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.

Provider Subject Specialization
Sciences & Technology
Business & Management
21741 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
191 Reviews for Linear Algebra - Foundations to Frontiers

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6/10 starsCompleted
4 years, 8 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
4 years, 8 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
4 years, 8 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
4 years, 8 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
4 years, 8 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
4 years, 8 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
4 years, 8 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
4 years, 8 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
4 years, 7 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
4 years, 7 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
4 years, 7 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
4 years, 7 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
4 years, 7 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
4 years, 7 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
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10/10 starsCompleted
  • 1 review
  • 1 completed
4 years, 7 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
4 years, 7 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
4 years, 7 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
4 years, 7 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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8/10 starsCompleted
  • 1 review
  • 1 completed
4 years, 7 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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10/10 starsCompleted
4 years, 8 months ago
I successfully completed this course, though I'm not a student of engineering, physics or mathematics. My field is medicine, so knowledge of this course doesn't directly contribute to my work, but I believe linear algebra knowledge will help me understand statistics. Finally, I could enjoy this course, and this is the best course of linear algebra I've ever taken. Thank you, Professor Robert!
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1/10 starsCompleted
4 years, 8 months ago
Very difficult to understand and the material was poorly taught. It would have been nice if there were more practice problems.
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10/10 starsCompleted
4 years, 8 months ago
This is a very good course: * Concepts explained clearly * Plenty of sample problems * Good videos and other material * Interesting programming assignments * Up to date and relevant Can't find any fault with it at all!
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10/10 starsCompleted
4 years, 8 months ago
This is a really good course. I would recommend everyone to try it. And it is really easy to do the assignments.
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Ahmad Alhour profile image
Ahmad Alhour profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
4 years, 8 months ago
This was a very interesting course. I have been trying to dedicate sometime for Linear Algebra for a long time now, but only with the help of edX and the professors of this course that I only had the chance to schedule my time and efforts around this course. I feel I'm confident now to dig deeper into the domain of Applied Linear Algebra and Machine Learning. Thanks for all the people who made this happen.
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10/10 starsCompleted
4 years, 8 months ago
Excellent course. Needs constant hard work but you learn something. Great instructors -- very committed and actually care for the students. Extremely rare for a MOOC! Bottom line, if you want to learn Linear Algebra, just take the course ... you won't regret it!
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8/10 starsCompleted
4 years, 8 months ago
The first time I took linear algebra, about 40 years ago, we didn't have computers for the course. I hated it. It was too easy to make tedious simple arithmetic mistakes and get the final answer wrong. So I took this course the way I wanted to with the following personal objectives: 1\. Understand how to use modern tools such as Octave, R, NumPy, Lapack, understand the linear algebra semantics and apply them appropriately in real world engineering and big data settings. 2\. Get some familiarity with how to do the hand calculations (maybe do it a few times), but I don't want to dwell on this. (I discovered LU decomposition in Octave does not necessarily give the same answers as the course, so I automated the steps of the hand calculations the course way, in python, to get the same answer using the same steps. Did the same for row echelon form to avoid the tedium of writing on paper.) 3\. Get some familiarity of the semantics from the ... The first time I took linear algebra, about 40 years ago, we didn't have computers for the course. I hated it. It was too easy to make tedious simple arithmetic mistakes and get the final answer wrong. So I took this course the way I wanted to with the following personal objectives: 1\. Understand how to use modern tools such as Octave, R, NumPy, Lapack, understand the linear algebra semantics and apply them appropriately in real world engineering and big data settings. 2\. Get some familiarity with how to do the hand calculations (maybe do it a few times), but I don't want to dwell on this. (I discovered LU decomposition in Octave does not necessarily give the same answers as the course, so I automated the steps of the hand calculations the course way, in python, to get the same answer using the same steps. Did the same for row echelon form to avoid the tedium of writing on paper.) 3\. Get some familiarity of the semantics from the proofs and derivations, but again a secondary concern. 4\. Have some awareness of computational cost of operations. (This is where the course is novel for me, and I appreciate it, esp. since I work in the software field.) Also, I appreciate a robust introduction into slicing and dicing, since this is a practical consideration when things may not all fit into memory, or the need to split up the job into for parallel computation. Because of the availability of modern tools (Python, Octave), I felt the course could've spent more time with higher level abstractions, perhaps in the second half of the course, such as eigen decomposition, SVD, with a focus on meaning and appropriate application rather than the mechanics of hand calculations. Having now done both Cousera and EdX formats, I felt EdX was ideal for this course. EdX seems to allow for very small lectures, on a single topic, followed immediately with small exercise. And there are lots of these. It is much more fine grained in feedback than Coursera, and in some ways ideal for this course.
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10/10 starsCompleted
4 years, 8 months ago
If you want a course that is friendly but at the same time challenging, well this is the course. Been enjoying it since day one
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10/10 starsCompleted
4 years, 8 months ago
Love this course! It is challenging but with professional and friendly support of Maggie Myers and Robert van de Geijn it is possible to learn and enjoy the class!!! Thank you!
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10/10 starsCompleted
4 years, 8 months ago
I really love this course! Very clear theory explains + examples of how to apply theory in practice.
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10/10 starsCompleted
4 years, 8 months ago
I studied LA at university 15 years ago (in a very "pure" way) but needed a refresher and was keen on the computational/applied approach of this course. I now understand so much more than I did before and I really appreciate how carefully the course has been structured. Thank you!
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