Desvl

2021

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 Localization The Grothendienck Group

2020

Study Vector Bundle in a Relatively Harder Way - Tangent Bundle A continuous functional 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

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