Linear Algebra - Foundations to Frontiers

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Linear algebra

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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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22837 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
208 Reviews for Linear Algebra - Foundations to Frontiers

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10/10 starsCompleted
4 years, 5 months ago
I took this course as a refresher course. I had previously taken an Intro to Linear Algebra course that was strictly for math majors with no programming involved. It had been several years and I had only used linear algebra once since then. This course was perfect for me, because I also have a CompSci minor, so the focus on the algorithms for programming was very interesting to me. Note that the programming part is optional, you can do the course without doing the programming exercises (there is an option to skip those, and I had to skip them nearer the end due to time constraints). Also, this course simply helped me tie together the concepts much better than my first introduction to linear algebra, and covered topics that I don't even remember covering in my first class. I highly recommend to anyone interested in learning about linear algebra. Another note: although I had prior experience, I believe that the way the subject i... I took this course as a refresher course. I had previously taken an Intro to Linear Algebra course that was strictly for math majors with no programming involved. It had been several years and I had only used linear algebra once since then. This course was perfect for me, because I also have a CompSci minor, so the focus on the algorithms for programming was very interesting to me. Note that the programming part is optional, you can do the course without doing the programming exercises (there is an option to skip those, and I had to skip them nearer the end due to time constraints). Also, this course simply helped me tie together the concepts much better than my first introduction to linear algebra, and covered topics that I don't even remember covering in my first class. I highly recommend to anyone interested in learning about linear algebra. Another note: although I had prior experience, I believe that the way the subject is presented would be quite good for a first time exposure to the subject. Excellent video lectures, materials, and solutions!
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6/10 starsDropped
4 years, 5 months ago
I'm afraid I couldn't get past the first week of the course. I had/have an interest in linear algebra, but my limited experience with computer programming was 35 years ago. I couldn't get past the complexity of installing and learning MATLAB as well as learning linear algebra. Those who dive in must really be prepared to spend the 8 hours/week.
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10/10 starsCompleted
4 years, 5 months ago
Marvellous course offered by UTA through edX.One find it easy going only with strong base of the subject.Concepts easily demonstrated in the videos and exercises can be completed well within the stipulated time.Content gets tough in Week 10,11,12 & requires more work. This is the lengthiest course I have done so far. Be calm and a lot of paper work is needed with usage of Matlab. The quality of the questions tickle your brain,while the detailed explanation ease the pressure.Takes a minimum of 10 weeks to complete,better if you upgrade to verified certificate early, I delayed and missed a certificate from UTA !!! I recommend to go ahead in Linear algebra those who have found glory and others can learn anytime easily.One can do 5-6 courses a year from the user friendly platform of edx and these require low bandwidth of data which soothes the long journey. Many math courses are available where you build your future.
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10/10 starsCompleted
4 years, 6 months ago
Time and time again, I have run into problems when applying linear algebra in a variety of other projects and courses. I have taken some linear algebra before, but it wasn't very practical. For example, about a year ago, I tried to write a program to solve a very large matrix with cramers rule. Needless to say, it didn't work out very well. If I had taken this course first, I could have easily made a program to solve that matrix in an efficient manner. Overall, I feel this course taught the theory extremely well, while grounding that theory in practical programming. The last few chapters are a little rushed, but I suppose that's to be expected with an already-long course. I highly recommend it to anyone wanting a very solid understanding of basic linear algebra, and exposure to many of the more advanced topics. This course exceeded my expectations.
