Linear Algebra - Foundations to Frontiers

The University of Texas at Austin via edX

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Details

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Provider

edX
Pricing

Free Online Course (Audit)
Languages

English
Certificate

$99.00 Certificate Available
Duration & workload

15 weeks, 6-10 hours a week
Sessions

On-Demand
Level

Intermediate
Subtitles

English

Found in

Overview

Linear Algebra: Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets. Students appreciate our unique approach to teaching linear algebra because:

It's visual.
It connects hand calculations, mathematical abstractions, and computer programming.
It illustrates the development of mathematical theory.
It's applicable.

In this course, you will learn all the standard topics that are taught in typical undergraduate linear algebra courses all over the world, but using our unique method, you'll also get more! LAFF was developed following the syllabus of an introductory linear algebra course at The University of Texas at Austin taught by Professor Robert van de Geijn, an expert on high performance linear algebra libraries. Through short videos, exercises, visualizations, and programming assignments, you will study Vector and Matrix Operations, Linear Transformations, Solving Systems of Equations, Vector Spaces, Linear Least-Squares, and Eigenvalues and Eigenvectors. In addition, you will get a glimpse of cutting edge research on the development of linear algebra libraries, which are used throughout computational science.

MATLAB licenses will be made available to the participants free of charge for the duration of the course.

To see what former learners have to say about the course, read reviews on coursetalk.

We invite you to LAFF with us!

Syllabus

Week 0 Get ready, set, go!
Week 1 Vectors in Linear Algebra
Week 2 Linear Transformations and Matrices
Week 3 Matrix-Vector Operations
Week 4 From Matrix-Vector Multiplication to Matrix-Matrix Multiplication
Exam 1
Week 5 Matrix-Matrix Multiplication
Week 6 Gaussian Elimination
Week 7 More Gaussian Elimination and Matrix Inversion
Week 8 More on Matrix Inversion
Exam 2
Week 9 Vector Spaces
Week 10 Vector Spaces, Orthogonality, and Linear Least Squares
Week 11 Orthogonal Projection and Low Rank Approximation
Week 12 Eigenvalues and Eigenvectors
Final

Taught by

Robert van de Geijn and Maggie Myers

Reviews

4.1 rating, based on 15 Class Central reviews

4.8 rating at edX based on 13 ratings

Start your review of Linear Algebra - Foundations to Frontiers

Life Is Study

LAFF requires a major time commitment. Unless you are already familiar with some of the topics, you'll probably spend 5-8 hours a week. It is clear that a tremendous amount of effort went into producing the materials for this course. There are multiple homework exercises after almost every video and most weeks have one or more programming exercises where you implement and visualize linear algebra functions using tools the instructors have created. The instructors were also active on the forums, which was nice to see.
Anonymous

I was expecting a course that would make linear algebra interesting, one where I would understand what it it is used for and why it is useful. Instead, I found a course hugely dependent on Matlab and some weird "Flame" notation that seems to be uniq…

I was expecting a course that would make linear algebra interesting, one where I would understand what it it is used for and why it is useful. Instead, I found a course hugely dependent on Matlab and some weird "Flame" notation that seems to be unique to them. You will never use this anywhere else, and it is not free like Octave.

There were occasional huge leaps with no real preparation. e.g. the beginning of chapter 5 where the law of cosines is "assumed" (but in a totally different form from what most people have probably learned). Since the instructor blows past that part, you are bound to be lost for the rest of the chapter.

For intuitions on how and why matrices work, I found other online materials far far more helpful. This class actually turned me off of a subject I was excited to learn.
Venu

This is an excellent introductory course in Linear Algebra (LA). If you are taking this course as a lifelong learner - this will be an excellent start. Everything is explained well in an easy to understand manner. The course focuses on computationa…

This is an excellent introductory course in Linear Algebra (LA).

If you are taking this course as a lifelong learner - this will be an excellent start. Everything is explained well in an easy to understand manner. The course focuses on computational aspects of LA. I've ignored these in the first pass (I intend to go back to them later) without any impact on my understanding of the subsequent sections (excl the problems ofcourse)

However, do note that this is an introductory course and if you are looking for the MOOC to complement your college course, this may not sufficiently cover your syllabus. My recommendation is to start with this course (the concepts are explained very well) and then take another MOOC.
I can recommend Linear Algebra, Part 1 from RICE on edX. ALAFF - the advanced version of LAFF is potentially another one. I've signed up for it, but not yet started. Will update this review once I finish it. Also looking forward to Part 2 of the RICE course that is apparently scheduled for release in a few months (summer of 2022)

I've also written an indepth review (by and large an expansion of this review) here - https://www.classcentral.com/report/review-linear-algebra-foundations-to-frontiers/
Anonymous

I think this course is just really lazy - doesn't explain concepts in-depth and heavily relying on unconventional FLAME app and MATLAB. I was expecting something that are really related to the math concepts and coding but this one is rather it's just a follow along and skip everything type of course. There are so many errors (and didn't even bother to fix), and practically almost every other lecture has errata, and system they try to teach is kind of outdated and boring. I am not sure why it has such a high rating. I would rather do the math-heavy linear algebra first and then move on to the coding part with more popular coding languages not MATLAB.
Anonymous

Hesitated between 4 and 5 stars, ended up putting 5 because I think the 2-stars given by some people are a bit of a stretch. The course covers enough basics of linear algebra to be used as prerequisites by other courses who need some "basic" LA. It…

Hesitated between 4 and 5 stars, ended up putting 5 because I think the 2-stars given by some people are a bit of a stretch.

The course covers enough basics of linear algebra to be used as prerequisites by other courses who need some "basic" LA. It is overall well put out.

Many people complain about MATLAB and Flame which come up during the course, and I understand that. I have to admit that it has been a bit tedious at times BUT in the end I'm glad that they put that in. Some slight coding is allways nice when you study algorithms, and the basics methods of operations on matrices can be viewed as algorithms.
Flame give some sort of a visual to see what is going on inside the matrix during your loops, and I really felt that it help visualize and understand what I'm trying to do.

Now, it is possible to argue that one disliked these added tools, but I think it's at least unfair to tell that this is useless.
Overall I got exactly what I wanted out of this course. It was well put together, there are enough exercises to practice most things and the concepts are reasonably well explained throughout.

I just recommend this course if you want the basics of linear algebra, it is worth the time.
Anonymous

Instructors are nice. However.. So far, I have been quite disappointed in this course. There seems to be a substantial reliance on matlab, and FLAME notation, which comes up a lot during the course. While they emphasize that this is useful for unde…

Instructors are nice. However..

So far, I have been quite disappointed in this course. There seems to be a substantial reliance on matlab, and FLAME notation, which comes up a lot during the course. While they emphasize that this is useful for understanding the computer science aspect of linear algebra, I really wasn't able to make much of a tangible connection.

The class is also a bit disorganized. They expect you to unzip a file, and then periodically update the files with certain missing items and materials as you go through the course. They then expect you to somehow link that up with their online version of matlab, which I am still trying to figure out.

I am very tempted to abandon this course, as it hasn't really given me much application to real world settings, (which is ironic given that they are aiming to do just that).
Anonymous

Great course. I found it challenging but rewarding. You can always find help in the discussion section or an informative video explaining the answer. You can tell a lot of dedication went into creating this course.
Stojan Karlusic
Elia Schelokov
Catherine Lee
Mauro Sgarzi @maurosgarzi
Gaetano Pagani
Mark Henry Butler
Charles Starbuck
Gershom Tripp