Project Proposal
Our project is a host of educational resources to help students better understand the Singular Value Decomposition. Our goal is to make the concepts behind the SVD more accessible and eliminate the technicalities that frequently hinder other explanations. We are formatting our project mainly as two zines, or a DIY books, that can be printed at home and distributed to students either as supplemental material or as an introductory reading assignment. We are also publishing these on a website that includes supplemental material and videos that go over the same ideas as the zine.
The SVD is a key concept in linear algebra, yet many linear algebra students fail to understand it even when they have knowledge of its individual components. Meanwhile, students in high school algebra courses are often introduced to linear algebra concepts without knowing why they matter. Our first zine is an introduction to the linear algebra concepts necessary to understand the SVD, designed to be accessible for high school algebra students. Our second zine dives into the conceptual and mathematical understanding of the SVD, including examples of code and applications.
We have to balance the depth of our information with its accessibility. We want to front-load the logic behind the SVD, rather than start with mathematical proofs. Many students find that a more abstract or logic-based discussion of math concepts is more accessible than a symbolic, proof-based one. By beginning with this abstraction, we believe students will have an easier time following along with the more specific mathematical concepts. Our zines will not necessarily be a resource for being able to do SVD problems by hand (oof!), but a resource for understanding how programs like MATLAB perform it and why it matters. We do, however, want to provide math-minded students with the resources to further explore the depths of the SVD and all the math that makes it possible.
We don’t want our zines to look or feel like a math paper or textbook. We want to make sure that students don’t feel discouraged just by looking at it. We are exploring different methods of organizing information to make it more approachable and to inspire further inquiry rather than stifle it. By setting clear learning goals in section headings, beginning with abstractions and images, and moving into specific technical ideas, we hope to bring an understanding of the SVD to more students.