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10/10 starsCompleted
4 years, 6 months ago
ROTFLAFFMAO Absolutely The Best Math-Math Course I Have Ever taken. Absolutely The Best Learning Experience I Have Ever Had. The best in all respects; The best professors; clear, concise, knowledgeable, interesting, interested, concerned, leading edge contributors, expert presenters, easy to understand, provide a deeper view than in an ordinary course in this subject area. Prof v. d. Geijn’s participation level in the discussions board is amazing. A great subject: of current topical interest to me, inherently interesting in and of itself, lends itself well to a MOOC format and schedule flexibility. The algorithmic emphasis is very valuable to me both here and beyond the course area – a new way to see the light in areas where it may have been neglected in our rush for answers. A great course philosophy; to meet the needs of different students with differing objectives, needs, backgrounds. A complete integrated l... ROTFLAFFMAO Absolutely The Best Math-Math Course I Have Ever taken. Absolutely The Best Learning Experience I Have Ever Had. The best in all respects; The best professors; clear, concise, knowledgeable, interesting, interested, concerned, leading edge contributors, expert presenters, easy to understand, provide a deeper view than in an ordinary course in this subject area. Prof v. d. Geijn’s participation level in the discussions board is amazing. A great subject: of current topical interest to me, inherently interesting in and of itself, lends itself well to a MOOC format and schedule flexibility. The algorithmic emphasis is very valuable to me both here and beyond the course area – a new way to see the light in areas where it may have been neglected in our rush for answers. A great course philosophy; to meet the needs of different students with differing objectives, needs, backgrounds. A complete integrated learning system; outstanding lectures as well as complete background and supporting materials for mainstream/core and enrichment topics. Interesting homework/exercises; which support the learning and are much more than rote application of formulas. Some are quite challenging (at least to me). The process of interleaving the lectures and the homework is very powerful. The sequence of questions also brings insights. Access to outstanding tools; MATLAB, FLAME, Spark, Timmy. Access to MATLAB alone is worth the price of the course. I wish I could justify a personal copy.
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10/10 starsTaking Now
4 years, 6 months ago
The course is very good at tackling simple matrix and vector operations. The many ways of slicing and dicing matrices and vectors aided my understanding of the material, and this perspective of slicing and dicing improved my grasp on the properties of matrices. Furthermore, coding on MATLAB also provided an excellent test of my understanding. The course offers many excellent exercises to show the properties of special matrices like upper, lower, diagonal, symmetric, and the identity matrix, and are supplemented by simple proofs in many notations like the FLAME notation. In the second part of the course, applications of matrix operations using slicing and dicing were given such as the QR factorization. Even though LAFF is just an introductory course, I learned a lot even though I haven taken an introductory undergraduate course in linear algebra in the past. The enrichment activities and readings also made me appreciate linear alge... The course is very good at tackling simple matrix and vector operations. The many ways of slicing and dicing matrices and vectors aided my understanding of the material, and this perspective of slicing and dicing improved my grasp on the properties of matrices. Furthermore, coding on MATLAB also provided an excellent test of my understanding. The course offers many excellent exercises to show the properties of special matrices like upper, lower, diagonal, symmetric, and the identity matrix, and are supplemented by simple proofs in many notations like the FLAME notation. In the second part of the course, applications of matrix operations using slicing and dicing were given such as the QR factorization. Even though LAFF is just an introductory course, I learned a lot even though I haven taken an introductory undergraduate course in linear algebra in the past. The enrichment activities and readings also made me appreciate linear algebra techniques. For those who are totally new to linear algebra, it helps to go over the notes, exercises, and answers.
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10/10 starsCompleted
4 years, 6 months ago
This course is a very solid foundation for future work with linear systems. The pace of the course is well designed as well as how the various pieces fit together. In some mathematics course, there can be significant jumps along the way, but this course presents the material in a logical sequence without frustrating gaps in the explanations. It is obvious that a lot of thought and hard work went into creating this course, and I am very grateful to the instructors for all their hard work. As background, I had seen some of the material before taking the course but was self-taught. I worked for many years as an electrical engineer, so I have also seen some of the applications of linear algebra. This course filled in significant gaps in my understanding.
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10/10 starsCompleted
4 years, 9 months ago
Material presented clearly. Their approach is different from other linear algebra courses by sharing MATLAB algorithms that eliminate most of the programming challenges working with matrices - dealing with element indices. They call the approach "slicing and dicing" and it helped work through a lot of problems. Both instructors very responsive to questions posted on discussion board. Both instructors speak clearly in their numerous videos. Course notes are very clear and almost stand alone if you are a Reading Learner.
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10/10 starsCompleted
4 years, 9 months ago
Very clear, nice teachers and an easy approach to linear algebra for beginners. I appreciated this course and I recommend it. I liked it so much that I will take it again!
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Sergey Polgul profile image
Sergey Polgul profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
4 years, 9 months ago
I found the homework AND grading system to be extremely helpful. there is immediate gratification on each step of the way and the instructors hand - hold you on the journey to learn linear algebra.
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10/10 starsCompleted
4 years, 9 months ago
The Perfect Course for a Computer Science Undergrad who is about to enter Graduate School after a break. Enabled me to gain a firm grasp on the concepts along with the modern day technology and algorithms used in the domain.
