Linear Algebra - Foundations to Frontiers

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edX online courses
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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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22630 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
202 Reviews for Linear Algebra - Foundations to Frontiers

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Atul Rajdhar profile image
Atul Rajdhar profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
5 years, 5 months ago
This is really a great course. I knew linear algebra a bit but did not get time to map it to programming. This course fulfilled that thirst. These are the main points that I want to point out: 1\. Slicing and dicing matrices - Viewing the matrix as a collection of vectors and applying vector operations to matrices made matrix manipulation a lot easier. It not only helped to get insight into the mathematics behind matrix manipulation but also changed the way we write programs for matrix operations. 2\. Extended deadlines: Though at the beginning the course had strict deadlines, realizing that it is delivered online to people with various levels of commitment, deadlines were extended. I think, this is important for such a MOOC, especially a MOOC related to mathematics. This is because mathematics requires (at least for me) a lot of time to understand. It is not the case that you view the videos, review some solved problems, and then go... This is really a great course. I knew linear algebra a bit but did not get time to map it to programming. This course fulfilled that thirst. These are the main points that I want to point out: 1\. Slicing and dicing matrices - Viewing the matrix as a collection of vectors and applying vector operations to matrices made matrix manipulation a lot easier. It not only helped to get insight into the mathematics behind matrix manipulation but also changed the way we write programs for matrix operations. 2\. Extended deadlines: Though at the beginning the course had strict deadlines, realizing that it is delivered online to people with various levels of commitment, deadlines were extended. I think, this is important for such a MOOC, especially a MOOC related to mathematics. This is because mathematics requires (at least for me) a lot of time to understand. It is not the case that you view the videos, review some solved problems, and then go and do the homework. What I found important while doing this course is, if you understand the concept well and if you are able to get insight into it, then it is very easy to solve any problem based upon that topic. For example, if you are able to understand linear transformations, then it is very easy to understand linear dependence and independence which in turn makes it easy to understand orthogonality. It also makes programming easier. 3\. The FLAME library: The algorithms that were discussed in the course helped me to map theory to practice. The best part I liked about the FLAME library is - you have to focus only on the problem at hand i.e. what you want to actually do. Though I never used any math library until now, I think FLAME notation is a revolutionary approach for solving problems related to linear algebra. In short, what I think is, though there are some issues with the course, the content and the approach with which the course is delivered largely outweigh them. ...will be looking forward for other such great courses from Prof. Robert and Prof. Maggie. Thanks to both professors and their team.
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10/10 starsCompleted
5 years, 5 months ago
This course operates at three levels, I think. First, it helps you get some important principles around computational science and why efficient algorithms are fundamental to computation. Second, it gives you the rationale, foundations, and logic about the principles of matrix manipulation. And third, certainly not least, you get to learn the mathematics and specific practical skills to work with matrices and linear algebra. Having said all of that, I suggest that to get maximum benefit you a) do allocate the 8 hours per week, b) use this time to practice problems and review as you go, and c) delve into the enrichment problems, and they are where the gold is. Having said all of that, it is a course I will personally go back and review when I have more time, and that has additionally inspired further questions. While I have not done a math course of this type for 30 years, and then at a similar level, Robert and Maggie (you do feel you... This course operates at three levels, I think. First, it helps you get some important principles around computational science and why efficient algorithms are fundamental to computation. Second, it gives you the rationale, foundations, and logic about the principles of matrix manipulation. And third, certainly not least, you get to learn the mathematics and specific practical skills to work with matrices and linear algebra. Having said all of that, I suggest that to get maximum benefit you a) do allocate the 8 hours per week, b) use this time to practice problems and review as you go, and c) delve into the enrichment problems, and they are where the gold is. Having said all of that, it is a course I will personally go back and review when I have more time, and that has additionally inspired further questions. While I have not done a math course of this type for 30 years, and then at a similar level, Robert and Maggie (you do feel you know them at the end!) have excelled in providing a learning standard for this area and level and fulfilling most or all of the likely student needs of someone doing this course. In short, it made sense, is was achievable and it assisted in understanding the application of linear algebra to the world around me.
