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reviw due Wed Dec 13

For Wednesday December 13 lecture: Complete your student ratings for this course. As you prepare for the final exam, write responses to the following questions. There is a study guide available here . Which ideas, topics, and theorems do you think are most important out of those we have studied?  I feel like you've pretty well condensed everything on the final exam. For the whole semester, the Master Thm stands out as being important, as does the whole section on statistics, and the Fourier transforms. I fail to see the importance as of yet of the wavelets, mostly because I have yet to fully understand them. What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out. You mentioned today in your office that the point of Monte Carlo methods is to approximate integrals with/as sums. If we could see that, that would be great. Also problems 4 and 5 on t...
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8.7, due Monday dec 11

Difficult: I think I need to go back and review compact support. Also, much like the last section, I don't think I'll fully understand this one until I do the HW and/or code it up. Application: I feel like every section says, 'the last approximation is good for some things, but not for this new thing'. It's just interesting.
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8.6, due Friday 12/8

Difficult: Honestly, this whole thing is a bit fuzzy to me. I'm not quite sure how it works. I feel like I won't fully understand until I do a lab on it. Application: well, the picture of the mandrill was interesting. How sure are we, though, that this is how the FBI does fingerprints?
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8.5 due wed Dec 6

Difficult: I'm not 100% sure what a wavelet is or how they relate to the Fourier stuff we've been doing. Application: I suppose that this section, should I understand it better than I do, gives us a way to represent even non-periodic functions nicely. That seems really useful.
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8.4 due Mon Dec 4 17

Difficult: I don't fully understand the Nyquist frequency. Why would making the Fourier coefficients 0 after a certain k make things more accurate? I can see that they do, but I don't know why given that this is a periodic function. Application: As mentioned, aliasing and such are used with radio signals, digital image filtering, etc. I don't fully see how they work with digital signals, though.
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8.2 due wed 11/28

Difficult: Why is x_l = l(delta)? (top of pg 293). Also, I think that we could have used just a bit more explanation on what DFT/FFT's are. Application: In general, the DFT seems really cool based on what I've seen of Michael's pictures from Physics and such, but I can't seem to understand how exactly they work.
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8.1, due Nov 27 17

Difficult: The hardest part was following all of the integrals going on. The idea of fourier transforms is interesting, but I don't know how well I'll actually be able to follow it. Also, how is having a basis for only a subset of F make a suitable basis for all of the functions/signals we care about? Application: I've seen some of what DFT/FFTs can do, and it's super cool. I'm excited to see how we can apply this to audio and visual conversions!
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