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10/10 starsCompleted
  • 2 reviews
  • 1 completed
4 years, 9 months ago
This course was so amazing, Excellent motivation, presentation and Exercises (to get insights and intuition). The staff was very active in the discussion forum. This course was like a dream, this was a FREE high quality education. Really guys I don't know how to thank you, you should so proud for what you offer
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10/10 starsCompleted
4 years, 9 months ago
Those who want to touch data science, machine learning, process, and/or text mining, computer graphics and recognition watch necessarily. Without orthogonal and singular decompositions, eigenvectors and eigenvalues, projections and normal equations at your fingertips there is nothing to do, ctrl+space will not help. Brilliant course by ,y mind. Тем, кто хочет пощупать data science, machine learning, process and/or text mining, computer graphics & recognition смотреть обязательно. Без ортогональных и сингулярных разложений, собственных векторов и значений, проекций на подпространства и нормального уравнения на кончиках пальцев там делать нечего. Совсем нечего, ctrl+space не поможет.
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10/10 starsCompleted
4 years, 9 months ago
Everything about this course is amazing! I don't usually write reviews that are so unilaterally good but this class really fits the bill. The instructors have put so much effort into the course and it really shows. I'm so glad that I took this class.
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10/10 starsCompleted
4 years, 9 months ago
may be it will be better to divide this course in two parts... sometimes it is hard to follow a mooc with 15 weeks of length because of other duties... i prefer to have moocs with 7-8 weeks. anyway it was a wise think to do: open all the deadlines till the end of the course.
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10/10 starsTaking Now
4 years, 9 months ago
In short, I now understand how linear algebra works. I see the matrix or an equation with matrices and understand what kind of manipulation it does. Previously it was a black box for me.The platform, materials and forum are great. Instructors reply to forum questions within hours or a day and their replies are always helpful.
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10/10 starsCompleted
4 years, 9 months ago
It was a great time spending these 12 weeks with LAFF staff!! I had linear algebra courses during my university time so many years ago but this LAFF course is really digging into the foundations and the reasons of the topic. I took several MOOC also in other platforms; the LAFF course is definitely one of the best I had. Once again I have to thank the staff for dedication to the course. I am looking forward to take one more course in an advanced topic about linear algebra with LAFF staff !!! Thanks Robert, thanks Maggie!!
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10/10 starsTaking Now
4 years, 9 months ago
This class is the best math class I've taken, on or offline. It is obvious how much care and craft went into its planning and execution. The organization is also exceptionally clear and easy to navigate compared to most MOOCs. As a former English major who has been away from math for about 15 years, I found this class challenging to say the least! But I also found that there were enough resources to overcome most trouble spots.
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10/10 starsCompleted
  • 1 review
  • 1 completed
4 years, 9 months ago
I have done several MOOCs so far and, by my experience, they fall into 4 categories: 1 - Those that does not deserve any mention (poor material, poor teaching strategy, poor teacher/student interaction...) 2 - Those that have a motivated and participant instructor that unfortunately fails to provide a good learning environment. 3- Those that have a very well crafted material that, by itself, is able to deliver good results to engaged students, even with the lack direct interaction between instructors and students. 4 - Few that are able to provide not only a very well made material as also have instructors that are really engaged in the course all the time. This course stands into the latter. Professors Robert and Maggie not only presents the course masterfully as also interact and respond every single question posted in the forums. Also, you will find most of the exercises and demonstrations very well written and many of those... I have done several MOOCs so far and, by my experience, they fall into 4 categories: 1 - Those that does not deserve any mention (poor material, poor teaching strategy, poor teacher/student interaction...) 2 - Those that have a motivated and participant instructor that unfortunately fails to provide a good learning environment. 3- Those that have a very well crafted material that, by itself, is able to deliver good results to engaged students, even with the lack direct interaction between instructors and students. 4 - Few that are able to provide not only a very well made material as also have instructors that are really engaged in the course all the time. This course stands into the latter. Professors Robert and Maggie not only presents the course masterfully as also interact and respond every single question posted in the forums. Also, you will find most of the exercises and demonstrations very well written and many of those with videos in which the instructors themselves guide you step-by-step. I took this course as a refresher, since I had a previous undergraduate course in Linear Algebra but, not only I was able to review many of the topics I wanted, as also I was presented to some techniques (Flame notation, slicing and dicing...) that really improved my knowledge. There is only one negative aspect of the course in my opinion, and that is their choice to use matlab in the programming assignments instead of python from the last offering. However, even with that, the material is well documented and there are examples in python as well (but I really hope they change back to python in the next editions) Anyway, it was an amazing course and I really recommend it to anyone willing to learn or review the topics of a undergraduate course in Linear Algebra.