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Greg Hamel profile image
Greg Hamel profile image
8/10 starsCompleted
  • 116 reviews
  • 107 completed
5 years, 5 months ago
Linear Algebra - Foundations to Frontiers is an introductory linear algebra course that teaches linear algebra in the context of computing. If you don't have any familiarity with programming or python, the computing component is going to be hard to follow. You can, however, skip all of the programming parts and just go through the lecture videos and quizzes. Topics include vectors, linear transformations, matrix vector operations, matrix multiplication and inversion, vector spaces, orthogonal projection and bases and eigenvalues and eigenvectors. 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 al... Linear Algebra - Foundations to Frontiers is an introductory linear algebra course that teaches linear algebra in the context of computing. If you don't have any familiarity with programming or python, the computing component is going to be hard to follow. You can, however, skip all of the programming parts and just go through the lecture videos and quizzes. Topics include vectors, linear transformations, matrix vector operations, matrix multiplication and inversion, vector spaces, orthogonal projection and bases and eigenvalues and eigenvectors. 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. If I were to judge this course solely on the amount of content and quality of exercises, it would be 5/5. That said, I didn’t find the instructor engaging on a human level. Math can be boring; instructors that are excited about the topics they teach can go a long way toward mitigating the dryness. The instructor was robotic in his presentation and I often found the lectures hard to follow. When I decided to watch some of Salman Khan’s linear algebra videos on Khan Academy to review for the final, I found his presentation of the same concepts more engaging and easier to understand. I came out of this course feeling like I didn’t learn as much as I could have because the material is not always presented in a way that is easy to follow and my interest waned from time to time. LAFF provides everything you need to build a solid foundation in linear algebra—if you are able to remain attentive despite the dry presentation.
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10/10 starsCompleted
5 years, 6 months ago
My lack of linear algebra was beginning to show in my stat classes. This class has been a lot of work, but was just what I needed. It can be done as a first class in linear algebra, but I wouldn't try it as such without some familiarity with programming.
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Thirumal Venkat profile image
Thirumal Venkat profile image
10/10 starsCompleted
  • 2 reviews
  • 2 completed
5 years, 5 months ago
The most fun course I've ever completed. The staff are really helpful If this is offered again please don't miss it if you did not have a formal treatment of linear algebra.
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10/10 starsCompleted
5 years, 5 months ago
Trust me, this is the best linear algebra course in the world. I mean the best, rather than one of the best. That's awesome! I really hope to have a graduate linear algebra course from you guys in the later
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10/10 starsCompleted
5 years, 5 months ago
I am 75, and a retired professor. I did my work every week, and enjoyed every moment of it. My hope had been to see what a good MOOC course can be and I found out! Prof Geijn and Dr Myers did right to place emphasis on learning, being generous to let us see the expected answers any time. Several times, I was able to understand the math better because the right answer was available to figure out my mistakes. இந்த கோர்ஸை நடத்தினது உங்களுடைய பெரிய சாதனை! முதல் க்ளாஸ்! எங்களுடைய நன்றி! SRam
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10/10 starsCompleted
5 years, 5 months ago
Absolutely fantastic course. Aside from exploring standard linear algebra, this course brought out the computational perspective, and most special of all, a window into a cutting edge research programme, and what looks to me to be a new paradigm in the field. In addition to the uniqueness of the material, Robert, Maggie and the staff were endlessly enthusiastic and helpful. I can't imagine the course being nearly as successful without their labour being above and beyond the call of duty. Many, many thanks from this student.
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10/10 starsCompleted
5 years, 5 months ago
This has been a wonderful introductory course on Linear Algebra. Although by introductory I do not mean basic. Robert and Maggie really make an effort to show you real applications of Linear Algebra. Also, I quite liked the rigour put on showing theorems with proofs which was solidly backed up by more practical numerical and algorithmic calculation in python. Personally, I think I am a really visual learner, so I found particularly interesting how lecturers made an effort to geometrically show how some of the more abstract concepts work. All in all, you cannot go wrong taking this course. Thank you Robert and Maggie!
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10/10 starsCompleted
5 years, 5 months ago
Huge Effort by the professors Robert and Maggie resulted in one of the best MOOCs on edx or Coursera. For me the best part of this course is the emphasis on learning above testing. All answers to everything in the course were provided and this helped me immensely. I learned a ton. I wish more MOOC professors would have this approach. Here's hoping for a part two of this course.
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10/10 starsCompleted
5 years, 5 months ago
Thank you Robert and Maggie. That was a great job. I learned this course using your experence. Slicing and Dicing method is a great approach that helps me to see any matrix as a collection of vectors. One other name which fits this course is "Linear Algeblar made easy."
