Desvl's blog
2023
The Structure of SL_2(F_3) as a Semidirect Product
A Separable Extension Is Solvable by Radicals Iff It Is Solvable
Picard's Little Theorem and Twice-Punctured Plane
SL(2,R) As a Topological Space and Topological Group
Artin's Theorem of Induced Characters
Chinese Remainder Theorem in Several Scenarios of Ring Theory
Projective Representations of SO(3)
The Quadratic Reciprocity Law
Vague Convergence in Measure-theoretic Probability Theory - Equivalent Conditions
2022
The Pontryagin Dual group of Q_p
The Haar Measure on the Field of p-Adic Numbers
Every Regular Local Ring is Cohen-Macaulay
The abc Theorem of Polynomials
A Step-by-step of the Analytic Continuation of the Riemann Zeta Function
Properties of Cyclotomic Polynomials
Calculus on Fields - Heights of Polynomials, Mahler's Measure and Northcott's Theorem
Hensel's Lemma - A Fair Application of Newton's Method and 'Double Induction'
Irreducible Representations of GL_2(F_q)
Segre Embedding And Heights
The Calculus of Fields - Absolute Values
Irreducible Representations of SO(3) and the Laplacian
Study Irreducible Representations of SU(2) Using Fourier Series
The Fourier Transform of exp(-cx^2) and Its Convolution
A Detailed Proof of the Riemann Mapping Theorem
Examples in Galois Theory 3 - Polynomials of Prime Degree and Pairs of Nonreal Roots
Examples in Galois Theory 2 - Cubic Extensions
Examples in Galois Theory 1 - Complex Field is Algebraically Closed
The Group Algebra of A Finite Group and Maschke's Theorem
2021
The ring of trigonometric polynomials with complex scalars
The ring of real trigonometric polynomials
Characters in Analysis and Algebra
The Banach Algebra of Borel Measures on Euclidean Space
The concept of generalised functions (distributions) and derivatives
Curse of Knowledge
Elementary Properties of Cesàro Operator in L^2
Left Shift Semigroup and Its Infinitesimal Generator
Quasi-analytic Vectors and Hamburger Moment Problem (Operator Theory)
Quasi-analytic Classes
(Kind of) Missing Content in Your Linear Algebra Class (Still on Progress)
Dedekind Domain and Properties in an Elementary Approach
Several ways to prove Hardy's inequality
Tensor Product as a Universal Object (Category Theory & Module Theory)
Why Does a Vector Space Have a Basis (Module Theory)
Rings of Fractions and Localisation
The Grothendienck Group
2020
Study Vector Bundle in a Relatively Harder Way - Tangent Bundle
A Continuous Function Sending L^p Functions to L^1
Study Vector Bundle in a Relatively Harder Way - Definition
The Big Three Pt. 6 - Closed Graph Theorem with Applications
Partition of Unity on Different Manifolds (Part 1. Introduction)
Stirling公式的几种经典估计
A proof of the ordinary Gleason-Kahane-Żelazko theorem for complex functionals
The Big Three Pt. 5 - The Hahn-Banach Theorem (Dominated Extension)
A long exact sequence of cohomology groups (zig-zag and diagram-chasing)
The Fourier transform of sinx/x and (sinx/x)^2 and more
The Riesz-Markov-Kakutani Representation Theorem
The Big Three Pt. 4 - The Open Mapping Theorem (F-Space)
The completeness of the quotient space (topological vector space)
Introducing Riemann-Stieltjes Integral
Basic Facts of Semicontinuous Functions
An Introduction to Quotient Space
关于《第三次忍受》
The Big Three Pt. 3 - The Open Mapping Theorem (Banach Space)
Cauchy sequence in group theory
A Brief Introduction to Fréchet Derivative
An elementary introduction to profinite groups
线性ODE（四）——常系数高阶线性微分方程的普遍解法
A continuous function is 'mostly' nowhere differentiable
The Big Three Pt. 2 - The Banach-Steinhaus Theorem
The Big Three Pt. 1 - Baire Category Theorem Explained
Jordan标准形的求法——以一个四阶矩阵为例
矩阵Jordan标准形的原理
More properties of zeros of an entire function
Linear ODE but Quotient Spaces
Prove Picard's Existence and Uniqueness Theorem on Different Levels
线性ODE（三）——初探高阶线性方程
关于《有人弄乱了这束玫瑰花》
线性ODE（二）——用矩阵表示方程组
线性ODE（一）——线性方程的思想与一阶方程
高等数学入门——理解无穷小的阶（微积分的“科学计数法”）
The Lebesgue-Radon-Nikodym theorem and how von Neumann proved it
Counterexamples of Fubini's theorem
Fubini's theorem in Euclidean space (Understanding 'almost everywhere')
Topological properties of the zeros of a holomorphic function
准素分解与准素标准型
线性空间的循环分解
线性变换不变子空间的导子及其性质
线性空间的循环子空间与简单应用
抽象Lebesgue积分的构建