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Michael George

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  • 2 reviews
  • 2 completed
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Having completed this course, I must comment that it is memorable, and I feel that despite its brevity, it is certainly one of the best courses I have ever taken. That said, one tends to derive from a course benefits proportional to the effort one puts in, and at least one other reviewer for this course, who wrote a rather short review, seemed to have dedicated essentially no effort, possibly because he or she has had the material at the freshman or sophomore level. That is, inherently, a rather superficial level. Furthermore, I do not feel that this course, overall, was taught at that level, although one might receive a passing grade of 60 out of 100 by approaching the course in this way. If that is all you want, don't read on. My review is not for you. But if you are interested in something of deeper value, this is what my review addresses. I have graduate degrees in mathematics and physics, and some prior experience studying functional analysis, but not in some of the areas in which this course focused. I found that this course compares favorably with other math courses I have taken at about the junior or senior level (or perhaps first-year graduate level). (There seems to be a lack of correspondence between European and American levels: This course seems to be at about a sophomore level for Europeans. It's a little hard to be certain. I teach math in the United States, and I must say it is not a sophomore level course, at least not for most students I encounter.) I took this course as a "nontraditional" student, who otherwise would not find courses of this quality available. This, as we all recognize, is the enormous advantage of MOOCs over traditional courses: Many people in the world now have access to high quality, sometimes very high quality, as in this course, courses, who otherwise would have few if any educational alternatives. The video lectures focused on developing intuition and insight. The fact that one can view the video lecture multiple times, and the fact that there is an active forum for the course makes a substantial difference over traditional courses, and I feel represents a possible improvement if one does not become a dilettante with respect to these MOOCs but really applies oneself seriously. However, my experience with online classes is that most students take the courses (often intentionally) as dilettantes, and fail to derive much. The video lectures were informative and insightful. The pdfs associated with the course went into more depth and detail, and helped to fill in some of the important material that could not be covered in the lectures. I found I also had to consult references. A very useful reference, at least for part of this course, is Berberian's text on Hilbert spaces. However, I also recommend that you have a good reference available for real analysis. Rudin's Principles of Mathematical Analysis seemed to be a favorite of many students. I used his text on real and complex analysis, which is a graduate level text. The quizzes were useful and helped sharpen my knowledge. I liked the fact that we could take most of the quizzes twice, as this allowed me to understand the mistakes I was making. Unfortunately, one can "game" many of the quizzes and obtain high scores that are unrepresentative of one's true level of achievement. The written homework (submitted for grading) involved proofs that provided some challenges. Writing proofs that will be graded by one's fellow students forces one to try to communicate as best one can. I definitely feel this was positive, as one often simply takes it for granted that a teacher or assistant will be able to decipher one's homework write-up, however obscure. In the end, after taking the final exam assessment, I could see that I was much more aware of whether or not I was communicating clearly. Overall, on these assessments, there seemed to be a lot of evidence for plagiarism despite severe penalties. Hopefully the future courses like this will introduce procedures to reduce this. The course had a lively discussion forum that was very interesting and worthwhile to contribute to. I was mostly interested in more "philosophical" issues than the pragmatics of most of the forum discussions. However, one could see that there was "room" enough for all of us, whether practical or theoretically inclined. This is quite a profound improvement over traditional courses. This alone makes MOOCs substantially of interest for students. It opens new territory that one does not ordinarily see in traditional courses. I found that the course subject matter lies close to my interests in physics and mathematics, and gave me a nice start for independent study and research. From applying myself seriously, I found that my level in this area improved significantly. Achieving this improvement, despite my good background in mathematics and physics, often meant working at the course beyond the 4 to 6 hours per week that is recommended in the description of the class. I typically spent 8 - 11 hours per week or more on this course. However, it did "pay off" in terms of learning as I made substantial progress. I also found that this course was able to capture some of the deep beauty of pure mathematics that makes us somewhat expect that this subject is applicable in physics and engineering. The last part of the course, and the very beginning portion, focus on applications to physics and math. As a "sophisticate", I have to say that the applications are quite impressive, although we in physics have our own approaches to what was addressed, the mathematical perspective was very elegant. I came to the course with pretty good preparation in mathematics, but I definitely think the course would be of value to a diverse student population. Certainly, the course is a serious time sink if one does not have a very good background, and the extent to which one could benefit is somewhat dubious, even if one tries when one does not have an adequate background. When I refer to "junior or senior level", as I did about this course previously, I meant as a major in pure mathematics. I disliked having to grade student homework, and each of us was required to grade at least five homework papers per week. This was too time-consuming for the limited time I had available each week to dedicate to the course. However, I do believe that evaluating homework was helpful in my own understanding. I was concerned that the course might prove to be too time-consuming overall as it is very intense for 8+ weeks. Also, the final exam was, albeit of moderate difficulty, quite long. However, I was able to manage time satisfactorily. My goal was to get well-enough prepared to study and apply more modern theory of functional analysis and partial differential equations, and for this purpose, this course was superb. I strongly recommend this course for people who work in an area sufficiently closely related to this area of analysis.
