# Notes on Graph Theory (Updating...)

PDF (without proof) PDF 1 Basic counting: sets and tuples This section lacks a formal definition of the cardinality of a set, offering instead an intuitive explanation of the concept (which re...

Zhiyu Wang

PDF (without proof) PDF 1 Basic counting: sets and tuples This section lacks a formal definition of the cardinality of a set, offering instead an intuitive explanation of the concept (which re...

Definition (Eigenvalue, eigenvector) Let $A$ be an $n \times n$ matrix over $\mathbb{F}$. Then $\lambda \in \mathbb{F}$ is an eigenvalue of $A$ if there exists a non-zero vector $\mathbf{v} \in ...

After installing Arch Linux and fiddling with it, I encountered an issue where the Bluetooth option was visible but I was unable to activate it. Bluethooth button fails to function Check Bluetoo...

1. Introduction 2. Foundations 2.1 A_functions exact if your goal is ⊢ A and you have a term x : A, then exact x will close the goal sorry this tactic closes the...

Introduction Riesz’s representation theorem is a powerful result in functional analysis, particularly in the study of Hilbert spaces. It characterizes continuous linear functionals in terms of the...

Introduction In this post, we look at identities built from vector operators. These operators behave both as vectors and as differential operators, so that the usual rules of taking the derivative...

Basics Definition 0.1 (Chromatic number) The chromatic number of a graph $G$ is defined as [\chi(G) = \text{min}{k \geq 1 ~ ~ G \text{ is } k \text{-colourable}}.] R...

I recently leveled up my Mac terminal for convenience and fun. Here is how I did it. Install Homebrew In your command line, type the following: /bin/bash -c "$(curl -fsSL https://raw.githubusercon...

Packages We first import necessary packages: numpy is the main package for scientific computing with Python. matplotlib is a library to plot graphs in Python. h5py is a Pythonic interface to...

As the days stretch on, my thoughts often wander back to the cherished moments spent at the Hicks Building at University of Sheffield, where everyone can unapologetically show the love of mathemati...