Linear Algebra - Foundations to Frontiers

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9/10 stars
based on  191 reviews
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Course Details

Cost

FREE,
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  • On demand

Course Provider

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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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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10/10 starsCompleted
2 years, 1 month ago
I have taken this course before and have been interrupted by life as I was this time. I will take it one more times so I can cover all the topics. Definitely, a course and subject of great value.
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10/10 starsCompleted
2 years, 1 month ago
This is a good class for you to get familiar with linear algebra. The video and instruction notes are well prepared. I believe you will learn a lot from this class.
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10/10 starsCompleted
2 years, 1 month ago
I would like to thank professor Robert and all the staff for this incredible course. For providing us this kind of material and their knowledge. Thank you all. I'm seeking my master in mathematics, so I saw this course as an opportunity to enhance my knowledge and study harder to make my dream come true.
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10/10 starsCompleted
  • 1 review
  • 1 completed
2 years, 1 month ago
Excellent course with perfect delivery. The instructors lay a solid foundation of Linear Algebra, and each topic is made firm by plenty of both problems and programming exercises. The best parts are the enrichment sections where the topic under consideration if taken towards direct applicability in real world. Robert and Maggie, the creators of the course are always reply to our queries and and actually come across as our friends and teach us in similar way. Currently the mooc is offered in Matlab, but one can do it in Paython too. Thanks Robert and Maggie, and "LAFF Long and Prosper" I surely will LAFF-On Programming for Correctness, zafar
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Elglebakson Guei profile image
Elglebakson Guei profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
2 years, 1 month ago
During the 12 weeks I learned a lot. The videos allowed a very good understanding of the courses. The homework were good but sometime difficult. No enough exercices in the videos for which can allow to do the homework. So much thanks to Robert van de Geijn and all instructor .
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Antonio Rodriguez profile image
Antonio Rodriguez profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
2 years, 1 month ago
I enjoyed this course immensely! I will say that it accelerated quickly for the last 4 weeks or so, and some earlier things I sped through needed to be re-visited afterwards for a better foundation. However, I would have liked to see more demonstrations on how certain things work, and how they're used outside of the math department.
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10/10 starsCompleted
  • 1 review
  • 1 completed
2 years, 1 month ago
Brilliantly designed course. The exercises were structured in such a way that you learned a lot in reasonably small increments. More accurately, the exercises were designed in such a way that you discovered linear algebra for yourself. If only all MOOCs were designed like this course.
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10/10 starsCompleted
  • 1 review
  • 1 completed
2 years, 1 month ago
One of the best courses I've taken till now. Most of the lectures and notes are short, sweet and to the point, except some of the last weeks might have been including more practical examples, but again maybe that's just me. Since we've introduced a little bit of scripting here, I would personally include optional real world programming assignments at the end of each week.
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10/10 starsCompleted
  • 1 review
  • 1 completed
2 years, 1 month ago
Introductory course to Linear Algebra. I already took a class in linear algebra at university, covering more or less the same topics, but I found the approach of LAFF innovative, making me understand better basic stuff I just crammed in my mind during my previous course, plus some stuff I never had the chance to look at. I joined the course in order to have a quick refresher of the main topics of linear algebra, and I can say I am satisfied with the result.
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Student

10/10 starsCompleted
2 years, 1 month ago
The instructor was very good and presented a structured approach to the material where each learning step was based on previous steps. This course is appropriate but will be tough for those without previous experience in linear algebra. I found it VERY helpful to watch the Khan Academy lectures on Linear Algebra at the same time I tool this class. Additionally, this class is relatively long for an online course (4 months) and will require your concentration - I wasn't able to take other online courses at the same time (excepting watching linear algebra videos on Khan academy). At completion there are still aspects of the course that I only understand theoretically but am unable to compute by hand.
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10/10 starsCompleted
2 years, 1 month ago
Very nice and interesting course. I had a lot of experience and fun with this course. My friends and I had some hot discussions about problems in course. Sometimes it was not easy to make exercises but now they done.
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Student

