What is LAFF?

LAFF is an experiment in a number of different dimensions.

• It is a resource that integrates a text, a large number of videos (more than 270 by last count), and hands-on activities.

• It connects hand calculations, mathematical abstractions, and computer programming.

• In encourages you to develop the mathematical theory of linear algebra by posing questions rather than outright stating theorems and their proofs.

• It introduces you to the frontier of linear algebra software development.

Who should LAFF?

Here are some people who may want to consider LAFF:

• The Independent Beginner. There were MOOC participants for whom LAFF was their first introduction to linear algebra beyond the matrix manipulation that is taught in high school. These are individuals who possess a rare talent for self-learning that is unusual at an early stage in one's schooling. For them, LAFF will be a wonderful playground.

• The Guided Beginner. We do not believe that MOOCs will educate the masses. Or, more precisely, we do not think they are an effective way for introducing a typical freshman to introductory material. What we hope to deliver with LAFF is a resource for someone who is an effective facilitator of learning (what some would call an instructor) to be used in a small to medium size classroom setting. While this individual may or may not have our level of expertise in the domain of linear algebra, what is important is that they know how to guide and inspire.

• The Refresher. At some point, a student or practitioner of mathematics (in engineering, the physical sciences, the social sciences, business, and many other subjects) realizes that linear algebra is as fundamental as is calculus. This often happens after the individual has already completed the introductory course on the subject and now he/she realizes it is time for a refresher. From our experience with the MOOC, LAFF seems to particularly delight this category of learner. We sequence the material differently from how a typical course on ``matrix computations'' presents the subject. We skip subjects that have little or no practical importance (like Kramer's rule). We focus on raising the participant's ability to think more abstractly. We link the material to how one should translate theory into algorithms and implementations. This seemed to appeal even to MOOC participants who had already taken multiple linear algebra courses.

• The Graduate Student. This is a subcategory of The Refresher. The material incorporated in LAFF are meant in part to provide the foundation for more advanced study of linear algebra. The feedback from those who had already taken linear algebra together with the fact that Robert teaches a graduate level course in numerical linear algebra for which the LAFF material provides a solid base makes it, in our opinion, a good choice for those who want to prepare for such a more advanced course. Robert will expect the students who take his graduate course to have the material covered by LAFF as a background, but not more.

• The Spectator. An occasional complaint about LAFF, when launched as a MOOC, was that is was not ``entertaining'' enough. Some participants demanded ``more enjoyable applications''. Often, these individuals had taken multiple linear algebra courses already.

  Here is the fundamental problem: A typical college or university offers at least three undergraduate linear algebra courses: Introduction to Linear Algebra; Linear Algebra and Its Applications; and Numerical Linear Algebra. LAFF aims to be that first course. In order to apply linear algebra in a meaningful way, you need to a background in linear algebra itself and in the area to which it is applied. Moreover, mathematics is not a spectator sport.

  Still, you are welcome to watch others LAFF! But LAFFing is contageous, so you may want to more actively partic

on CourseTalk.

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But What About Python?

We just Python to illustrate the abstractions and algorithms that you encounter in the course. However,

• You do not need to know any programming before you start!
  (We use programming and Python in a very limited way.)

• You will not learn Python from this course
  (Again: We use programming and Python in a very limited way.)

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Get the Notes! The "Notes to LAFF With" are a PDF book that becomes the "hub" through which the other LAFF material (e.g., the videos) can be accessed. It goes beyond the notes that were released as part of the edX MOOC by also providing an index into the materials and incorporating extensive solutions for the homework exercises. View the video on the left to get an idea of how this document helps you LAFF.

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You pick your price! We are trying a different approach to distributing this project. You get to decide how much you can afford and/or how much LAFF is worth to you. In part, we do this because we are too busy trying to get the materials done to have time to really think about what to charge. In part, it is to make sure that publishers don't make a rediculous profit at the expense of students. For the sake of full disclosure: Funds raised here will not go to UT-Austin or edX. The materials developed for the LAFF project are the intellectual property of the faculty who created it. What you pay will be used by the authors as they see fit. If enough funds are raised, we will feel considerable pressure to use these in part to create further materials for LAFF or followup projects. This site is self-funded by the authors.

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This is a work in progress. Our goal was to make these notes available to participants of the LAFF MOOC hosted by edX as that course came to completion. You may have to come back and get a new copy every once in a while. For now (and maybe for always if this method of distribution works), getting an update will be free.

These materials come with no warrantee. Any defect in the materials will be corrected at the author's discretion. We reserve the right to take down these materials with no notice.

If you reside outside the state of Texas:	Pick your price Financially Strapped Student $20.00 USD Successful Professional $50.00 USD LAFF Lover $100.00 USD
If you reside in the state of Texas: (You will be charged Texas sales tax.)	Pick your price Financially Strapped Student $20.00 USD Successful Professional $50.00 USD LAFF Lover $100.00 USD
If you fall in one or more of the following categories: You already purchased the notes and wish to get the latest updated version. You cannot afford $20. You would like to look at "Notes to LAFF With" first before purchasing. You sent us multiple bug reports (which was much appreciated). Please accept the notes as our "Thank You" gift! You believe that LAFF is priceless and hence attaching a price to it is just wrong. Obviously, if most follow this path, the experiment will fail. We will then have to stop supporting LAFF and you will have to go back to purchasing your textbooks from traditional publishers.	Click to download for free