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10/10 starsCompleted
4 years, 9 months ago
I learned Linear Algebra before in school but didn't understand what I was doing. I just recited the calculations (Linear equations, LU, SVD, eigenvalues) and wrote it on the exam papers. It didn't left much or made some changes in my mind after the exam After I graduated from school and found LA is really really really important (Can't express the importance, it's just the language of some subjects). Therefore I took this course, the course well covers the foundations of Linear Algebra which you can find out from typical textbook (except Det) and most importantly, it will teach you how to think and make sense of concepts such as matrix, vector, factorization, eigenvalue, SVD, LU, QR factorization. This course builds my solid foundation and I can go further based on these 12 weeks. The course is easy to follow, self-paced [no deadline except final which is excellent policy for worker] As Robert wrote, A typical undergrad... I learned Linear Algebra before in school but didn't understand what I was doing. I just recited the calculations (Linear equations, LU, SVD, eigenvalues) and wrote it on the exam papers. It didn't left much or made some changes in my mind after the exam After I graduated from school and found LA is really really really important (Can't express the importance, it's just the language of some subjects). Therefore I took this course, the course well covers the foundations of Linear Algebra which you can find out from typical textbook (except Det) and most importantly, it will teach you how to think and make sense of concepts such as matrix, vector, factorization, eigenvalue, SVD, LU, QR factorization. This course builds my solid foundation and I can go further based on these 12 weeks. The course is easy to follow, self-paced [no deadline except final which is excellent policy for worker] As Robert wrote, A typical undergraduate linear algebra course offering includes a sequence of three classes: 1 Introductory Linear Algebra. [This course] 2 Applied Linear Algebra. 3 Numerical Linear Algebra. I am really looking forward to the latter two!!!
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David Han profile image
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10/10 starsCompleted
  • 2 reviews
  • 2 completed
4 years, 9 months ago
This is an exceptionally good foundation course to linear algebra. It will give you a strong intuition of how matrices work and why they behave the way they do. I learned more by taking this course than I did during university.
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10/10 starsCompleted
4 years, 9 months ago
Preporučam ovaj tečaj svakome tko nastavlja bilokakvo školovanje dalje od srednje škole, kako zbog sadržaja, tako i zbog naglašeno pedagoškog pristupa. Srednjoškolcima također, budući da započinje osnovama linearne algebre, i onda dalje u nešto apstraktnije vode.
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10/10 starsCompleted
4 years, 9 months ago
The Linear Algebra Foundations to Frontiers (LAFF) course taught by Dr. Robert van de Geijn and Dr. Maggie Myers is outstanding. I have an Honours Bachelor of Science degree (Biology/Forensics) but did not really have any linear algebra exposure beyond high school. I have recently developed an interest in statistics and computer programming and thought it would be useful to learn more about linear algebra, so I signed up. I’ll admit that I was intimidated at first, but after only a short time, I realized that this course was made for people like me with very little prior experience in this field; the concepts are carefully presented so that each builds upon the previous work with plenty of opportunities to reinforce the material through homework assignments, two midterm exams and a final exam. It is both challenging and yet, surprisingly intuitive, which I believe is because of how well the material is presented and also, the arr... The Linear Algebra Foundations to Frontiers (LAFF) course taught by Dr. Robert van de Geijn and Dr. Maggie Myers is outstanding. I have an Honours Bachelor of Science degree (Biology/Forensics) but did not really have any linear algebra exposure beyond high school. I have recently developed an interest in statistics and computer programming and thought it would be useful to learn more about linear algebra, so I signed up. I’ll admit that I was intimidated at first, but after only a short time, I realized that this course was made for people like me with very little prior experience in this field; the concepts are carefully presented so that each builds upon the previous work with plenty of opportunities to reinforce the material through homework assignments, two midterm exams and a final exam. It is both challenging and yet, surprisingly intuitive, which I believe is because of how well the material is presented and also, the array of tools that are used to help visualize the concepts (Spark, PictureFLAME, Timmy, MATLAB). The emphasis is on truly learning and understanding the material rather than just achieving a passing grade; the instructors offer unlimited tries for every question and comprehensive answer keys are provided with each question so the student has the ability to try solving the problems as many times as necessary without penalty and is never left wondering how to find the answer. The instructors are active on the discussion board and always willing to answer questions. It was an amazing opportunity to be able to complete this course for free, and I would highly recommend it to anyone with an interest in the STEM-related fields (Science, Technology, Engineering, and Mathematics), but especially to women, since we are underrepresented in all of those fields - try it out! If you complete every assignment and watch every video (which I recommend doing), the estimated 8 hours/week time commitment was accurate, but it IS absolutely worth your time to LAFF with them. -Kathy D.-
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10/10 starsTaking Now
4 years, 9 months ago
Excellent. The only limitation was my own time and ability. While I did not complete the course, I will keep trying and now with a better foundation. The amount of effort in preparing this material and presenting it, is nothing short of remarkable. Thanks!
