Linear Algebra - Foundations to Frontiers

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9/10 stars
based on  180 reviews
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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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Sciences & Technology
Business & Management
21322 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
180 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
4 years, 4 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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Victor Bustos profile image
Victor Bustos profile image

Victor Bustos

10/10 starsCompleted
1 month, 2 weeks ago
I had seen the topics with more depth before, but I took the course because I wanted to remember some things. The truth was, I remembered a lot and also make me see the things a little different. Also now I could do the course at my own pace, without the stress of the formal class room, with the dates always over your head. So If you want to start or just remember some things, is very advisable
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DBDB A profile image
DBDB A profile image

DBDB A

8/10 starsCompleted
3 months, 2 weeks ago
Very good course. Highly recommended. I on a self-taught track and this course reminded me of important concepts and methods linear algebra. It also provides a glimpse of abstraction about slicing and dicing. The whole program needs some redecoration as there are some typo things since several years ago but the typos are patched even though not so nicely done. But the professors are very active and supportive. Highly recommened.
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Marshall Krassenstein profile image
Marshall Krassenstein profile image

Marshall Krassenstein

8/10 starsCompleted
3 months, 3 weeks ago
I took this course with no background in linear algebra with the hope that I could learn the fundamentals before beginning my online masters in data analytics. Robert and Maggie are great instructors but this class is highly focused on algorithms for completing operations rather than understanding how they apply in data science. That's not to say that this was a bad course. For those searching only for the fundamentals of linear algebra, just know that you will not be able to skim through this one and that there will be more focus on abstraction than you might find in an ordinary course.
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Saurabh Kumar Raina profile image
Saurabh Kumar Raina profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
4 months, 2 weeks ago
Two decades ago I took in college the LA course in a formal setting, only solved problems for exams, never viewed LA as such an important foundational course for almost everything in Computer Science. LAFF is not just another MOOC, it is a fantastic conglomeration of basic concepts to brush up, potential ideas to gain insights, showcase of LA applications, and the gateway towards Advanced LA course, laid out in a very educative and supportive manner which is enticing, challenging, and revealing. On a humorous note, in this family MOOC, Robert and Maggie 1) created awesome lecture videos with perfect lengths, 2) set up very intuitive patterns for problem sets, 3) tirelessly and patiently responded to each post (never seen on any other MOOC), and 4) on the top made learning fun by sometimes dropping witty statements in between. Overall, I think they are a dedicated couple committed to educate anyone interested in Linear Algebra. Kudos ... Two decades ago I took in college the LA course in a formal setting, only solved problems for exams, never viewed LA as such an important foundational course for almost everything in Computer Science. LAFF is not just another MOOC, it is a fantastic conglomeration of basic concepts to brush up, potential ideas to gain insights, showcase of LA applications, and the gateway towards Advanced LA course, laid out in a very educative and supportive manner which is enticing, challenging, and revealing. On a humorous note, in this family MOOC, Robert and Maggie 1) created awesome lecture videos with perfect lengths, 2) set up very intuitive patterns for problem sets, 3) tirelessly and patiently responded to each post (never seen on any other MOOC), and 4) on the top made learning fun by sometimes dropping witty statements in between. Overall, I think they are a dedicated couple committed to educate anyone interested in Linear Algebra. Kudos to both the Professors. I wish we had more similar problem sets by them. मैंने वास्तव में पाठ्यक्रम का आनंद लिया है। मैं रॉबर्ट और मैगी से ऐसे कई पाठ्यक्रम प्राप्त करना चाहता हूं। Thanks a ton!! Saurabh K Raina
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Student from Jan-May2018 offering profile image
Student from Jan-May2018 offering profile image