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This course is strongly oriented toward both an introduction, and a synthesis of basic digital signal processing techniques. Since I am strongly interested in autonomous robotics and systems engineering, this course was very helpful to me. I had studied signal processing on my own, having read the text Signals and Systems, by Oppenheim et al., and also part of the text Discrete-Time Processing, by Oppenheim and Schafer, but I had not taken a course in signal processing prior to taking this class. There were definitely a number of concepts for which I had not developed a satisfactory framework, my intuition for the subject was limited, and there were also several basic concepts I did not understand. I found this course chiefly helpful in developing intuitions about digital signal processing, and the video lectures are very clear and helped me to understand concepts better. Furthermore, all of the techniques introduced in the course are nicely synthesized in developing a communications system example in the last several lectures of the course, which was very impressive and insightful. A number of the other lectures, too, proved to provide some superb insights. The homework problems were oriented directly toward the video lectures, and were sometimes enjoyably challenging and difficult. I felt, too, that they sometimes helped me go beyond the lectures in developing my skills, and provided insights related to future lectures. Due to the difficulty of some of the problems, I simply had to accept that sometimes I was not going to solve problems correctly. This gave the course and edge of difficulty I enjoyed, but I can see that some people might find the homework problems unpalatable, especially because one's grade on the course comes from the degree to which the problems are solved successfully. As a beginner in this area, I simply had to accept that sometimes I was not going to do as well as I would have liked. The course does have a strong "hands-on" flavor, oriented toward people with engineering backgrounds. I am more of a theoretical type, with a pretty good background in physics and mathematics. Still, I was able to complete the course, despite certain deficiencies in my background, and found the video lectures and the homework problems to be very rewarding. The presentation of techniques in an intuitive way, and the synthesis of techniques in some rather beautiful examples certainly make the course worthwhile, and the two instructors for the course are outstanding. I also thought that the staff, in helping students in the student forum, displayed a high level of competence and knowledge. For me, the one weak point in the course was that I did not find the text to be very useful in supplementing the lectures. My study time was limited to about 10 hours per week, due to my time constraints, and I just did not have enough time to read the text properly, which often discussed topics not considered in lecture. I personally feel that I would have to spend 15 to 20 hours per week to properly read the text. Compared to another course I have taken from Coursera, I found that the student forum was not as lively, and the questions being asked by students on the whole were not very interesting to me. However, I often found the answers supplied by the instructors or staff to be interesting, and this somewhat balanced out an otherwise tepid forum. Of course, in part, I have only myself to blame for this, as I could have contributed to the forum more often. I am not blaming anyone, but the atmosphere of the course just did not seem to foster lively debate. My dislikes about the course are very minor. The course is definitely superb and worthwhile taking, provided one has some background in math or engineering that is appropriate for the level of the course, which, relative to courses in the United States, is about a junior or senior college level. I was very happy with the course, and felt that it prepared me well to go on to more advanced studies. I strongly recommend this course for people interested in signal processing, who want to consolidate some of the basics, and see the integration of some of the important techniques in a valuable intuitive way.