Xiaoshuo Lin 
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Undergraduate at USTC |
About Me
2022.09–Present: Undergraduate, in the Hua Loo-Keng Talent Program in Mathematics, School of Mathematical Sciences, University of Science and Technology of China.
2019.09–2022.06: Senior High School, The Affiliated High School of South China Normal University.
My research interests lie in Geometry and Topology.
In Spring 2025, I am serving as the teaching assistant for MATH3702E: Complex Analysis (Honors).
Course Resources
Here are some course resources that might be helpful! :)
All works created by me are licensed under CC BY-NC-SA 4.0
Mathematical Analysis 数学分析
Real Analysis 实分析
Real Analysis (Honors) Homework Assignments PDF
Complex Analysis 复分析
Complex Analysis (Honors) Homework Assignments PDF
I am updating an Errata to Complex Analysis by Stein and Shakarchi.
Visualize complex mappings with Visualizer 1 and Visualizer 2
Move the mouse around to explore the beautiful group, \(\operatorname{SL}(2,\mathbb{Z})\)
Special Functions 特殊函数
Costa’s Minimal Surface — Asymptotics of the Ends and Symmetry of the Surface Slides
Functional Analysis 泛函分析
Introduction to Differential Equations 微分方程引论
Notes (on ODEs) and Homework Assignments PDF
Handwritten Notes on PDEs PDF
Errata to Partial Differential Equations by Lawrence C. Evans PDF
Linear Algebra 线性代数
Abstract Algebra 近世代数
Notes and Homework Assignments PDF
Visit Group Names, Group Explorer, and Number of Small Groups for an excursion among groups
Abstract Algebra @BSU Videos
Solutions to exercises from Abstract Algebra by Dummit and Foote
Commutative Algebra 交换代数
“Commutative Algebra” by Richard E. Borcherds Videos
Homological Algebra 同调代数
“Introduction to Homological Algebra” by Richard E. Borcherds Videos
Lie Groups and Lie Algebras 李群与李代数
Probability Theory 概率论
Notes and Homework Assignments Part 1 Part 2 with Guide on Exercises
Applied Stochastic Processes 实用随机过程
Slides (Spring 2024)
1. Preliminaries Slides
2. The Poisson Process Slides
3. Renewal Theory Slides
4. Markov Chains Slides
5. Continuous-Time Markov Chains Slides
6. Martingales Slides
7. Random Walks Slides
8. Brownian Motion and Other Markov Processes Slides
Selected Solutions to Stochastic Processes by Sheldon M. Ross PDF
Handwritten notes on Chapters 4–8 PDF
Foundations of Geometry 几何学基础
Lecture Notes on Foundations of Geometry PDF
General Topology 拓扑学
Corrections to Lee’s Introduction to Topological Manifolds PDF
\(\pi\)-Base — a community database of topological counterexamples
Dan Ma’s Topology Blog — expository articles in general topology
Differential Geometry 微分几何
Differential Geometry (Honors) Homework Assignments PDF
Hints and Extensions to Chapters 1–5 by Rui Xiong PDF
Differentiable Manifolds 微分流形
Differentiable Manifolds (MATH5003P) Homework Assignments PDF
Corrections to Lee’s Introduction to Smooth Manifolds PDF
- “Manifolds and Geometry” by Jiaqiang Mei Videos
Riemannian Geometry 黎曼几何
Algebraic Topology 代数拓扑
Algebraic Topology Homework Assignments PDF
Videos available online Seminar NTU NCTS Nankai Andrews Univ.
Characteristic Classes 示性类
Characteristic Classes by J. W. Milnor and J. D. Stasheff PDF
Vector Bundles and K-Theory by Allen Hatcher PDF
“Characteristic Classes” by Geometry Potsdam Videos
Fiber Bundles, Characteristic Classes, and Index Theorems @BIMSA
Algebraic Geometry 代数几何
“Algebraic Geometry” by Richard E. Borcherds I: Varieties II: Schemes Extra Topics
The Stacks project — an open source textbook and reference work on algebraic geometry
Freshman Seminar “科学与社会”研讨课
Asymptotics and Numerical Approximation of the Riemann \(\zeta\) Function Slides
Scientific Programming with Python 科学计算基础
A Python Project for Random String Plucking and Overtone Generation PDF
General Physics 普通物理
- Handwritten notes Mechanics Thermotics Optics Atomic Physics
Useful Links
USTC
Mathematics
Approach Zero — a math-aware search engine
LaTeX
Overleaf — Online LaTeX Editor
The TeXromancers — a group that TeX’s up old book and modernizes notation in them