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10/10 starsCompleted
4 years, 9 months ago
I took this course because I had tried to take the Stanford Machine Learning course but discovered that I did not know/remember enough linear algebra. (Actually some of the subjects did not exist when I first took linear algebra in college.) The linear algebra review included in the machine learning course was not adequate. This course, however, more than adequately prepared me to take the machine learning course. In fact, several of the subjects included in this course were described as advance linear algebra subjects by Dr. Ng in the machine learning course. In addition, I now feel quite comfortable with matrix notation and even Matlab vectorization. Previously I had tried to relearn linear algebra with Dr. Strang's book and lectures, but the lack of "homework" problems with good feedback was not adequate. This course covers the material well and has good online homework with excellent backup material. Thank you
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10/10 starsCompleted
4 years, 9 months ago
I took this course thinking in making some kind of refresh to then make a better study of Digital Signal Procesing. But I was surprised of the whole bunch of things that I didn't know about the foundation of Linear Algebra. There is a lot to learn in this course, and a lot of work of course! not to be taken lightly.
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10/10 starsCompleted
4 years, 9 months ago
Thank you Maggie and Robert! This class was wonderfully helpful. I really loved the way the content was presented. I did not make through all of the enrichment material, but otherwise found that I was spending the expected amount of time on LAFF per week (circa 7-8 hours).
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10/10 starsCompleted
4 years, 9 months ago
Excellent and well done Linear Algebra course. I recommend it very much to everyone interested or in need to understand LA. Will be useful for students interested in theory and also for those using LA in software industry. The theory is very well presented and explained. MatLab is used for practical exercises. Prof. Robert van de Geijn and Maggie Myers were answering themselves every question posted on discussion forums. Probably that was the reason I learned a lot useful information from discussion forums. I also appreciate flexible due dates, there was only one final due date, so I could work on my own pace and successfully complete the course. There is also the textbook available made by course instructors which was extremely helpful. It's probably between best LA textbooks I've seen. Also course is long and need some patience and time commitment specially towards the end when subjects become more advanced. Overall bet... Excellent and well done Linear Algebra course. I recommend it very much to everyone interested or in need to understand LA. Will be useful for students interested in theory and also for those using LA in software industry. The theory is very well presented and explained. MatLab is used for practical exercises. Prof. Robert van de Geijn and Maggie Myers were answering themselves every question posted on discussion forums. Probably that was the reason I learned a lot useful information from discussion forums. I also appreciate flexible due dates, there was only one final due date, so I could work on my own pace and successfully complete the course. There is also the textbook available made by course instructors which was extremely helpful. It's probably between best LA textbooks I've seen. Also course is long and need some patience and time commitment specially towards the end when subjects become more advanced. Overall between the best MOOCs I 've taken.
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8/10 starsCompleted
4 years, 8 months ago
This course provides a good introduction to linear algebra ideas and a nice foundation for future studies; however, someone who's interested in immediate application and a deeper understanding will need to take a more in-depth course. Either way, this is a good starting point and a very nicely organized class!
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6/10 starsCompleted
  • 5 reviews
  • 5 completed
4 years, 9 months ago
It's an o.k. course to me. The content is focusing on simpler side of Linear Algebra, but I would love to learn more advanced content such as SVD -- so the word 'Frontiers' isn't well represented. One thing particularly annoying is that in home works, professor asks you to practise a lot slicing and dicing on matrix calculation. by 'a lot', I really meant 'a lot', it made me very sick. If you want a soft start, it's not a bad course, and I hope the slicing and dicing practice gets reduced in the future offerings.
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