Desvl

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 Important Posts of This Blog 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 Implicit Mapping Theorem of Complex Variables and Riemann Surfaces 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 The ring of real trigonometric polynomials 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)Rings of Fractions and Localisation The Grothendienck Group

2020

A Continuous Function Sending L^p Functions to L^1 A Continuous Functional Sending L^p Functions to L^1 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)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

2019

并不新颖的观点：不要追求生产力、效率了高等数学入门：上下确界及其极限形式调和级数发散的若干证明洛必达法则的几种不同的证明优美的 Fourier 级数（二）: 有界差分下的收敛(Jordan 判别法)优美的 Fourier 级数（一）: 绝对不只是求表达式的问题压缩定理和其应用