Welcome to Jeff Anderson’s Applied Linear Algebra Fundamentals (ALAF) textbook project homepage.

Here you will find my larger vision for this work, links to my most recent content, and other resources to support excellent applied linear algebra curriculum that I make available to the world for no required paywall.

If you enjoy this work, please check out my support page to learn more about how you can become part a larger community of people who help to transform this dream into a reality.

Introduction

Linear algebra is one of the most powerful fields in applied mathematics. I like to say that linear algebra is the workhorse of modern day mathematical modeling. Students who learn to use linear algebraic theory to solve applied problems in their chosen field of interests can change their world.

Starting in the 1950s and continuing to present day, universities, governments and private industries have invested hundreds of billions of dollars to design and iteratively improve computer hardware and software to implement linear algebraic techniques at super fast speeds. This investment has been centrally focused on empowering scientists, engineers, and mathematicians to use linear algebra as a fundamental tool to solve applied problems. For a demonstration of the power of linear algebra, check out the following two lists of the top 10 algorithms of the 20th century:

Depending on how you count, between 5 - 10 of those algorithms are directly dependent on linear algebraic techniques. Google’s PageRank algorithm, quantum computing, artificial intelligence, and scientific computing would not exist in their current form without the power of linear algebra.

However, many introductory linear algebra textbooks fail to provide students with the type of support they need to get excited about this field and to create deep technical expertise to support innovative mathematical modeling. My favorite quote about the design of most mathematics textbooks, including many popular linear algebra textbooks, comes from Jo Boaler’s book Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching by and reads:

“Expertise in mathematics requires 10,000 hours of working mathematically. We do not need students to take a single method and practice it over and over again. That is not mathematics; it does not give students the knowledge of ideas, concepts, and relationships that make up expert mathematics performance. Someone working for 10,000 hours would need to be working on mathematics as a whole, considering mathematical ideas and connections, solving problems, reasoning, and connecting methods.

Most textbook authors in the United States base their whole approach on the idea of isolating methods, reducing them to their simplest form and practicing them. This is problematic for many reasons. First, practicing isolating methods induces boredom in students; many students simply turn off when they think their role is to passively accept a method and repeat it over and over again. Second, most practice examples give the most simplified and disconnected version of the methods to be practiced, giving students no sense of when or how they might use the method.” p. 43

Textbook content is only part of the problem. Another feature of this problem is the structure of the college textbook market. Most best-selling linear algebra textbooks are funded via a business model in which large publishing companies put high price tags on textbook content. This method of funding traditional textbooks implies that authors often write their work to help teachers to maintain a harmful status quo rather than to transform college education to empower students. For more information about how the textbook market harms students, see this article and that one too.

No more! No more expensive textbooks that channel students’ money to powerful publishing companies. No more textbook content that is devoid of modeling contexts related to students academic interests. No more supporting a world which enforces artificial scarcity in college STEM education by weeding out close to 60% of students with the largest impact on low-income and students of color. No more teaching linear algebra in ways that kill the creativity of and oppress the majority of learners for the benefit of an small group of elite scholars.

We can and should do better.

I am working to show what is possible when we put students, not publishing companies and academic journals, at the center of our professional careers as authors and researchers. The goal of my Applied Linear Algebra Fundamentals (ALAF) textbook project is to fundamentally transform the way college students can learn mathematics and to empower students to create new mathematical knowledge while solving applied problems that they care about.

This textbook and the auxiliary resources help readers learn to apply linear algebra in the context of meaningful modeling problems related to their academic and career interests. To learn more about this textbook, please click on and read any of the links below:

One very fun and challenging feature of this project is my desire to provide this work to the world with no required paywall. I choose not to sell my work to a large publishing company or to align myself with organizations who are invested in the status quo.

Instead I want to develop this work to be both transformational and accessible at the click of a button without requiring readers to pay for access. In my day job as a college math professor at an open admissions community college that educates the top 100% of students, I work with students who are homeless, food insecure, and experience severe financial difficulties. As an author, researcher, and content creator, I want all students, especially those who are most disadvantaged by our socioeconomic and political systems, to enjoy access to excellent educational experiences. Thus, I dedicate my authorship work to creating this type of world.

I am learning to ask for and accept help from people who believe in this approach to content creation and have the means to support it. For more about my approach to content creation, please click on and read any of the following links:

In the coming months and years, I plan to provide more information about how you can give me feedback on this project. I also plan to create detailed editing systems to welcome other people to be a part of my editing team. I plan to post that information here. If you have an interest in supporting this project, please check back in the future for updates.

With all that said, I provide my most recent content in the links below. May you enjoy reading this content as much as I have enjoyed writing it. Cheers to your learning and thank you for your attention!

Textbook Content

FRONT MATTER

PREFACE
CONTENT TITLE PLAYLIST
PREFACE
INTRO PLAYLIST

BACKGROUND THEORY AND HISTORICAL CONTEXTS

FUNDAMENTALS OF MATHEMATICAL MODELING
Content Title YouTube Videos
Introduction to Math Modeling (.pdf)
Modeling Playlist
Different Types of Mathematical Models
Types of Models Playlist
The Major Problems of Applied Linear Algebra
Major Problems Playlist
The Three Pillars of Applied Mathematics
Three Pillars Playlist

SECTION 2: THE LINEAR SYSTEMS PROBLEM

THE DETERMINANT FUNCTION
Content Title YouTube Videos
Discover the Determinant Function
Intro to Determinants Playlist
INTRODUCTION TO PERMUTATIONS
  1. Intro to Permutations: Lesson Notes (.pdf)
  2. Intro to Permutations: Exercise Solutions (.pdf)
Intro to Permutations Playlist
The Major Problems of Applied Linear Algebra
Major Problems Playlist
The Three Pillars of Applied Mathematics
Three Pillars Playlist