LAFF started as a Massive Open Online Course (MOOC) funded in part by the
University of Texas System
and the National Science Foundation (grant ACI-1148125), created by
Prof. Robert van de
Dr. Maggie Myers at
The University of Texas at Austin, and launched on the
The materials continue to be available with edX until Sept. 15, 2014 .
Register for the Spring 2015 LAFF offering on edX
This webpage makes the materials developed for that course
available in the form of an e-book that integrates the videos and
interactive activities. It will remain active even after the edX
course is closed on Sept. 15, 2014.
Watch the edX LAFF "Sizzler"
What is LAFF?
LAFF is an experiment in a number of different dimensions.
Our hope is that this will enable you to master all the standard topics that are taught in typical introductory undergraduate linear algebra course.
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:
If you are still trying to decide whether LAFF is for you, you may want to
read some of the
Reviews of LAFF (The MOOC) on CourseTalk.
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 were
individuals who possess a rare talent for self-learning that is
unusual at an early stage in one's schooling. For them, LAFF was
a wonderful playground. Others like them may similarly benefit from
What we also 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, for example, in a 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 she/he can use the LAFF materials to guide, inspire, and teach.
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 delight this category of learner. We
sequence the material differently from how a typical course on
"matrix computations" presents the subject. We focus on fundamental
topics that have practical importance and 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 and/or already
had advanced degrees.
The Graduate Student.
This is a subcategory of The Refresher. The material that is incorporated in LAFF are meant in part to provide the
foundation for a more advanced study of linear algebra. The feedback
from those MOOC participants who had already taken linear algebra
suggests that LAFF is a good choice for those who want to prepare for a
more advanced course. Robert will expect the students who take his
graduate course in Numerical Linear Algebra to have the material covered by LAFF as a background,
but not more.
But What About Python?
We use IPython Notebooks to help you master the abstractions and algorithms that you
encounter in the course. However,
So, don't let Python stop you!
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.)
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.
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.
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
Pay via PayPal
| If you reside in the state of
(You will be charged Texas sales tax.)
Pay via PayPal
If you prefer not using PayPal, purchase on lulu.com:
(We prefer you use one of the options listed above.)
Financially Strapped Student Pricing
Successful Professional Pricing
(after you buy on LULU.com,
the additional materials)
| If you fall in one or more of the following
You already purchased the notes and wish to get the latest
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.
Click to download for free
Obviously, if few choose to pay, the experiment will
fail. We will then have to stop supporting LAFF and you may
have to go back to purchasing traditional textbooks from traditional
In addition to LAFF, which is an introductory undergraduate
treatment of linear algebra,
Robert has videotaped most of his graduate course on Numerical
Linear Algebra this past fall.
The notes, with links to the videos, for this course are now
Linear Algebra: Foundations to Frontiers - A Collection of Notes on
Numerical Linear Algebra .
Still very much a work in progress. Enjoy!
LAFF was carefully designed to be an online course. It
took a year of hard work on the part of several authors to
design that course,
create a book, and produce about 270 videos. In contrast, the
graduate course is an ongoing project where Robert simply
taped his lectures with a camera and made the same materials
available to the world as he makes available to his own
students. In other words, it does not receive the same
level of tender loving care as LAFF did. One could say it is
receiving NO tender loving care at all... For some lectures,
he forgot to turn on the camera...
Use them as you feel
fit, but don't expect any support.