Axiomatized Set Theory: ZFC Axioms
Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC) is a widely accepted formal system for set theory. It consists of nine axioms.
Manifolds and Local Structures
A local-to-global guide to submanifolds, embeddings, regular values, manifolds with boundary, and smooth partitions of unity.
Discrete Memoryless Channels
Notes on discrete memoryless channels, channel capacity, coding theorems, and general channel models.
Source Coding and Lempel-Ziv
Notes on source coding through typicality, polynomial-time coding, variable-rate compression, and Lempel-Ziv coding.
I-Measure and Information Diagrams
Notes on the I-measure, information diagrams, lattices of random variables, and entropy space.
Typicality and the Asymptotic Equipartition Property
Notes on Typicality
Detection and KL Divergence
Notes on Neyman-Pearson detection, error exponents, Bayesian hypothesis testing, and estimation.
0-Error Data Compression
Notes on 0-Error Data Compression
Shannon Information Measures
Notes on entropy, relative entropy, mutual information, information inequalities, and their extensions to continuous random variables.
MathJax Update and Fix
Somehow this site’s mathjax suddenly stopped working. This post is to test that.
李群和李群的李代数
My understanding of Lie-group and its Lie-algebra. The statement “Lie-algebra is approximation of Lie-group” is inaccurate since they essentially live in different spaces. This post is not finished. Check posts under Lie Group and/or Lie Algebra where I rewrote and added more aspects of Lie group and Lie algebra.