Recommended YouTube channels
The Bright Side of Mathematics
A brilliant series of mathematically rigorous lectures on various mathematical topics, made by Dr. Julian P. Grossmann In a calm voice and using minimalistic digital white board style presentations, he presents advanced mathematical topics in a pedagogical and systematic manner.
Example playlists:
Michael Penn
Michael Penn is Professor of Mathematics at Randolph College in Virginia.
From his channel, "Math videos covering a wide variety of topics from theory to application. Calculus, Differential Equations, Number Theory, Proofs, unique problems and much more."
His videos are entertaining and avoid all the flash and glam associated with modern YouTube content.
He also has a second channel, MathMajor, with more "serious" mathematics lecture video, and is associated with his teaching activities: https://www.youtube.com/@mathmajor
Example videos:
Gilbert Strang videos on linear algebra
This is a playlist of the eminent linear algebraist and teacher Gilbert Strang. From MIT Open Courseware.
Richard Borcherds
A British mathematician and Fields medalist who has a great reputation as a teacher, and a YouTube channel with many video lectures. According to the description it is "mostly mathematics lectures for graduate courses on algebraic geometry, commutative algebra, and group/rings fields."
Example videos:
Frederic Schuller
A YouTube channel sporting highly engaging and information rich lectures by the mathematical physicst Frederic Sculler at the University of Twente in the Netherlands.
Video examples:
- Logic of propositions and predicates, https://www.youtube.com/watch?v=V49i_LM8B0E&list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic&index=1
- Banach spaces https://www.youtube.com/watch?v=Px1Zd--fgic&list=PLPH7f_7ZlzxQVx5jRjbfRGEzWY_upS5K6&index=2
Graduate Mathematics
A channel with a broad variety of videos. I find the old documentaries to be really worthwhile.
Video examples: