Linear Algebra - Foundations to Frontiers

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9/10 stars
based on  218 reviews
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Course Details

Cost

FREE,
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Upcoming Schedule

  • 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
23852 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
218 Reviews for Linear Algebra - Foundations to Frontiers

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Rankings are based on a provider's overall CourseTalk score, which takes into account both average rating and number of ratings. Stars round to the nearest half.

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student

10/10 starsCompleted
6 years, 1 month 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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Nam Hoang profile image
Nam Hoang profile image

Nam Hoang

10/10 starsCompleted
2 weeks, 1 day ago
Really interesting course for any Data Scientist. I would like to recommend to anybody who is interested in machine learning, data science. You will be taught fundamental knowledge for further research of any Data scientist projects.
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Alina Naseeb profile image
Alina Naseeb profile image

Alina Naseeb

10/10 starsCompleted
3 weeks, 6 days ago
course content was good but i would say please exclude the spark part from it .it really got me confused,i was just looking for basic algebra that i found most in last 3-4 weeks but spark is way too much to understand with all slicing and dicing but overall course was good .pdf files were really helping and also it is self paced so that's make people learn it even after their work and house chores.
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student

10/10 starsCompleted
4 weeks, 1 day ago
I came into this course with no previous structured experience in learning linear algebra. It introduces the important topics in a logical manner and while you may feel challenged or stretched by the material it's ultimately very well worth it. Fully recommend that if you have an interest in the subject area you give LAFF a go.
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Steffen Eisenblätter profile image
Steffen Eisenblätter profile image

Steffen Eisenblätter

10/10 starsCompleted
1 month ago
Amazing course! As a physicist with PhD from alread 1996 I had algebra education long ago and the course was meant to be a refresher only. But I not only refreshed my knowledge I also learned alot of new things, different vieving angles and new techniques. Will help me a lot in my AI and machine learning field I just entered. Strongly recommended!
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Ammar Mohamedy profile image
Ammar Mohamedy profile image

Ammar Mohamedy

10/10 starsCompleted
1 month, 1 week ago
This is one of the most elegant courses for linear algebra out there, it simply connected to the up-to-date frontiers of the field and have a computational intuition. I recommend anyone wants to start a journey of the inevitable field of Linear Algebra.
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Nicole Fanelli profile image
Nicole Fanelli profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
1 month, 3 weeks ago
Excellent overview of the main topics in Linear Algebra, and it even goes a little in depth at some points. The enrichment sections are wonderful and led me to various topics that I now wish to pursue further. A must if you need a solid foundation to go for more advanced topics.
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Mohamed Rondoz profile image
Mohamed Rondoz profile image
10/10 starsCompleted
  • 0 reviews
  • 0 completed
2 months, 4 weeks ago
I really love the iterative method of exposing us to the subjects. You begin with the very basic ideas and then you move on to the next topic until you get to the advanced topics with the feeling of how exactly you got here. The upside of this is that each new topic is like an application of the prior knowledge. Hence, these hard to grasp concepts get very solidified each week, which is great :).
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h y profile image
h y profile image

h y

10/10 starsCompleted
2 months, 4 weeks ago
It is very helpful. I recommend it. The videos are very interesting and useful. He teaches with a passion. He uses simple language so the concept is very easy to understand. I really like the questions after every video. It helps you to understand better.
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Yifan Liu profile image
Yifan Liu profile image

Yifan Liu

10/10 starsCompleted
4 months, 3 weeks ago
A very good beginning for me. A wonderful course for those who are not familar with linear algebra. The lectures videos covered most enssential topics in linear algebra with nicely made solution instructions. My favourite part is the programming excercise.
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Jerry Lee profile image
Jerry Lee profile image

Jerry Lee

8/10 starsCompleted
4 months, 3 weeks ago
A wonderful course for those who are not familar with linear algebra. The lectures videos covered most enssential topics in linear algebra with nicely made solution instructions. My favourite part is the programming excercise and the abundant exteral resources the instructor provided.
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Sourav Roy profile image
Sourav Roy profile image

Sourav Roy

10/10 starsCompleted
7 months, 3 weeks ago
In one word it was excellent. The foundations laid in terms of matrices being a linear transformation of vector, provided the right introduction into the subject. I came in with no experience of the subject, but I am leaving now with ability to approach more advanced topics in this field.
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Tianyu Liao profile image
Tianyu Liao profile image