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6/10 starsCompleted
5 years, 6 months ago
Although this course was UTAustin's first try at this MOOC, I expected better quality. The material wasn't made in advance, which left the instructors playing "catchup" the whole time. Without much time on their hands, the quality was greatly diminished. For instance, the transcripts and videos were often mismatched so I was seeing transcripts from week 1 on videos from week 12! The format of the lectures was basically the instructor drawing on slideshows (which contained many mistakes and were hard to understand). They contained 2D visuals which were helpful and 3D visuals containing up to 10 vectors which were impossible to decipher. Certificates from this course are completely meaningless because not only do they give you the whole course to complete assignments (exams included), but they even gave you an infinite number of submissions for each problem (exams included), they also let you see the answers at anytime and answer the q... Although this course was UTAustin's first try at this MOOC, I expected better quality. The material wasn't made in advance, which left the instructors playing "catchup" the whole time. Without much time on their hands, the quality was greatly diminished. For instance, the transcripts and videos were often mismatched so I was seeing transcripts from week 1 on videos from week 12! The format of the lectures was basically the instructor drawing on slideshows (which contained many mistakes and were hard to understand). They contained 2D visuals which were helpful and 3D visuals containing up to 10 vectors which were impossible to decipher. Certificates from this course are completely meaningless because not only do they give you the whole course to complete assignments (exams included), but they even gave you an infinite number of submissions for each problem (exams included), they also let you see the answers at anytime and answer the questions after viewing the answers (exams included)! So anyone can 100% the course without learning a single bit of linear algebra. In the introductory video they say: "In this course you will learn all the standard topics in an undergraduate linear algebra course." At the end of the course, they wrote: "Twelve weeks is not enough time to cover all topics." No surprize when they spent the first 5 weeks covering matrix-matrix multiplication! They LAFF software worked fine for the first 7 weeks or so but after that, I was unable to access any of the software past week one! I did learn some linear algebra, but the quality of the course severely hampered my ability to learn.
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5/10 starsCompleted
5 years, 6 months ago
The course covers a lot of algorithms for vector and matrix manipulation which are written in Python. My count is close to 50 of such exercises. Unfortunately that did not leave enough time to cover Singular Value Decomposition or Eigenvalues and Eigenvectors in satisfying detail. And they skipped Principal Component Analysis entirely. Additionally, the course could have done a much better job of connecting the material to the real world. I do not know when it is appropriate to use many of the techniques that were covered. What should I look for to realize, "Hey, I know how to solve this." More quick videos showing demos would have been better.
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10/10 starsCompleted
5 years, 6 months ago
A difficult course, because of the subject. But very well explained by Maggie Myers and Robert van de Geijn. As a programmer, I think, in particular, the explanation of the algorithm and the flame notation are brilliant.
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10/10 starsCompleted
5 years, 6 months ago
This is not the usual undergraduate linear algebra course and is not one that I would recommend as a first course in linear algebra. Much of the course is devoted to teaching about using “slicing and dicing” as a method for efficiently programming algorithms in linear algebra. This I found fascinating but I don’t think I could have handled if I had not already been familiar with most of the material. On the plus side, the videos were excellent, the explanations were detailed and clear. Also help was readily available and Professor van de Geijn himself promptly answered almost all questions that were posted. I don’t know how he and his team kept up with all the work that was required to produce and run this course. I learned a great deal by working through the course. I thank the team for their hours of hard work and I thank edx for making the course possible. bil bonnice
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2/10 starsCompleted
5 years, 6 months ago
Very disappointed in the course. The course was taught backward and at ver uneven levels. On some levels it is like a freshman high school course, on others it is like 2nd year computer science. The course is very poor on applications (almost none), very poor on concepts (general vector spaces, subspaces, basis etc.) It spends way too much time on computational efficiency and elimination etc. The coding the Matrix course on Coursera platform by Brown University is a much more enjoyable Linear Algebra Course
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9/10 starsCompleted
5 years, 6 months ago
If you wish to learn Linear Algebra either as a refresher or as a first time learner of the subject, you cannot do better than take this course. The effort put into explaining the subject matter clearly and in multiple different ways by Robert and Maggie is excellent and truly enhances learning and a grasp of the material. The enrichment modules point to additional relevant topics for the motivated student. I commend everyone involved in producing this course and HIGHLY RECOMMEND IT. KUDOS to ALL and THANKS EdX!
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10/10 starsCompleted
5 years, 6 months ago
This has been my first full linear algebra course. At the same time I have been taking several courses which have directly applied Linear Algebra. Robert and Maggie really break down the material to make it simple and build it back up again. Without this course, I would have been very clueless in my other classes. Thank you!