Student from Jan-May2018 offering

10/10 starsCompleted
4 months, 3 weeks ago
Awesome introductory course to Linear Algebra because the instructors for this course are excellent. It was the first time taking a MOOC and I am new to Linear Algebra, but took the course to prepare for a graduate CS program. I don't think Linear algebra is an easy topic to teach (or learn, in my case (^^;)) but Robert and Maggie did an amazing job. I felt the material was extraordinarily well prepared - a combination of written text, videos (explaining concepts as well as showing how to solve a problem), homework, self assessment exams, and a discussion forum. They respond to questions quickly and with clarity too. Thank you Maggie and Robert!
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Alex Sing Yu Chu profile image
Alex Sing Yu Chu profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
4 months, 3 weeks ago
Excellent. I took another on-line course from another top famous University, and it was hard to follow, and I was totally lost when I arrived at the lesson talking about rank of a rectangular matrix. A typical course will start from linear equations, determinants, Cramer's rule, then vector space, etc. This course has a new approach of starting with vectors and linear transformations. Also the various vector and matrix algorithms really help gave me solid and clear ideas of column spaces and rows spaces, and different kinds of vector/matrix operations and their implications: on the right, on the left, partitioning, etc. I also found the exercises very helpful in enforcing the concepts in my mind. Overall, I would give this course A++.
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Brian A profile image
Brian A profile image

Brian A

8/10 starsCompleted
4 months, 3 weeks ago
I learned a lot from the first 5 sections, but the later sections were difficult and very time consuming likely because lack of understanding. Now I need to find a course that applies linear algebra to real-world-like situations.
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Michael Smith profile image
Michael Smith profile image

Michael Smith

10/10 starsCompleted
4 months, 3 weeks ago
Amazing quality and clarity and coverage. Topics are presented in an expert procession that builds upon itself, truly teaching the subject. I took Linear Algebra over 30 years ago, in classroom format, and learned far less. I did rely on other web resources to help solidify geometric/spatial concepts, but this, my first MOOC, exceeded my expectations. Bravo!
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aldo teran profile image
aldo teran profile image

aldo teran

10/10 starsCompleted
5 months ago
Great course. Content is hand-picked by the instructors to give you the most insightful introduction to linear algebra. Exceptional teaching by the instructors and always attentive to those who post questions on the discussion forum. Totally recommended.
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Nimnath Withanachchi profile image
Nimnath Withanachchi profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
5 months, 2 weeks ago
This was my first MOOC course. My first math course at undergraduate level. The videos and lecture materials cover the introductory areas of linear algebra thoroughly. The first 8 weeks covers the basics of vector and matrix operations, and LU factorization. The last 4 weeks cover subspaces, QR factorization, eigen vectors /diagonalization amongst other things. Last 4 weeks need quite a bit of investment in time. I made a mistake of rushing through at first and getting stuck later on. Since I was weak in set theory, I took another MOOC course-- 'Introduction to mathematical thinking'. Also, I watched the 3BLue1Brown videos on linear algebra to getter better geometric understanding of vector spaces. After that I was able to grasp the contents of Week 9-12 thoroughly. In reality the lecture materials and videos cover the areas well and you do not need other resources if you invest enough time to absorb the content. Additional materia... This was my first MOOC course. My first math course at undergraduate level. The videos and lecture materials cover the introductory areas of linear algebra thoroughly. The first 8 weeks covers the basics of vector and matrix operations, and LU factorization. The last 4 weeks cover subspaces, QR factorization, eigen vectors /diagonalization amongst other things. Last 4 weeks need quite a bit of investment in time. I made a mistake of rushing through at first and getting stuck later on. Since I was weak in set theory, I took another MOOC course-- 'Introduction to mathematical thinking'. Also, I watched the 3BLue1Brown videos on linear algebra to getter better geometric understanding of vector spaces. After that I was able to grasp the contents of Week 9-12 thoroughly. In reality the lecture materials and videos cover the areas well and you do not need other resources if you invest enough time to absorb the content. Additional materials are available especially in the enrichment section. I felt the assessments were easy. I wish they were more challenging. All in all this is a gem of a course. Highly recommended!
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Chananya Choosak profile image
Chananya Choosak profile image
8/10 starsCompleted
  • 1 review
  • 1 completed
6 months, 1 week ago
I knew this course because my instructor had used this to reference his lesson. So, I decided to learn LAFF in edx along with my university's class. I understood the lessons a lot.
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Student from Switzerland profile image
Student from Switzerland profile image

