## **How to Read This Directory Under this Holy Fucking Putain Repository?** To read this repository in markdown, use: 1. [Obsidian notebook](https://obsidian.md/), for best reading experience; 2. VS Code, for editing. <!--For Obsidian Publish --> $ \newcommand{\R}{\mathbb{R}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\N}{\mathbb{N}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\e}{\mathbf{\vec{e}}} \newcommand{\mse}[1]{\text{MSE}\left[#1\right]} \newcommand{\expect}[1]{\mathbb E\left[#1\right]} \newcommand{\cov}{\text{Cov}} \newcommand{\var}[1]{\text{Var}\left[#1\right]} \newcommand{\bias}[1]{\text{Bias}\left[#1\right]} \newcommand{\pr}{\text{Pr}} \newcommand{\argmin}[1]{\underset{#1}{\operatorname{argmin}}} \newcommand{\prox}{\operatorname{prox}} \newcommand{\pprox}[1]{\underset{#1}{\operatorname{prox}}} \newcommand{\env}{\operatorname{env}} \newcommand{\Limsup}[1]{\underset{#1}{\operatorname{Limsup}}} \newcommand{\Liminf}[1]{\underset{#1}{\operatorname{Liminf}}} \newcommand{\Lim}[1]{\underset{#1}{\operatorname{Lim}}} \newcommand{\dist}{\operatorname{dist}} $ ### **Environments and setting up Obsidian Notebook** A latex plugin for Obsidian Notebook is mandatory to display the mathematics in all markdown files properly. Latex preset (file: premeable.sty) for latex in Obsidian notebook is under the root directory of the Obsidian Vault. To use the latex preset in Obsidian, we use `Extended Mathjax`. For example: $\newcommand{\p}{\widehat{\mathbf{p}}}\p$ (please check the sources yeah). The `preamble.sty` should be under the root directory of this file. Here is a backup on the display of the full content of the preamble file: ```latex \newcommand{\R}{\mathbb{R}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\N}{\mathbb{N}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\e}{\mathbf{\vec{e}}} \newcommand{\mse}[1]{\text{MSE}\left[#1\right]} \newcommand{\expect}[1]{\mathbb E\left[#1\right]} \newcommand{\cov}{\text{Cov}} \newcommand{\var}[1]{\text{Var}\left[#1\right]} \newcommand{\bias}[1]{\text{Bias}\left[#1\right]} \newcommand{\pr}{\text{Pr}} \newcommand{\argmin}[1]{\underset{#1}{\operatorname{argmin}}} \newcommand{\prox}{\operatorname{prox}} \newcommand{\pprox}[1]{\underset{#1}{\operatorname{prox}}} \newcommand{\env}{\operatorname{env}} \newcommand{\Limsup}[1]{\underset{#1}{\operatorname{Limsup}}} \newcommand{\Liminf}[1]{\underset{#1}{\operatorname{Liminf}}} \newcommand{\Lim}[1]{\underset{#1}{\operatorname{Lim}}} \newcommand{\dist}{\operatorname{dist}} ``` If all things are correctly configured, the following symbols and operators should be clearly displayed. #### **Symbol Sets for fields, and vectors** $ \R, \Z, \N, \Q, \e $ #### **Operator Set, for statistics and analysis** $ \begin{aligned} & \mse ?, \expect?, \cov?, \var?, \bias ?, \pr, \argmin{x\in \R} \\ & \Limsup{x\rightarrow \bar x}, \Liminf{x\rightarrow \bar x}, \Lim{x\rightarrow \bar x} \\ & \prox_{f}, \env_{f}^\alpha \end{aligned} $ #### **Other Recommended Settings** 1. Enable strict line break in the editor settings inside the Obsidian Notebook. 2. Other useful plugins to display information fully in Obsidian notebook: - [highlightr](https://github.com/chetachiezikeuzor/Highlightr-Plugin) - [Automatic Table of Content](https://github.com/johansatge/obsidian-automatic-table-of-contents) --- ### **Katex Interpretor in VS-Code** To read the markdown filess in VS Code, use [Markdown all-in-one](https://marketplace.visualstudio.com/items?itemName=yzhang.markdown-all-in-one) for VS Code, then copy the following for the user settings (`settings.json` file) in VS Code to set up the Katex interpretor properly. ```json "markdown.extension.katex.macros": { // Katex Macros for Markdown all in one "\\e": "\\mathbf{\\vec{e}}", "\\Q": "\\mathbb{Q}", "\\R": "\\mathbb{R}", "\\Z": "\\mathbb{Z}", "\\uvec": "\\boldsymbol{\\hat{\\textbf{#1}}}", "\\expect": "\\mathbb E\\left[#1\\right]", "\\var": "\\operatorname{Var} \\left[#1\\right]", "\\pr": "\\mathbb P", "\\cov": "\\operatorname{Cov}", "\\bias": "\\operatorname{Bias}\\left[#1\\right]", "\\mse": "\\operatorname{MSE}\\left[#1\\right]", "\\argmin": "\\underset{#1}{\\operatorname{argmin}}", "\\prox": "\\operatorname{prox}", "\\pprox": "\\underset{#1}{\\operatorname{prox}}", "\\env": "\\operatorname{env}", "\\Limsup": "\\underset{#1}{\\operatorname{Limsup}}\\;", "\\Liminf": "\\underset{#1}{\\operatorname{Liminf}}\\;", "\\Lim": "\\underset{#1}{\\operatorname{Lim}}", "\\dist":"\\operatorname{dist}" }, ``` The latest VS-Code update points to the setting ID`markdown.extension.katex.macros` to configure this extension. --- ## **What is This God Damn Directory of This Bloody Repository About?