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9/10 starsTaking Now
5 years, 6 months ago
I wanted to redo some learning about this topic because it was 50 years ago I did have Linear Algebra at Free University Amsterdam (when I was 17 or 18 years old). Lots of the stuff was somewhere still present but not very related and clear. This course was very good in explaining the stuff. Giving newer and better methods to do things and solve problems. With very much students, and so questioners, it was remarkable how quick questions were answered even by both teachers themselves. Also there were quick modifications of the text when someone noticed a mistake (which can be easily be overseen because of the lots of work for preparing such a course for the first time with too little time). Thanks for offering the opportunity to learn more about this topic.
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10/10 starsCompleted
5 years, 5 months ago
Thanks Robert and Maggie. It was an elucidating experience following your course.I hope you will be able to pursue your vision of the subject. Now something in my 'tribal' lang: Obilo zdravja in osebne sreče vama želim.
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10/10 starsCompleted
5 years, 5 months ago
This is a great course that makes linear algebra easy and comprehensible. It goes from the very basics to complex ideas without you noticing. Although it runs for a few months there is plenty of time to submit the exercises, midterm and final exam. It was definitely worth sticking to it even though I felt lost at times. Robert and Maggie are excellent guides and provide lots of examples and different ways to approach the subject. I'm looking forward to the next one!
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10/10 starsCompleted
5 years, 5 months ago
Great work Robert and Maggie. I found this course very useful in setting the grounding well. The aspect I liked was the ability to show insights at each level which one would not typically get from reading a text book.
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10/10 starsCompleted
5 years, 5 months ago
Soy estudiante de matemáticas y física y este curso me ha sido de mucho provecho. Puedo decir sinceramente que ha sido uno de los mejores cursos que he tomado. Agradezco mucho a los profesores Robert van de Geijn y Maggie Myers por tomarse el tiempo para brindarnos este curso. Muchas gracias
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10/10 starsCompleted
5 years, 5 months ago
Thank you Robert and Maggie. I enjoyed the course and learned a lot. Slicing and Dicing Really makes obsolete the use indexes.
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10/10 starsCompleted
5 years, 5 months ago
I wish I had had this course when I was first learning linear algebra. It builds concepts one atop another in a very logical, systematic way. The programming segments might be difficult for someone with no programming experience, but someone like me who has not worked with Python before but has worked with other programming languages should be able to manage fairly easily. The highlight of this course was the enrichment material covering computational complexity and how linear algebra software libraries can decrease the number of memory operations. I would very much like to take a more advanced EdX course on linear algebra or vector calculus taught by the same professors. For instance, this course rarely used complex-valued vectors or matrices and completely omitted calculus topics, like Jacobian matrices, both of which I would like to study further.
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Trevor Farley profile image
Trevor Farley profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
5 years, 5 months ago
Congratulations to Robert, Maggie and the LAFF team for putting on a superb course. I understand many of the difficulties you may have faced and the enormous amount of time you must have spent in creating and running this course. I also want to compliment you on the rigor you exercised in constructing and delivering the material, you have rekindled my love of Mathematics! I look forward to hearing any news from LAFF in the future. Regards and Best Wishes, Trevor Farley (Australia)
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10/10 starsCompleted
5 years, 5 months ago
I am basically a mathematics student but still i take this course. This course taught me topics in a different way from our professors. Nice course. Everyone who loves algebra would have to take this basic course and the way our professors Robert Van De Geijn and Maggie Myers taught was excellent. The Videos and the exercises were really amazing and also challenging. Their teaching methods and the way they approach a problem were really nice.I learn a lot from this course.
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10/10 starsCompleted
5 years, 5 months ago
Excelente curso de Introdução à Álgebra Linear. Para quem quer revisar ou aprender a matéria pela primeira vez, a didática é ótima.
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8/10 starsCompleted
5 years, 5 months ago
This was a good class, I appreciated the computer code to help explain the linear algebra concepts. It probably does not cover as much material as a normal linear algebra class, but it gets you pretty far.
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Julio Bautista profile image
Julio Bautista profile image
8/10 starsCompleted
  • 1 review
  • 1 completed
5 years, 5 months ago
Thanks to Dr. Maggie Myers and professor Robert van de Geijn for exposing, slicing and dicing the beauty of Linear Algebra. Regards from Madrid/Spain Julio Bautista
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