Linear Algebra - Foundations to Frontiers

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edX online courses
Harvard University, the Massachusetts Institute of Technology, and the University of California, Berkeley, are just some of the schools that you have at your fingertips with edX. Through massive open online courses (MOOCs) from the world's best universities, you can develop your knowledge in literature, math, history, food and nutrition, and more. These online classes are taught by highly-regarded experts in the field. If you take a class on computer science through Harvard, you may be tau...
Harvard University, the Massachusetts Institute of Technology, and the University of California, Berkeley, are just some of the schools that you have at your fingertips with edX. Through massive open online courses (MOOCs) from the world's best universities, you can develop your knowledge in literature, math, history, food and nutrition, and more. These online classes are taught by highly-regarded experts in the field. If you take a class on computer science through Harvard, you may be taught by David J. Malan, a senior lecturer on computer science at Harvard University for the School of Engineering and Applied Sciences. But there's not just one professor - you have access to the entire teaching staff, allowing you to receive feedback on assignments straight from the experts. Pursue a Verified Certificate to document your achievements and use your coursework for job and school applications, promotions, and more. EdX also works with top universities to conduct research, allowing them to learn more about learning. Using their findings, edX is able to provide students with the best and most effective courses, constantly enhancing the student experience.

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19058 reviews

Course Description

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 assignme...

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.

We invite you to LAFF with us!

Reviews 9/10 stars
162 Reviews for Linear Algebra - Foundations to Frontiers

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Rankings are based on a provider's overall CourseTalk score, which takes into account both average rating and number of ratings. Stars round to the nearest half.

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student

10/10 starsCompleted
3 years, 6 months ago
To former and future students looking to LAFF: Over at ulaff.net, Robert and Maggie just released all of the notes in a downloadable PDF with embedded hyperlinks to the videos. It's a whopping 900 pages of some of the best linear algebra instruction you will ever find, with accompanying videos, homeworks, exams, and notebooks. Best of all, it is available on a generous "pick your price" model ensuring everyone can have access to this great material regardless of income. It looks like the instructors have plans to update and refine the material as time progresses, and supporting them in that effort is a worthy cause. This material is so fundamental to many different areas that everyone should be able to LAFF with Robert and Maggie! To the course staff: Thanks so much for one of the most well done MOOCs I've ever taken!
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student

10/10 starsCompleted
2 weeks ago
Instructors and course were great! They were very present in discussions (would reply within 24 hours from my experience), and they were very helpful. They provided information at a good level (alluded to but did not delve into topics above the level of the course) both in the course and in the discussions. It was clear they care and put in a lot of effort.
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Rob Weatherston profile image
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Rob Weatherston

6/10 starsCompleted
3 weeks ago
This course is focused on the algebra and computer science aspects of linear transformations. It is particularly strong on 'slice and dice' algorithms for calculating matrix and vector operations and their implementation, in a Matlab framework only. It will be of particular interest to computer scientists who want to speed up their calculations. The instructor engagement is excellent and the course material is very well supported. In my opinion the course would benefit from having a much deeper geometrical aspect, there was very little intuition of how the operations translate geometrically. I studied in parallel with the 3brown1blue content on youtube, which was helpful. I would have liked to have a couple of weeks more material on SVD and sparse matrices. For practical use, course material in python (which it was previously) would be much more useful to me than the Matlab implementations. Overall a good course.
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Peter Osusky profile image
Peter Osusky profile image
8/10 starsCompleted
  • 0 reviews
  • 0 completed
1 month, 1 week ago
I have taken Linear Algebra course previously, during my first year in college and I just wanted to refresh my memory and concepts I may have forgotten. Suprisingly, LAFF not only helped me remember things I have learned back in a day (except for a few missing, such as deriving of a Cofactor formula), but introduced me to a whole "computational" part of Linear Algebra as well. E.g. creating various algorithms using slicing and dicing and evaluating them with the regards to flops and memops etc. Thank you Robert, thank you Maggie it's been a pleasure for me to be your student, at least for a while. Ďakujem!
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10/10 starsCompleted
20 hours ago
Excellent course! I highly recommend it. The instructors and course content/format were awesome. I wanted a refresher on linear algebra to help my understanding of its use in machine learning/neural networks. It was exactly what I needed. I loved linear algebra back in my college days and enjoyed it once again.
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David Scott profile image
David Scott profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
3 days, 18 hours ago
Overall, this is a great course on linear algebra. Instructors Robert and Maggie were quick to respond to comments and questions. Many of the work problems had available a video of an instructor working through the problem, explaining each step (if I got stuck). I especially enjoyed the enrichments, which gave us a taste of different applications. I like the way they start with scalars, then vectors and then work with "slices" of vectors and matrices. I think some more graphical analogies would help with understanding. Also, I would have benefited from more practice problems. Often I found myself going back to a previous section to review the available practice problems to help drill in certain concepts. I liked having access to online Matlab for the duration of the course, which helped with much of the computation. Since Matlab is a commercial software (and may be cost prohibitive for many), I want to point out that Scilab and Octav... Overall, this is a great course on linear algebra. Instructors Robert and Maggie were quick to respond to comments and questions. Many of the work problems had available a video of an instructor working through the problem, explaining each step (if I got stuck). I especially enjoyed the enrichments, which gave us a taste of different applications. I like the way they start with scalars, then vectors and then work with "slices" of vectors and matrices. I think some more graphical analogies would help with understanding. Also, I would have benefited from more practice problems. Often I found myself going back to a previous section to review the available practice problems to help drill in certain concepts. I liked having access to online Matlab for the duration of the course, which helped with much of the computation. Since Matlab is a commercial software (and may be cost prohibitive for many), I want to point out that Scilab and Octave look like good free alternatives to perform many of the tasks which Matlab will do.
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Alena Sorokina profile image
Alena Sorokina profile image

