Fourier Series and their Convergence (Proof!) (Theory of Machine Learning)

[@sophiaxiao5071]

I’m interested in this topic. What perfect timing! My real analysis class has covered a little bit of Fourier analysis at an undergraduate level, but only up to Fourier series and the completeness of a few families of functions. Interestingly enough, my summer research project will combine concepts from harmonic analysis and machine learning.

[@pabloagogo1]

Isn't the definition at the beginning of the function where when x=y we get 1, and when x!=y we get 0, is this not a definition of the Kronecker Delta? Just curious.

[@JoelRosenfeld]

Yep! When you take inner products between orthonormal vectors you get the kronecker delta function

[@user-qp2ps1bk3b]

very nice video! Thank you!

[@JoelRosenfeld]

I’m glad you like it!

[@positivobro8544]

Hello, This is one of the issues I have been stuck with for years and don't know how to continue because I don't have a math background so I don't even know what exactly my problem is called. I want to see how Fourier TRANSFORM can be seen as a basis transformation in Hilbert spaces. However with the same analogy you have uncountably many basis vectors which is a small scale mindfuck. İs this a legit way to approach Fourier transforms? Do uncountably many dimensional function spaces exist and is this one of them?

[@alexander5597]

Math is much more interesting and exciting than ML.

[@JoelRosenfeld]

Yeah, this is a whole series on Hilbert Spaces and Functional Analysis. The ML applications are to help relevancy and marketing, and ML engineers often want to know these things anyway. You can check out the other videos on my channel if you are interested. The control theory playlist has a whole series on distribution theory and the Laplace transform. I have a series dedicated to undergraduate analysis, etc. I’m a professor of mathematics. Analysis is my thing. What bothers you in particular about machine learning?

[@mathjitsuteacher]

Amazing video. I really enjoyed how you managed to present all the crucial stuff without getting lost in the technicalities that would make you waste time. I have a small youtube math channel called mathjitsu. I would love to get your feedback on some of my videos from my most recent playlist whose link is below. kzbin.info/aero/PL16TOne3TP9H2n30jvBGf-LjxUEwIB_Jd&si=XsmrIBefvTyhmR-l This playlist is in Portuguese and I am solving Real Analysis problems from one of Brazil's most famous math writers. I suppose the language is not a big deal since the math is not that hard to follow.

[@JoelRosenfeld]

I’m happy you enjoyed my content! I think it’s great that you are producing content for a Portuguese audience. I think if you want to improve your videos, eliminate the slides. It’s not really very engaging, and I’d get pretty bored looking at a single slide for that long. Cut to you talking to the camera. Have elements where you are at the board. Look for physical examples and also coding examples. Engage the viewers on multiple levels.

[@mathjitsuteacher]

​@@JoelRosenfeldI will try producing less boring videos in the future. I am a standard boring mathematician so I don't think I will ever be able to engage people like Ted Shiffrin or Gilbert Strang. Anyway the idea of this playlist is to provide step by step solutions and teach the audience how to write Mathematics in a rigorous way. Thanks for the feedback.

[@JoelRosenfeld]

@@mathjitsuteacher you can’t be too boring, since you also do Brazilian jujitsu lol There is an art to making engaging content on KZbin and it just takes practice. Check out the channel Film Booth to get an idea of some of the things you can do.