Linear Algebra - Foundations to Frontiers

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9/10 stars
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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
22557 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
199 Reviews for Linear Algebra - Foundations to Frontiers

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10/10 starsCompleted
5 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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Hanjie Deng profile image
Hanjie Deng profile image
10/10 starsCompleted
  • 0 reviews
  • 0 completed
1 week, 6 days ago
The course is well-structured and has many good exercises to help consolidate the foundational concepts of Linear Algebra. I took it to review but I learned more than expected.
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Dominik J profile image
Dominik J profile image

Dominik J

10/10 starsTaking Now
3 months, 3 weeks ago
Great and very rigorous course. I had a very basic understanding of linear algebra when I started and made some definite progress. It is challenging, but I am sure it will provide a good base for many other professional interests. Necessary time commitment for me (next to professional life) was about 3x the advertised time In a few aspects, the course could have a slightly better connection to the geometric interpretation of the algebraic concepts (i.e. determinant). It worked well for meto refer to the 3blue1brown series on LA for that
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Simone Ragusa profile image
Simone Ragusa profile image

Simone Ragusa

8/10 starsCompleted
4 months, 2 weeks ago
EN The course is very well structured and this allows you to properly understand each topic at the right time. Learning "slicing and dicing" I think is very useful, also to better understand the abstraction of some operations such as the matrix-matrix multiplication. The presence of graphic examples is also of great help in understanding "what is happening". Thanks for this experience! ----- IT Il corso è strutturato molto bene e questo permette di comprendere correttamente ogni argomento al momento giusto. Imparare lo "slicing and dicing" ritengo sia molto utile, anche per capire meglio l'astrazione di alcune operazioni come la moltiplicazione fra matrici. La presenza di esempi grafici è anch'essa di grande aiuto per capire "cosa sta succedendo". Grazie per questa esperienza!
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Steven Rawstorne profile image
Steven Rawstorne profile image

Steven Rawstorne

10/10 starsCompleted
4 months, 4 weeks ago
I'd never taken a linear algebra course before and apart from UK 'A level' mathematics at school (in 1974!) have otherwise only recent MOOCs to compare with this course. That said, although I found the course challenging at times it was a very enjoyable experience and I would recommend it to anyone with even a vague interest in maths. The course content was logically presented and well-paced though I can't comment on the completeness of the areas covered. The lectures were clear as were the explanations following homework problems. What could be better? The errors in the videos which were corrected in the text were a little annoying and it would be excellent if these could be updated at some point. I've also found the recording of excerpts from some live lectures to students in other MOOCs really engaging so maybe consider for future courses. All in all a very positive experience and a big thankyou to the faculty!
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6/10 starsCompleted
  • 0 reviews
  • 0 completed
5 months ago
This course was well done to understand compute and programming. The instructor was not totally clear with his words tho. The topics were very objective. The matrix part was the best in the course. I don't have really much experience in linear algebra because is a new theme for me, but this course help to understand it more. It was useful tbh not a waste of time.
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John V profile image
John V profile image
10/10 starsCompleted
  • 0 reviews
  • 0 completed
5 months, 2 weeks ago
Terrific course! I have a degree in mechanical engineering and obviously took Linear Algebra in college about 5 years ago. I was able to go through the content quickly due to my prior experience but even so I would say that this course was much better than what is usually offered in an undergraduate linear algebra course. I did miss some of the parts with calculus but I can also see why they were pushed into follow-up class. Regardless, if your goal is (as mine is) to use linear algebra in computing/programming this class is an absolute gem. The algorithmic focus and understanding of linear algebra is terrific. This is how the subject ought to be taught to every engineer and scientist.
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Yingfei Gao profile image
Yingfei Gao profile image

Yingfei Gao

10/10 starsCompleted
6 months ago
I think the course content is helpful. I had taken a linear algebra class in my college but I dropped that class. I think the content in EDX is much easier to understand especially with the following homework. After the chapter, it also provides a brief summary which allows me to review and review the content so that I can better move to the subsequent chapter.
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10/10 starsCompleted
  • 0 reviews
  • 0 completed
7 months ago
I finally completed this course - although it is stated to be a introductory level, there is a significant amount of detail covering a wide variety of topics and a large number l of exercises to (optionally) do. Providing the answers proved to be a key enabler since it allowed me to understand exactly where my understanding was weak and correct my errors. I extend my thanks to the team that assembled this material - it is obvious how much effort was involved. There is no way I will remember all the material so having the PDF and pointers to many other related topics will provide an excellent reference. THANKS AGAIN...
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Albert Lai profile image
Albert Lai profile image

Albert Lai

8/10 starsCompleted
9 months, 3 weeks ago
I really enjoyed taking this course! Not at all a steep learning curve but super heavy on the programming. Explained super clearly and if you try hard, you will finish it easily.
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m ruland profile image
m ruland profile image

m ruland

10/10 starsTaking Now
10 months ago
I really enjoyed the class but am disappointed that it really wasn't "self-paced" since it is ending and it appears the material is being archived. I had been taking my time to investigate all the nuances and extra material and only made it about half-way through the material. I don't see any further offering for the course either.
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Rio Rinaldi profile image
Rio Rinaldi profile image
10/10 starsCompleted
  • 0 reviews
  • 0 completed
10 months ago
What a fun experience and such a great course. It is one of the few formal online courses in linear algebra that tries to be comprehensive and really fulfill its role as a stepping stone to more advanced concepts. Some areas were a little rushed and you might need to take some initiative on the side, but again, this is an introductory course. The materials were great, instructors were very helpful. And although I never posted questions, the two instructors replied to all of them. It does require a significant amount of work. And given their system of grading, I would recommend everyone to get the certificate. It is not too difficult to fulfill, and you get to support edX's awesome mission.
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Alex Les profile image
Alex Les profile image