Alena Sorokina

10/10 starsCompleted
1 week, 1 day ago
It is so advanced level as I hoped! You can do as many of those exercises as you feel you need in order to get the point. Now i have graduate level and anderstand the numerical linear algebra.
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Shaun Zen profile image
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Shaun Zen

10/10 starsCompleted
1 week, 3 days ago
This was the most accessible course to linear algebra I have taken. But the course doesn't dumb down the materials (there quite a number of proofs and applications). Although this was meant to be a refresher, I think I will go back to this course and the online notes on numerical linear algebra for further studies. Thank you Robert and Maggie! It's been a pleasure.
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Francis Dooley profile image
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Francis Dooley

10/10 starsCompleted
1 week, 6 days ago
This was a great course that allowed me to brush up on my linear algebra skills but in the very modern context of cost effective computer algorithms. I am grateful for this course, especially as linear algebra is so essential in areas such as machine learning.
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Ashish Sarode profile image
Ashish Sarode profile image

Ashish Sarode

10/10 starsTaking Now
2 weeks ago
Excellent course to learn Linear algebra (specifically for person with software engineering background). I had no idea about Matlab before starting this course, but instructor has helped in all possible ways to make the subject and related tool learning (like matlab) easy to progress in this course. You have to survive, what feels like torture of first 3-4 weeks and then the fun begins. The course has all the important topics I wanted to learn about linear algebra, most importantly the assignments ensure that you do not proceed without learning the concept. Although the Matlab based assignments have low value from score perspective they give lot of insight about the subject.
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Abdullah Emad profile image
Abdullah Emad profile image

Abdullah Emad

10/10 starsCompleted
1 month ago
I think the course content is amazing. It does not just focus on materials being taught in a traditional Linear Algebra course, but it also introduce us to more advanced materials. I also liked the fact that I was having programming assignments and talking a look at various algorithms for computing with a matrix. The instructor was great. He presented the material clearly. As a computer science student, I am pretty satisfied with the course.
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S A

8/10 starsCompleted
1 month, 3 weeks ago
It was my great pleasure to enroll in this course. It gave me the essential information about matrices and linear systems. Although I couldn’t use matlab nor python on my iPad,but I took the advantage of learning quick performing matrix multiplication and solving linear systems. Thanks for edx,thanks Robert and Mary , thanks for all who participated to make this knowledge available.
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S A

8/10 starsCompleted
1 month, 4 weeks ago
I enjoyed the course .. It is very useful to me. However I would like to practice more programming because using my iPad I couldn’t get the free version of matlab nor python .. But anyway the course helped me review many things about matrices and taught me new skills and techniques on solving linear equations... Thank you Edx .. Thank you instructors and thanks for all the team who worked to make this material available for students worldwide...
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Student

10/10 starsCompleted
4 months ago
Absolutely thankful for this course. I have not taken Linear Algebra in college, and used to regret it a lot. Now because of Robert and Maggie, it becomes possible to learn what I wanted. There may be a few parts you want to supplement with Khan Academy video for a more plain-word explanation, but overall the content is very rewarding! Really enjoyed this course though I didn't do the Matlab part.
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DHIVYA NAGASUBRAMANIAN profile image
DHIVYA NAGASUBRAMANIAN profile image

