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Here are some tutorials that I made to teach myself (not error-free).
Follow the links below. They are mainly about:
Decision-making under uncertainty
Optimization
Theoretical Computer Science
Code Breaking Game
Use information theory to solve code breaking game and draw connection between decision tree and such game
https://drive.google.com/file/d/1Lpn1iwDvjAuTBFaihrwo-Igs2pOpHCPD/view?usp=drive_link
guessing_game.pdfGame Theory
Explain and derive proofs about Nash Equilibrium
https://drive.google.com/file/d/1f1PiA7Yl5nuYJgq6MWFZLGQtmLYtEjlZ/view?usp=drive_link
game_theory.pdfPrincipal Component Analysis (PCA)
Derive the PCA algorithm rigorously and explain kernel PCA.
https://drive.google.com/file/d/1ay_BEbY_5xkebZ9UQG17L4IpYBHGQ0_H/view?usp=drive_link
PCA.pdfFully Observable + Partially Observable Markov Decision Processes
Explain MDP and introduce POMDP.
https://drive.google.com/file/d/1ZCdNM13MNvbKhSun0_vh9CPbIyH6ezA2/view?usp=drive_link
MDP_POMDP (1).pdfThree Dimensional matching:
Explain the proof of NP-completeness of the three-dimensional matching problem. Fun fact: the proof that constructing an optimal binary decision tree is NP-complete is proved by reduction from three-dimensional matching.
https://drive.google.com/file/d/1BxU81Hr4DQaIAroHRu0PXPLwwmpdmll9/view?usp=drive_link
3_dim_matching.pdfSurfaces and Lagrange Multiplier
Notes I took during my real analysis class about proving the implicit function theorem and the Lagrange multiplier. I'm still working on giving more intuitive explanations for these theorems, e.g. try to derive them in lower dimensions or for simpler function classes.
https://drive.google.com/file/d/1AVxd6Q9RRtO5mL2m4OsXVWl_74djBRdc/view?usp=drive_link
lagrange_multiplier.pdfPage updated
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