of students.

  • I plan to produce full solutions to the undergraduate-level exercises at the end of each section. My current plan is to offer these on my Patreon account for my JAM Patrons. At present, I do not plan to provide solutions for graduate and post-graduate-level problems though I am open to those projects in the future if feasible.
  • I want this textbook to be open access meaning that we make this available for no required paywall. I work with many students who do not yet have the money to pay for an expensive textbook. I want to ensure that those students get free access to all learning materials they need to thrive. To do this, I invite those of us who can afford to pay for this type of work to join a larger community of people who fund this project. To learn more about how you can support this work, please visit my Support webpage. To learn more about my financial plans for the money I earn, please visit my Financial Plan webpage.
  • For every textbook section I write, I produce and publish a sequence of open-access YouTube videos that cover the same content. I work hard to ensure that this YouTube content is ADA compliant and can be used to support flipped learning classrooms. By providing video access to the textbook content, students have more options for engaging in learning. Students who want to read the textbook can do so while students who prefer guided video lectures can use those instead. The goal is to provide multiple options for student engagement and to support each student in choosing the resources they believe will best support their learning. Below I provide two samples of textbook sections along with their corresponding YouTube video playlist which presents the written material to students in video form:

Current Progress

Below I include some of my most recent progress on this project. Note: The section symbol § is a character for representing individually numbered sections of a document.