This lecture doesn't have a lot of interaction, probably due to its mathematical content. Make sure to ask for questions if the students seem lost at any point.
Here the instructor summarizes what will be done in this lecture:
finishing inversions, integer multiplication, and some background for the FFT
(FFT is short for Fast Fourier Transform). Next lecture will be the main
discussion of FFT.
The instructor says that the point of the last few lectures has been understanding the intuition behind Divide and Conquer techniques by looking at several Divide and Conquer algorithms, with the goal that students can apply this intuition to new Divide and Conquer algorithms in the future.
Review of inversions. Since you will have just watched the previous lecture this should be very clear.
Review of inversions.
Here we see that the combine step is the most difficult part of this algorithm, and start to think about how we would perform the combine step.
We've seen that we need to make the combine step easier, so we sort the sublists; this sorting is the key to merging the subresults efficiently.
This slide is skipped in the lecture; this is an activity for the BUAA class.
The instructor summarizes the inversion counting algorithm.
At 10:52 the instructor asks the students if they have any questions; stop the video here.
This is an activity slide.
This is an activity slide. Show the explanation of the algorithm up to about 14:15 before stopping for the activity.
At 19:10 the instructor stops to ask for questions. You should also stop the video here.
The instructor explains that today he will discuss the background and motivation for the FFT, and in the next lecture he will introduce the algorithm. He also says that while the students are likely to forget the details of the FFT, it is more important for them to remember higher-level things, like what the FFT computes and what it is used for.
At 20:20 the instructor says "going from an nlog(n) algorithm to an n^2 algorithm." A student points this out and he corrects himself: "going from a n^2 algorithm to an nlog(n) algorithm."
At 23:20 the instructor writes several lowercase w's but refers to them as "omega"; this is the lowercase Greek letter omega. There is a lot of notation in the next few slides; this might cause confusion if some of the notation is unfamiliar.
On the 3rd bullet point, the capital "A" should be a lowercase "a".
"Unity" here just means "1".
beta should be sqrt(2)/2, not sqrt(2).
At 29:29 the instructor asks for the 16th roots of unity. Stop here to let the students answer.
At 31:34, the instructor asks, "How do we verify it's an nth root of unity?" Stop here to let the students answer.
At 34:16, the istructor asks, "What is the sum of the geometric series?" It might be good to stop here and guide a student discussion toward the value of the sum (the instructor asks for the value of the sum at 34:50).
We discuss the convolution here because it's what we'll use the FFT for and it's why the FFT is useful.
At 39:00, a student points out a small notational error on the slide. It's not important.
A*W is the notation for "the convolution of A and W".