** This directory contains markdown files. The markdown files contains mathematics. I am a absolute crazy person and I learned a lot of mathematics in my life disregarding whether it's useful or not. But in general we have the following topics covered, ordered in level of relevance: 1. My own musing on everything that is not directly related mathematics. 2. Some C++ related shit I learned when I was taking High Performance Computing in University of Washington as a graduate student. 3. Topics in Applied mathematics from the classes I took as a master student, covering dynamical system, numerical linear algebra, high performance computing. Learned in [University of Washington applied mathematics program](https://amath.washington.edu/master-science-applied-mathematics) for my Master Degree. 5. For contents in numerical Algebra, the content followed the interests of master my advisor: [Anne Greenbaum](https://fr.wikipedia.org/wiki/Anne_Greenbaum). 6. Classes I took from my PhD degree specializing in mathematical optimizations theory. Specifically, convex optimizations with nonsmooth structure and some basics of nonsmooth variational analysis in finite Euclidean Spaces. 7. Topics in Mathematical Optimizations, covering Nonsmooth Analysis, Convex Analysis, Operator Theories, Duality and Algorithms, and many more. Following prominent researchers: 1. [Heinz Bauschke](https://cmps-people.ok.ubc.ca/bauschke/) , 2. [Ralph Tyrrell Rockafellar](https://fr.wikipedia.org/wiki/Ralph_Tyrrell_Rockafellar), 3. [Amir Beck](https://english.tau.ac.il/profile/becka), 4. [Yurri Nesterov](https://fr.wikipedia.org/wiki/Yurii_Nesterov). My PhD advisor is a world class researcher in the field. But I would like to keep it a secret. If you wanna know who they are, trying reading some of the files under mathematical optimizations and functional analysis. To onboard, consider reading the following files: - [Network Flow Algorithms Central Hub](AMATH%20514%20Combinatorics%20Optimizations/Network%20Flow%20Algorithms%20Central%20Hub.md) - [NESTEROV ACCELERATION CENTRAL HUB](MATH%20602%20Nesterov%20Acceleration/NESTEROV%20ACCELERATION%20CENTRAL%20HUB.md) - [PROXIMAL GRADIENT CENTRAL HUB](AMATH%20516%20Numerical%20Optimizations/Proximal%20Methods/PROXIMAL%20GRADIENT%20CENTRAL%20HUB.md) - [Convex Functions Central Hub](AMATH%20516%20Numerical%20Optimizations/CVX%20Analysis/Convex%20Functions%20Central%20Hub.md) - [Operators for Optimizations CENTRAL HUB](AMATH%20516%20Numerical%20Optimizations/Operators%20Theory/Operators%20for%20Optimizations%20CENTRAL%20HUB.md) - [Variational Geometry CENTRAL HUB](AMATH%20516%20Numerical%20Optimizations/Variational%20Geometry/Variational%20Geometry%20CENTRAL%20HUB.md) If these look too hard, may be read: - [Topology of Metric Space](MATH%20601%20Functional%20Analysis,%20Measure%20Theory/Functional%20Spaces/Topology%20of%20Metric%20Space.md) - [Bozano Weierstrass](MATH%20000%20Math%20Essential/Analysis/Bozano%20Weierstrass.md) - [Real Analysis Basics](MATH%20000%20Math%20Essential/Analysis/Real%20Analysis%20Basics.md) - [Taylor Series](MATH%20000%20Math%20Essential/Calc/Taylor%20Series.md) If it's still too hard maybe just stop the math and read: [Not Really about Math](Not%20Really%20about%20Math.md) Finally, there are a lot of mistakes in the math notes I am sure, especially the proofs, it may contains errors. Please do your homework while reading them. If you fixed it for me please send an email to `[email protected]`. I will appreciate that very much. --- ## **What Purposes does This Repository Serve???** Learning. For myself, not for you the readers who find this repository. sorry. I don't like reading some mathematics, or learning about any subject, just to forget about it, or like, with a very bad analogy, letting it comes in from one end and spilled out from the other end without any digestion.