Help Advance the World with Advanced Linear Algebra
Your contribution will make it possible for us to develop and offer Advanced Linear Algebra: Foundations to Frontiers (ALAFF) on the edX platform. ALAFF is a full semester graduate level introductory course that will also be offered as the course Advanced Linear Algebra for Computing through our Online Masters in Computer Science, to those who are admitted to that program.
We believe in affordable education for all. While the University of Texas Online Masters in Computer Science is a great deal at $1000/course, not all will be admitted to that program and not all can afford it. Your contribution will also make the course (but not the summative assessments used to award credit for the masters program) available on edX, for free to auditors and for a nominal fee to those who want to earn a Verified Certificate.
A Course in Three Parts
The course breaks down into logical parts. We may end up offering the material as three MOOCs of around 4-5 weeks each, or one MOOC of 14-15 weeks. This is a detail that is yet to be decided.
Part I: Orthogonality
The Singular Value Decomposition (SVD) is possibly the most important result in linear algebra, yet too advanced to cover in an introductory undergraduate course. To be able to get to this topic as quickly as possible, we start by focusing on orthogonality, which is at the heart of image compression, Google's page rank algorithm, and linear least-squares approximation.
Part II: Solving Linear Systems
Solving linear systems, via direct or iterative methods, is at the core of applications in computational science and machine learning. We also leverage these topics to introduce numerical stability of algorithms: the classical study that qualifies and quantifies the "correctness" of an algorithm in the presence of floating point computation and approximation. Along the way, we discuss how to restructure algorithms so that they can attain high performance on modern CPUs.
Part III: Eigenvalues and Eigenvectors
Many problems in science have the property that if one looks at them in just the right way (in the right basis), they greatly simplify and/or decouple into simpler subproblems. Eigenvalue and eigenvectors are the key to discovering how to view a linear transformation, represented by a matrix, in that special way. Practical algorithms for computing them also are the key to practical algorithms for computing the SVD.
What a Value for the World!
We are writing a book specifically for the course, authored with PreTeXt so that videos, exercises, and solutions can be embedded in the text. We used PreTeXt to author our notes for our third MOOC titled LAFF-On Programming for High Performance. Have a look at how it allows short videos and carefully scaffolded exercises to be embedded in the online materials for that course [LINK].
A PDF of the notes, with exercises, solutions, and links to videos, will also be made available free of charge and those who want a printed copy will be able to purchase it through lulu.com, a self-publishing platform (expected cost: $20-$30). Paperback books used for similar courses were written in the late 1990s and cost $70-$90.
Thank you and "see" you in class!