Linear Algebra - Foundations to Frontiers

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9/10 stars
based on  228 reviews
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Cost FREE , Add a Verified Certificate for $50
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Course Details

Cost

FREE,
Add a Verified Certificate for $50

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
24287 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
228 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 profile image
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student

10/10 starsCompleted
6 years, 10 months ago
To former and future students looking to LAFF: Over at ulaff.net, Robert and Maggie just released all of the notes in a downloadable PDF with embedded hyperlinks to the videos. It's a whopping 900 pages of some of the best linear algebra instruction you will ever find, with accompanying videos, homeworks, exams, and notebooks. Best of all, it is available on a generous "pick your price" model ensuring everyone can have access to this great material regardless of income. It looks like the instructors have plans to update and refine the material as time progresses, and supporting them in that effort is a worthy cause. This material is so fundamental to many different areas that everyone should be able to LAFF with Robert and Maggie! To the course staff: Thanks so much for one of the most well done MOOCs I've ever taken!
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Peter Grover profile image
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Peter Grover

10/10 starsCompleted
1 week, 3 days ago
The course was different than what I expected in that it was not just straight linear algebra math approach. The use of a matrix manipulating computer algorithm was used to do complex solutions to matrix calculations. The best thing about the course is hands on with Matlab. The instructors were good and the content for me, should have included more problems on row/col spaces, projections, and basis changes.
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Mark Dixon profile image
Mark Dixon profile image

Mark Dixon

10/10 starsCompleted
1 week, 5 days ago
Progress through the course was thorough, step by step. It was great to use Matlab and bespoke U of T software to tackle many of the more complex problems. There were links to more more advanced discussions of issues and current research in the area. But at every stage there were patient explanations of fundamental concepts and opportunities to gain experience of handling the basic math with graded problems. I found some parts hard going but really enjoyed working through this course. I thoroughly recommend it to anyone wanting to get a good grounding in linear algebra or to revise the fundamentals in an up to date presentation.
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Robert Thoelen profile image
Robert Thoelen profile image

Robert Thoelen

10/10 starsCompleted
1 month ago
This course was a great introduction to Linear Algebra. I found it helpful in understanding not only the concepts from a mathematical perspective, but how they go with computer science and algorithms. It enriched greatly my understanding of how high performance computer programs work, and what types of math they are doing. The slicing and dicing approach was very helpful in visualizing how to do operations computationally.
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Linh D. profile image
Linh D. profile image

Linh D.

10/10 starsCompleted
1 month, 2 weeks ago
What an excellent Linear Algebra course! I did not take Linear Algebra in college and used this as an introductory course to prepare for a Masters program in Data Science. I love the course materials, especially the practice quizzes on edX and Matlab problems. Prior to this, I did not know that an online course could be engaging...and fun. Thank you Robert, Maggie, and team for a great experience! Chương trình học rất hay và hiệu quả. Chủ đề đào tạo được chọn lọc kỹ lưỡng, vừa đa dạng, hấp dẫn kết hợp cả lý thuyết và thực hành!
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Jin profile image
Jin profile image

Jin

10/10 starsCompleted
3 months ago
This is how Linear Algebra should be thought at any institution of learning. The course fulfills its objective very well as to the relationship between mathematical abstraction and programming abstractions - a sustained focus of this objective is very obvious throughout the 12 weeks. I hope they would continue offering this course in the future. I have seen no better alternative to this type of Linear Algebra instruction. If you are a scientist or engineer, this one is for you. It shows the nuts and bolts of those linear algebra packages we continually use but never bothered to wonder what's inside those packages.
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Jim Pearson profile image
Jim Pearson profile image

Jim Pearson

10/10 starsCompleted
4 months ago
All great stuff. I already studied linear algebra but it was almost 20 years ago. I appreciate the emphasis on conceptualizing and presenting idea elegantly by partitioning the matrices. The animated eigenvector visualizations were fun and informative. They help solidify some of the theory and operations.
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Jonah Poczobutt profile image
Jonah Poczobutt profile image

Jonah Poczobutt

10/10 starsCompleted
4 months, 2 weeks ago
Very thorough and well thought out. Good balance between focus on fundamentals and computations while also providing theoretical backing. The enrichment material and final chpaters provide very challengin materials, in my view
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cheng wei profile image
cheng wei profile image
10/10 starsCompleted
  • 0 reviews
  • 0 completed
4 months, 3 weeks ago
A great fundamental course in linear algebra. The material was carefully prepared and the questions were replied to promptly. I had prior knowledge of linear algebra, but the course helped me gain insights from a different perspective. My favorite topics are programming implementation, slicing & dicing, and the graphs & animations for eigenvectors & matrix solution. I learned a lot from these topics. Thank Robert and Maggie for providing such a good course.
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Hongli Yu profile image
Hongli Yu profile image

Hongli Yu

10/10 starsCompleted
5 months, 3 weeks ago
A lot of details are provided, and if you got any questions professor will reply you within a few days. From my view, the exam questions can be more diverse, since so many interesting content are collected, for example the one about the weather prediction is awesome
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Mark C profile image
Mark C profile image

Mark C

10/10 starsCompleted
5 months, 3 weeks ago
Very effective and student-friendly course. May be recommended for both beginners and those just want to review specific topics of the fundamentals of the Linear Algebra.
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Sal Tom profile image
Sal Tom profile image

Sal Tom

10/10 starsCompleted
6 months, 2 weeks ago
Fundamental course, highly recommended. Wether you are a newcomer or an accomplished professional in the fields of software development, data science or machine learning, a solid foundation in Linear Algebra is essential and this course will give you that and more, such as tools to go deeper and even understand research papers at the frontier.
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Nam Hoang profile image
Nam Hoang profile image

Nam Hoang

10/10 starsCompleted
8 months, 2 weeks 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
8 months, 4 weeks 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
9 months 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
9 months 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
9 months, 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
9 months, 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
11 months 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
11 months 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
1 year 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
1 year 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
1 year, 3 months 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
1 year, 3 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
1 year, 4 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
1 year, 4 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
1 year, 4 months 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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 profile image

10/10 starsCompleted
  • 1 review
  • 1 completed
1 year, 4 months 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
1 year, 5 months 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
1 year, 5 months 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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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.