This course covers the concept of discrete convolutions, exploring their applications in probability, image processing, and Fast Fourier Transforms (FFTs). The learning outcomes include understanding where convolutions are used, adding random variables, implementing moving averages, performing image processing, measuring runtime, polynomial multiplication, and accelerating processes with FFTs. The course employs a tutorial teaching method through video lectures. It is intended for individuals interested in mathematics, computer science, data science, or anyone seeking to deepen their understanding of convolutions and their practical implications.
Overview
Syllabus
Another small correction at . I describe ON^2 as meaning "the number of operations needed scales with N^2". However, this is technically what ThetaN^2 would mean. ON^2 would mean that the number of operations needed is at most constant times N^2, in particular, it includes algorithms whose runtimes don't actually have any N^2 term, but which are bounded by it. The distinction doesn't matter in this case, since there is an explicit N^2 term.
- Where do convolutions show up?
- Add two random variables
- A simple example
- Moving averages
- Image processing
- Measuring runtime
- Polynomial multiplication
- Speeding up with FFTs
- Concluding thoughts
Taught by
3Blue1Brown
