Complex Numbers from A to ... Z (Titu Andreescu, Dorin Andri

Complex Number from A to Z

Publicly available lecture notes from universities mathematics classes

https://www.reddit.com/r/math/comments/9s5548/what_are_your_favorite_publicly_available_notes/

http://math.stanford.edu/~vakil/216blog/   

https://www.reddit.com/r/math/comments/4nbqag/lets_make_a_collection_of_lecture_notes/

https://dec41.user.srcf.net/notes/

https://www.reddit.com/r/learnmath/comments/98wwfv/undergraduate_lecture_notes_university_of/

https://www.reddit.com/r/math/comments/csgigv/collection_of_lecture_notes_on_mathematics_and/

https://www.maths.cam.ac.uk/undergrad/studentreps/tripos-specific-resources 

https://www.maths.cam.ac.uk/notes-web

Euler Disc and its mathematics

As described in wikipedia:

https://en.wikipedia.org/wiki/Euler%27s_Disk

Here are the videos where the Euler discs phenomenon is highlighted and explained:

https://youtu.be/f07KzjnL2eE?t=2351

https://youtu.be/eYBLAkJqMF0?t=2777

https://interestingengineering.com/math-behind-spinning-coin

https://www.youtube.com/watch?v=55gJgCoDld4  (interesting study of the Euler Disc motion from an engineering point of view).

https://www.real-world-physics-problems.com/eulers-disk.html   (here the mathematics is worked out in details - and quite easy to understand with undergraduate Physics as background)

https://www.techly.com.au/2015/09/28/eulers-disk-amazing-plastic-disk-will-melt-brain-hear/

https://www.youtube.com/watch?v=XXcWQWO-uHg

http://eulersdisk.com/pubs.html

https://research-repository.uwa.edu.au/en/publications/eulers-disk-examples-used-in-engineering-and-applied-mathematics-

https://www.nytimes.com/2000/04/25/science/simple-spinning-toy-poses-a-mathematical-challenge.html

https://aapt.scitation.org/doi/10.1119/1.1501117

https://pdfs.semanticscholar.org/cbd5/1d985ca03a177d9ca8c9bc4ccfb3d6b5bebe.pdf

http://www.maths.uwa.edu.au/~keady/papers.html

https://iopscience.iop.org/article/10.1088/1361-6404/aaaac9/meta   

https://physicslearning2.colorado.edu/QOTWSite/services/demos/demosd4/productinfo_d4-27.pdf 

https://arxiv.org/pdf/1706.10205.pdf

Mathematical Optimal Control Theory

https://math.berkeley.edu/~evans/control.course.pdf

https://courses.cs.washington.edu/courses/cse528/09sp/optimality_chapter.pdf

Bellman Optimality Principle:

Markov property of stochastic processes:

Optimal Value Function:

Computing the optimal action:

Bellman Equations:

https://www.youtube.com/watch?v=nC9NmNLVBCg 

https://www.youtube.com/watch?v=1wsAG4F2H0g 

https://www.youtube.com/watch?v=qlqzzNbqh0U 

https://www.youtube.com/watch?v=fCAkTKNkm0g 

https://www.youtube.com/watch?v=26sP4QIXgVA

https://www.youtube.com/watch?v=0CWkV2TMO6U 

 https://www.youtube.com/watch?v=Btups9v-KFo

http://liberzon.csl.illinois.edu/teaching/cvoc/cvoc.html

https://www.seas.upenn.edu/~ese680/archives/ese680-fall2011/

Exploring about Mandelbrot Set

https://www.youtube.com/watch?v=FFftmWSzgmk

And trying out the GeoGebra software:

https://www.geogebra.org/m/BUVhcRSv  (these files are from Ben)

To see the sequence of square operation and its path:

Construction of rotating ellipse in a plane

https://gist.github.com/tthtlc/ffdbc42cc06196561f828e96e7187aae

Constructions of various rotating hypocycloids

https://gist.github.com/tthtlc/5dbc7c931b0789036e70f819b53c193f