DHIVYA NAGASUBRAMANIAN

8/10 starsCompleted
2 months, 3 weeks ago
This course has all that we can expect to be covered from Linear Algebra. The professor keeps the course interesting by giving real life problems where linear algebra is used to derive solutions. The course is well paced and it does not add burden on the student.
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Wagner Oliveira profile image
Wagner Oliveira profile image

Wagner Oliveira

10/10 starsCompleted
3 months, 1 week ago
The course is very good! Instructors are very didactic and the material is quite comprehensive! I took it informally to review concepts prior to a regression analysis graduate level course and it was very good to remember those concepts and apply them to statistics. Even though my objective was not related to computation, the course was really very useful! Thank you very much Robert and Maggie!
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student

10/10 stars
3 months, 1 week ago
Thank you to the professor and the staff for organizing this amazing course. The lectures are excellent and very clear and the homework and exams are a brilliant source of learning and an excellent means to apply and practice the concepts and methods taught.
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Vincenzo Cassati profile image
Vincenzo Cassati profile image
10/10 starsCompleted
  • 2 reviews
  • 2 completed
6 months, 2 weeks ago
Some months ago I wanted to do something about machine learning. Why this? just to spend my spare time. Anyway my gaps about matrix calculus (or linear algebra, if you prefer) was too deep. In my early times it was just a sub branch of something called "Anlytical geometry" (year 1973, university of Pisa). Now I get my gaps filled AND i avoided watching TV for a considerable amount of my evenings. So Tanks Maggie and Robert . See you gin somewhere else
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Student

8/10 starsCompleted
6 months, 2 weeks ago
Thanks to this amazing course, I fell in love with Linear Algebra! Never thought I would say that because I hated it when I took it the first time in college. I especially love how this course help me to visualize abstract math concepts. I'm very visually orientated, but the previous linear algebra course I took was so abstract that I didn't understand anything! I also appreciate the components on Matlab and computation. This is not covered by MIT OpenCourseware, and it helps me connect abstract concepts I learned to applications. I have a few suggestions that might make future LAFF course even better. I find it hard to retain the knowledge without abundant practice problems. Although each video usually has a few exercise questions, it would be really helpful to have some problem sets at the end of each week. I found more practice problems on MIT Opencourseware to complement this course, and I found those problems extremely helpfu... Thanks to this amazing course, I fell in love with Linear Algebra! Never thought I would say that because I hated it when I took it the first time in college. I especially love how this course help me to visualize abstract math concepts. I'm very visually orientated, but the previous linear algebra course I took was so abstract that I didn't understand anything! I also appreciate the components on Matlab and computation. This is not covered by MIT OpenCourseware, and it helps me connect abstract concepts I learned to applications. I have a few suggestions that might make future LAFF course even better. I find it hard to retain the knowledge without abundant practice problems. Although each video usually has a few exercise questions, it would be really helpful to have some problem sets at the end of each week. I found more practice problems on MIT Opencourseware to complement this course, and I found those problems extremely helpful for me to consolidate knowledge and check what concepts I haven't mastered. Another suggestion is that maybe they can speed up some earlier weeks a little more so they don't have to jam all the more challenging materials such as projections and eigenvalues into the last two weeks. I noticed that the earlier weeks usually take me around 3-5 hours to fully understand the materials and complete all the exercises, but later weeks take a lot longer than that, and I had to frequently revisit those materials to achieve mastery. If you are motivated, these two issues shouldn't be a problem as you can find lots of problem sets online and speed up the pace yourself. I definitely recommend to seek more problems to practice from early on so that you can consolidate the knowledge along the way. Don't be like me: I thought I understood everything about projections because video lectures were really clear, until I went to Vegas for a weekend and realized that I forgot everything about projections when I got back!
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Student

10/10 starsCompleted
6 months, 2 weeks ago
This course was very informative. Coming into the course I had no knowledge of Linear Algebra but now I feel I can pursue more of the subject and other videos on the topic make sense. I spent some time looking through the videos from Gilbert Strang from MIT after taking this course and what seemed gibberish before the course is easy to follow. The professors for this course are very engaged as well. Questions asked on the forums are answered in very short order. I didn't feel negatively judged for asking a question. Looking over answers they gave to other students the same is true there too. These professors are there for you to learn this topic. If only normal college courses felt the same way I think more people would be engaged like they are in this course.
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Student

10/10 starsCompleted
6 months, 1 week ago
I loved the complete explanations on derivations and formulas. Visual aids help me understand the concepts. This course help me clarify some of the concepts and topics that I did not understand when I took linear algebra in college.
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10/10 starsDropped
6 months, 1 week ago
This is a great introduction to Linear Algebra. The course was well organized and I enjoyed the humorous email updates from the course instructors. I only completed part of the course as a refresher for before starting graduate school.
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Student

10/10 starsCompleted
6 months, 2 weeks ago
This course was very informative. Coming into the course I had no knowledge of Linear Algebra but now I feel I can pursue more of the subject and other videos on the topic make sense. I spent some time looking through the videos from Gilbert Strang from MIT after taking this course and what seemed gibberish before the course is easy to follow. The professors for this course are very engaged as well. Questions asked on the forums are answered in very short order. I didn't feel negatively judged for asking a question. Looking over answers they gave to other students the same is true there too. These professors are there for you to learn this topic. If only normal college courses felt the same way I think more people would be engaged like they are in this course.
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Tomasz Pankowski profile image
Tomasz Pankowski profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
6 months, 3 weeks ago
Great course difficult but very interesting. You will find here programing and normal mathematical exercises. Definitely worth effort and time. You will even get free matlab license.
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Student

10/10 starsCompleted
6 months, 3 weeks ago
This course is amazing and gives a gentle slope for a rather tough, foundational math subject. The enrichments at the end of each section are quite enjoyable. You also get a free license to Matlab for the duration of the course and get to learn Matlab. The learning is of a very active format wherein you watch a short video and answer some questions ... so it's quite engaging. Learning the proofs are incredibly satisfying as you actually understand why something is true as opposed to accepting something as being true. The little peek that they offer to the FLAME project at the University of Texas is astounding. Watching their code writing method was hugely inspiring for me.The instructors are incredibly humble and are not afraid to accept errors in the videos or sometimes in their calculations. This actually has the effect of giving the learner the confidence that if the instructor can make mistakes we can surely learn the material. S... This course is amazing and gives a gentle slope for a rather tough, foundational math subject. The enrichments at the end of each section are quite enjoyable. You also get a free license to Matlab for the duration of the course and get to learn Matlab. The learning is of a very active format wherein you watch a short video and answer some questions ... so it's quite engaging. Learning the proofs are incredibly satisfying as you actually understand why something is true as opposed to accepting something as being true. The little peek that they offer to the FLAME project at the University of Texas is astounding. Watching their code writing method was hugely inspiring for me.The instructors are incredibly humble and are not afraid to accept errors in the videos or sometimes in their calculations. This actually has the effect of giving the learner the confidence that if the instructor can make mistakes we can surely learn the material. Standardisation of the steps for matrix multiplications, finding solutions to systems of linear equations etc. and standardisation of variable naming conventions greatly aid the learning process by removing unnecessary decision making points which are often distractions. The mid-term and final exams are designed as excellent learning experiences rather than something that is made to judge you.
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Student

10/10 starsCompleted
7 months ago
The course content was paced well. I like that the emphasis was on learning and not scoring and the students were trusted with the answers. I enjoyed the SPARKS programming interface. Would definitely recommend to anyone looking for thorough linear algebra course.
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Student

10/10 starsCompleted
7 months, 1 week ago
This course is absolutely amazing! It really helped me to review LA, which I've already completed as university course. I will definitely recommend LAFF to our junior students.
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Student

10/10 starsCompleted
7 months, 3 weeks ago
Outstanding course. I recommend it to anyone interested to develop a solid foundation in linear algebra. Robert and Maggie, a big THANK YOU for all your efforts to make this course available on edX.
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Rohit Beri profile image
Rohit Beri profile image
10/10 starsCompleted
  • 0 reviews
  • 0 completed
7 months, 4 weeks ago
Really a good course. Last I formally studied Matrix algebra was in high school 20 years ago. This course took me from the vaguely remembered high school algebra to sound fundamentals in Linear Algebra. Now planning to study the notes on Numerical Linear Algebra. Wish there was a proper course dealing with that. Robert and Maggie, thanks a lot!
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Student

10/10 starsCompleted
8 months ago
Very much enjoyed the course (eDX. Starts you from square one and guides you through the material logically and clearly. Instructors were highly competent and excited about material. Only complaint is the number of corrections that were made to videos after they were posted, but this didn't detract from the course much. Would definitely recommend to anyone interested in the subject.
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