10/10 starsCompleted
2 years, 1 month ago
Great introductory course on linear algebra. Use of the "slide-and-dice" system, instead of loops and indices, made linear algebra infinitely more comprehensible! This system is used in advanced linear algebra, and so is not a toy system just for introductory linear algebra, and is well worth learning. The instructors provide links to many papers and books that use this system to reinforce this point. The homework and exams are designed for self-study rather than for assessment. Full course notes in PDF format with links to course videos on youtube is available from a website setup by the instructors! After this course there is still more linear algebra to be learned, to cover what a typical undergraduate student in science and engineering is expected to know. I plan to use Gilbert Strang's book and MIT OCW course, to learn the topics left out of this course. This course gives me a good foundation for this. I wholehe... Great introductory course on linear algebra. Use of the "slide-and-dice" system, instead of loops and indices, made linear algebra infinitely more comprehensible! This system is used in advanced linear algebra, and so is not a toy system just for introductory linear algebra, and is well worth learning. The instructors provide links to many papers and books that use this system to reinforce this point. The homework and exams are designed for self-study rather than for assessment. Full course notes in PDF format with links to course videos on youtube is available from a website setup by the instructors! After this course there is still more linear algebra to be learned, to cover what a typical undergraduate student in science and engineering is expected to know. I plan to use Gilbert Strang's book and MIT OCW course, to learn the topics left out of this course. This course gives me a good foundation for this. I wholeheartedly recommend this course to everyone: you will get to learn the "slice-and-dice" method even if you already know linear algebra. My heartfelt thanks to the instructors for putting in an unbelievable amount of work to deliver this course, and that for free too!
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10/10 starsCompleted
  • 26 reviews
  • 24 completed
2 years, 2 months ago
Definitely a 5 star course if others are . I have taken this course without the software part , and was able to fully follow the course teachings . I gained some great understanding that i had been longing for , through the course's Timmy-tools . So do not despair if you cannot run Matlab . To also learn software (algorithms) to aid mathematics , is an additional bonus this course has to offer , but no requirement for this course . Great course !
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Student

10/10 starsCompleted
2 years ago
LAFF rekindled my love for math and is truly a model for how math should be taught, the structure of the course enables deep understanding and recognition of core topics as well as creating understanding that can be applied further. Robert and Maggie, thanks so much!
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2/10 starsCompleted
2 years, 1 month ago
Too much logic and I had trouble downloading the coding packages for Python. The videos were slow and technical and made the page load slowly. The problems need more words and pictures rather than purely algebraic ways of phrasing questions. Youtube's 3Blue1Brown Linear Algebra videos were better for conceptual understanding.
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Student

10/10 starsCompleted
2 years, 1 month ago
Every thing is perfect. The teaching method and notes are excellent. The method to check the answers at the spot improve the capability and understanding of the topic. Thanks Saeed
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Student

10/10 starsCompleted
2 years, 1 month ago
Very interesting content, but requires a strong mathematical background, especially if you wish to delve into the more complex areas. Robert does an excellent job walking through the concepts from basic to deeper ones. The evaluation could be made more challenging.
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10/10 starsCompleted
  • 2 reviews
  • 2 completed
2 years, 1 month ago
The instructors are great, the material is enough to get you up to speed but not that much for me to start losing motivation. The instructors are great, the videos tend to be straight to the point, the homeworks build a lot of intuition so I'd recommend *always* doing them. It's a great course overall. I was so happy with it I decided to opt for a certificate. It's my first MOOC certificate, yay!
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10/10 starsCompleted
2 years, 1 month ago
Instructors are seriously fantastic. In addition to informative, helpful and easy to understand, they also have excellent personalities. I also enjoyed that the course dabbles in to programming. I would highly recommend this course for anyone looking to learn linear algebra.
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Henry Harya profile image
Henry Harya profile image
8/10 starsCompleted
  • 6 reviews
  • 5 completed
2 years, 1 month ago
The lectures and reference material were excellent! It took a few weeks before it was clear what the purpose of some exercises were, like the programming exercises. There were some errors in the videos that they acknowledged and I hope they correct in future runs. Also, I would have preferred doing the course work in Python and hopefully that will be supported in the future as well.
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Student

