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Help Advance the World with Advanced Linear Algebra

Raised toward our $75,000 Goal
289 Donors
Project has ended
Project ended on September 05, at 09:00 AM CDT
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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, a self-publishing platform (expected cost: $20-$30). Paperback books used for similar courses were written in the late 1990s and cost $70-$90. 




You now have three options to contribute:


  •  Make a tax deductible contribution to the project on Hornraiser.
  • Purchase Linear Algebra: Foundations to Frontiers: Notes to LAFF With at  and we will donate 100% of the purchase price.  This does mean your contribution is not tax deductible and your name will not appear on the "Donor Wall."
  • Send us a check made out to "The University of Texas at Austin indicating the check is for this fundraiser.  Please send that check to       Robert van de Geijn      2317 Speedway, Stop D9500      Austin, TX 78712  We will make sure it gets to the person who processes such donations.  This option is also tax deductible.  Please indicate whether you want your name to appear on the "Donor Wall."


Thank you and "see" you in class!




Choose a giving level


Contribute what you can

Contributing what you can will give us a thumbs up that you care. Any amount will be appreciated!


Fund the Foundation

The notes, videos, carefully scaffolded homework, and other activities are the foundation of this course. Help fund them!


Front the Frontier

As in our other MOOCs, we link the foundational material to the frontier of the field through enrichments at the end of each week. These are the "nuggets" that go beyond.


Underwrite a Unit

The materials have been chunked into convenient pieces that we call units. A typical unit incorporates videos and exercises to help discovery learning.


Subsidize a Section

A set of coherent units combine into a section. A section corresponds roughly to a topic covered in a lecture.


Advance LAFF

Advanced Linear Algebra: Foundations to Frontiers is a full semester course, with around 14 weeks of material. Each week focuses on an important topic in linear algebra. The week starts with a launch that gives a glimpse of what is to come. Upon concluding the core material for the week, enrichments expose you to the frontier. At the end of the week, the key concepts are summarized.

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