Explore the Fast Fourier Transform (FFT) and complete the O(log n) time algorithm for multiplying integers in this graduate-level lecture from Carnegie Mellon University's "CS Theory Toolkit" course. Delve into the properties, step evaluation, and matrix vector multiplication of FFT. Learn about the sum of odd columns and gain insights from recommended resources such as Donald Knuth's "The Art of Computer Programming" and Brent and Zimmerman's "Modern Computer Arithmetic". Taught by Professor Ryan O'Donnell, this 26-minute video is part of a semester-long program covering math and CS fundamentals for research in theoretical computer science.