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01 Mar 2023 Axiomatized Set Theory: ZFC Axioms  Archived

Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC) is a widely accepted formal system for set theory. It consists of nine axioms.

01 Feb 2023 Manifolds and Local Structures  Completed

A local-to-global guide to submanifolds, embeddings, regular values, manifolds with boundary, and smooth partitions of unity.

06 Dec 2022 Discrete Memoryless Channels  Archived

Notes on discrete memoryless channels, channel capacity, coding theorems, and general channel models.

22 Nov 2022 Source Coding and Lempel-Ziv  Archived

Notes on source coding through typicality, polynomial-time coding, variable-rate compression, and Lempel-Ziv coding.

08 Nov 2022 I-Measure and Information Diagrams  Archived

Notes on the I-measure, information diagrams, lattices of random variables, and entropy space.

25 Oct 2022 Typicality and the Asymptotic Equipartition Property  Archived

Notes on Typicality

11 Oct 2022 Detection and KL Divergence  Archived

Notes on Neyman-Pearson detection, error exponents, Bayesian hypothesis testing, and estimation.

12 Sep 2022 0-Error Data Compression  Archived

Notes on 0-Error Data Compression

06 Sep 2022 Shannon Information Measures  Archived

Notes on entropy, relative entropy, mutual information, information inequalities, and their extensions to continuous random variables.

30 Oct 2020 MathJax Update and Fix  Completed

Somehow this site’s mathjax suddenly stopped working. This post is to test that.

06 Jun 2018 李群和李群的李代数  Archived

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.