Student from Switzerland

10/10 starsCompleted
6 months, 3 weeks ago
If you want to learn linear algebra thoroughly from the basics up, and you know some programming, this is a great course. The instructors provide clear and detailed explanations throughout. The insights into more advanced topics in numerical linear algebra make this course especially interesting, but these topics are often optional, so there is no pressure to master advanced topics at a first pass.
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Peter Philippe profile image
Peter Philippe profile image

Peter Philippe

10/10 starsCompleted
6 months, 3 weeks ago
Ce cours est très bien fait, du début jusqu'à la fin. Cela permet de revoir toutes les bases fondamentales en algèbre linéaire. Pour des raisons de temps, je n'avais qu'une seule semaine pour répondre à toutes les questions (mon score n'a été que de 89%). Je recommande ce cours à toutes les personnes qui souhaitent se remettre sérieusement à l'algèbre linéaire de manière complète et efficace.
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H Shekhar Singh profile image
H Shekhar Singh profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
7 months, 1 week ago
If am buy this book,pdf version is same as of buying book.this course is to extra knowledge in linear algebra with algorithm. But I want buy a book of linear algebra: Foundation to frontier, The pdf version and 50 dollar book are same or not,please help
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Xiaoming Ji profile image
Xiaoming Ji profile image

Xiaoming Ji

10/10 starsCompleted
9 months ago
I studied this course as a review to my previous knowledge. It is a very good course and the concept is explained very well. In addition, this course combines the knowledge on how to make high performance linear algebra software through slice and dicing. This is an area that extended my knowledge and give me a very good base to understand more in-depth high performance computing on linear algebra. Thank you!
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Rob Weatherston profile image
Rob Weatherston profile image

Rob Weatherston

6/10 starsCompleted
11 months 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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student

10/10 starsCompleted
10 months, 3 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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Peter Osusky profile image
Peter Osusky profile image
8/10 starsCompleted
  • 0 reviews
  • 0 completed
11 months, 2 weeks 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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student

10/10 starsCompleted
10 months, 1 week ago
The course has clear explanation even for non-math students. It is easy to follow the instruction and I got useful insight about linear algebra and its applications. If you are looking for linear algebra course with intuitive instruction, this is recommended!
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Su Ro profile image
Su Ro profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
10 months, 1 week ago
This is a thorough look into the fundamentals of linear algebra. I found great value in building the algorithms. The algorithm exercises guided and challenged me through a myriad ways of implementing linear algebra. Prof Robert's videos are comfortable and on point. I have taken many courses where a professor is high strung and rambles on and on trying to teach a concept; Prof Robert is an example of someone who knows the subject and is able to teach the subject effortlessly. Thank you Prof Robert, Prof Maggie!
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Juan Florentino profile image
Juan Florentino profile image

Juan Florentino

8/10 starsCompleted
10 months, 1 week ago
This introductory course on Linear Algebra helped me understand the field in a very practical an intuitive way. The instructors are very enthusiastic and their passion for the field shows up on this course. They take a lot of time to also interact with the students on the board. There is a little bit more emphasis on programming than on a regular Linear Algebra course, which might make it a bit frustrating for some people. However, it enhances the learning experience if you are willing to make the extra effort or you can always skip the programming part, if you are not. One small suggestion to the team would be to renew some of the slides and material. You still find references to Ipython notebook (or something like that) whereas nowadays they use matlab and you find typos or mistakes here and there (although most of them are clearly labelled as such and corrected separately)
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student

10/10 starsCompleted
10 months, 1 week 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
10 months, 2 weeks 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
10 months, 2 weeks 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
Shaun Zen profile image

Shaun Zen

10/10 starsCompleted
10 months, 3 weeks 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
Francis Dooley profile image

Francis Dooley

10/10 starsCompleted
10 months, 3 weeks 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
10 months, 3 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
11 months, 2 weeks 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 profile image
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S A

8/10 starsCompleted
1 year 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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