Tianyu Liao

10/10 starsCompleted
8 months ago
It is a good and meaningful course. It is a good way to inform students and workers about the contents of Linear Algebra and promote high school students to learn more from the course to further their academic career. It is also good for students' college applications if students contrive to finish extra courses aside the regular curriculums in school. They can prove a larger interest in exploring more knowledge on more diverse aspects as well as the asipration of study.
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Alex Wu profile image
Alex Wu profile image

Alex Wu

10/10 starsCompleted
8 months ago
All I mainly wanted to do was to learn linear algebra, as I have not learned it before, and I have to say, I really like the way the Content, Instructors, and Provider all did a very appreciable and good job carefully explaining linear algebra, and giving me useful tools to help me learn(especially MATLAB), to me.
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Ryan Chan profile image
Ryan Chan profile image

Ryan Chan

10/10 starsCompleted
8 months ago
Robert and Maggie's course makes linear algebra approachable and more importantly fun (I never thought I would have so much fun with mathematics). It is absolutely incredible that all of this is "free". The explanations are clear and the steps taken to reach the more complicated concepts are cohesive. The exercises are thorough and all-in-all it is manageable as a self-study course. Probably the best resource available online besides paying for in-person lectures.
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Igor Nesterov profile image
Igor Nesterov profile image

Igor Nesterov

10/10 starsCompleted
8 months, 1 week ago
The best course on linear algebra I've ever seen. Presentation of the material is clean and consistent, explainations are exhaustive and insightful. One thing particularly great is that all the concepts learned are immediately translated into programming assignments, and that does make sure that you've really understood the material. It's entry level, but lays a solid foundation to rely on. Another great thing is: course team points to what you DONT get as a part of the course, so you know exactly where to look for your further studies.
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10/10 starsCompleted
  • 1 review
  • 1 completed
8 months, 3 weeks ago
About the content: I chose this course instead of studying classic Linear Algebra books. I cannot say that i regret this decision. Everything that i expected to learn was indeed learned throughout the course. I think its a good course for people who got out of highschool recently and wants a taste of how Linear Algebra and Computer Science are related. Throughout the course you will get a fair share of content that explains this relation deeply. About the Instructors: Definitely good instructors that check the comments regularly and answer your questions quickly. What else can you ask for? About the provider: Really good platform to learn all kinds of stuff. Easy to navigate and find what you need. TLDR: Great course, great detail about the relationship between Linear Algebra and Computer Science, very useful if youre no expert in math nor CS yet but want quality content for free.
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orestis orestis profile image
orestis orestis profile image

orestis orestis

6/10 starsCompleted
9 months, 1 week ago
About the content: Most of the times there was no explanation of possible implementation of the material which makes you lose interest About the instructor: The lecture slides were full of mistakes. About the provider: Edx is a solid platform.
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Stavros K profile image
Stavros K profile image

Stavros K

10/10 starsCompleted
9 months, 2 weeks ago
I had taken a couple of graduate level courses in Linear Algebra and a Numerical flavor of it more than 20 yrs ago so re-engaging in the topic demanded a refresher. The decision taking this course was right on target, thus, I completely enjoyed it to its last second. It starts from a clean slate of nothingness but it is structured on a learning curve with the right slope to lay out progressively more complex concepts on top of the previous layer with detailed proofs that reinforce comprehension in a very appealing way to the inquisitive brain. In the end you end up with a wealth of knowledge and plenty of well compiled take away material to review. Highly recommend it.
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Nick Gibian profile image
Nick Gibian profile image

Nick Gibian

10/10 starsCompleted
9 months, 3 weeks ago
The course is phenomenal. I came into this with zero knowledge of linear algebra concepts and now feel that I have an extremely good grasp on the fundamentals, and know enough to explore the advanced stuff on my own - or take another one of their classes! The videos were thorough. There were enough proofs to help solidify understanding, but they weren't done in such a way to put me to sleep. The programming stuff was good, although I skipped a lot of it, to be honest. No complaints whatsoever, I'm actually kind of sad that it's over, which I definitely did not expect.
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Hanjie Deng profile image
Hanjie Deng profile image
10/10 starsCompleted
  • 0 reviews
  • 0 completed
10 months, 1 week 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
1 year, 1 month 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
1 year, 2 months 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
1 year, 2 months 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
1 year, 2 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
1 year, 3 months 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
1 year, 3 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
1 year, 4 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
1 year, 7 months 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
1 year, 7 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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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.