6/10 starsCompleted
2 years, 1 month ago
The course is excellent for anyone interested in engineering and/or applied maths, economics, numerical analysis, etc.... Its main focus is computation and porgramming. I also liked the way the professor always motivated the topics before discussing them. However, it is not very useful for someone interested in analytical linear algebra, pure math, and as like, which for a person like me, made a great part of the course very boring.
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8/10 starsCompleted
  • 1 review
  • 1 completed
2 years, 1 month ago
Great course ! I've enjoyed it much. I'll be looking for the next steps. I had some hard times with some of the enrichments but I think I took the most important Cheers
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Student

8/10 starsCompleted
2 years, 1 month ago
Great course. My only complaint is I wish it had gone even further. I really wish we could have gone more into the applications of eigenvalues and eigenvectors and given SVD some more thorough study. Guess I'll still have to take a few more courses...
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10/10 starsCompleted
  • 1 review
  • 1 completed
2 years, 1 month ago
This course really does what it's supposed to do - it gave me really solid foundations for linear algebra. Most topics were covered in depth. All explanations were clear to me. I suggest watching videos at 1.5 rate since 1.0 was way to slow for me. I recommend this course to anyone that wants to learn linear algebra.
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Student

10/10 starsCompleted
2 years, 2 months ago
Great introductory course on linear algebra. Interesting lectures, insightful exercises. Programming exercises greatly help understanding linear algebra concepts and algorithms, but this is not a programming course.
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Student

10/10 starsCompleted
2 years, 2 months ago
Excellent introductory course on linear algebra. The course content explains the concepts very well, with exercises that are calibrated to develop mastery. The format allows a student to determine what level of mastery they would like to attain--for example specializing in computation, algorithms, proofs or all the above. There are both advanced exercises and basic ones to develop intuition. Very much appreciate that this course is available for free. The instructors give top-notch instruction. They put much effort into it, as well as expertise gained through years of research and teaching. Thank you!
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Student

8/10 starsCompleted
2 years, 4 months ago
The LAFF course used an interesting approach to present linear/matrix algebra content to a wide audience. Having taken math up to multivariable calculus, I was able to complete all assignments of this course within 3 weeks and hope to gain exposure prior to take calculus-based linear algebra. I found this course did an overall OK job. However, I would like to critique the PROGRAMMING portion of this course -- the course is missing the opportunity of furthering the MATLAB (or IPython). A lot of exercises were very insightful, however, with poor directions. The lectures were also quite dry. In addition, I believe the instructors could make the course more challenging by revoking access to some of the homework answers, certainly for the 3 exams. The course can also be improved by better organization: the concepts covered don't seem to require a full 12-week.
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kevin zhang profile image
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kevin zhang

10/10 starsTaking Now
2 years, 5 months ago
This course is awesome and it's the best course for all levels of learners! I wanna send a big thank you to all the stuff who make this course real!
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Patricio Barletta profile image
Patricio Barletta profile image

Patricio Barletta

6/10 starsCompleted
2 years, 8 months ago
I find no flaw in the instructor, nor the provider; my review is about the content. Now, if you are (wannabe) a CS student and/or have never been exposed to college-level linear algebra, then this course may prove useful. But, if you mainly care about learning linear algebra then this course does a poor job. In that case I highly recommend Gilbert Strang course @ MIT OCW. I think the Professor made a sincere, and big, effort to develop a new way to teach linalg but, sadly, it just didn't work. Gilbert Strang teaches this same subject in a much more old fashioned way (him and the blackboard) and, god, what a great set of lessons.
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Claudio Felicioli profile image
Claudio Felicioli profile image
6/10 starsCompleted
  • 58 reviews
  • 58 completed
3 years, 2 months ago
Elemental algebraic structures and algorithms are presented with a very strong focus on computation and time/space optimization. The content is very solid and interesting per se but, sadly, the lecture style is boring, the chosen programming environment is cumbersome and the assignments are only a little more than grinding.
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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.