Alex Les

10/10 starsCompleted
10 months, 1 week ago
Really good course, there's a lot of good material and I learned a lot. I would recommend supplementing some of the content with other resources, but great overall.
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Pablo Barría Urenda profile image
Pablo Barría Urenda profile image

Pablo Barría Urenda

8/10 starsCompleted
10 months, 1 week ago
This course intentionally strays from the path of traditional Linear Algebra courses by focusing on the matrix/vector operations more than on their geometric interpretations. It also has a strong interest on the computational aspects of LA, how expensive each algorithm is, etc. My only complaint about the material is that when the geometric aspects do come on, they feel a little bit rushed. Rushed, I must say, when compared to some of the other material taught on this same course, not necessarily more rushed than other courses out there. The course stays true to its promise of teaching the foundations while showing you the frontier, by which they mean the research the FLAME group is doing in developing algorithms for LA computation. I also believe some of the notation taught in the course is particular to these research group, but it is a notation that makes the underlying topics clearer, so it's helpful for beginners. The ins... This course intentionally strays from the path of traditional Linear Algebra courses by focusing on the matrix/vector operations more than on their geometric interpretations. It also has a strong interest on the computational aspects of LA, how expensive each algorithm is, etc. My only complaint about the material is that when the geometric aspects do come on, they feel a little bit rushed. Rushed, I must say, when compared to some of the other material taught on this same course, not necessarily more rushed than other courses out there. The course stays true to its promise of teaching the foundations while showing you the frontier, by which they mean the research the FLAME group is doing in developing algorithms for LA computation. I also believe some of the notation taught in the course is particular to these research group, but it is a notation that makes the underlying topics clearer, so it's helpful for beginners. The instructors are VERY committed to the course, and usually reply to questions right away. They are also committed to keeping this material available and making it reach as many people as possible, which is great. They are also very aware of how this course differs from others, so they will tell you when the nomenclature or they way some topics are covered may be different, so you will not be confused by other material. I think I am something of an edge case as I took this course on a slow connection over a VPN, but I must say that on those conditions the edX platform can be distractingly painful at times, unnecessarily adding up to an hour to the time I spent studying, at its worst. This applies even more to the MatLab platform on which the programming exercises for the course are offered. Again, I was on a particularly slow connection, so take these comments with a grain of salt. Overall a great course.
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N D profile image
N D profile image

N D

10/10 starsCompleted
10 months, 2 weeks ago
One of the best courses on linear algebra online. I would recommended this course to anyone who wants to become knowledgeable in the subject. The instructors were very good.
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Tianshuo Yang profile image
Tianshuo Yang profile image

Tianshuo Yang

10/10 starsCompleted
10 months, 2 weeks ago
Great course! I learned so much from the later chapters. In the beginning, it was quite easy because I learned a lot of the simple matrix operations. Towards the end, it started to get harder and challenging.
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Archana A profile image
Archana A profile image

Archana A

10/10 starsCompleted
10 months, 3 weeks ago
Completed the course successfully!!! Amazing course and all must try learning once. All the notes are available in links for further reading. I have taken this course to improve my knowledge in linear algebra. There was a gap in understanding algebra after my schooling. Had Wonderful experience in learning LAFF in edX.
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Jishuen Kam profile image
Jishuen Kam profile image

Jishuen Kam

10/10 starsCompleted
10 months, 3 weeks ago
I have taken linear algebra in college and this course really shines a new light on linear algebra. I did not really know the cost of matrix inversion and LU factorization when I was in college. Heck, I didn't even know LU factorization and Gaussian Elimination are equivalent! If you have taken linear algebra in college and will need a refresher again (because you need it for machine learning and what not ...), this is the best course online available at the moment (I would rate it on par with Strang's MIT lectures).
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Prabhath Ranjan Kumar profile image
Prabhath Ranjan Kumar profile image
10/10 starsCompleted
  • 0 reviews
  • 0 completed
10 months, 3 weeks ago
Its a wonderful way of learning with applications and the course content organization and delivery was really so good. I enjoyed it. Thank you so much.
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Ivana Escobar profile image
Ivana Escobar profile image

Ivana Escobar

10/10 starsCompleted
10 months, 4 weeks ago
Took the class to refresh fundamental concepts, and loved the extra readings. Wish they would have the graduate course offering available online. I spent most of my time reading the extra sections, and really enjoyed some of the papers suggested throughout the course. I would have liked to understand how to incorporate the professors' tools into my own research code for prototyping subroutines.
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Victor Bustos profile image
Victor Bustos profile image

Victor Bustos

10/10 starsCompleted
1 year, 1 month 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
1 year, 3 months 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
1 year, 3 months 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
1 year, 4 months 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
1 year, 4 months 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
1 year, 4 months 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
1 year, 4 months 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
1 year, 4 months 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
1 year, 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
1 year, 5 months 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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