Xiaoshuo Lin

Undergraduate student in USTC School of Mathematical Sciences, University of Science and Technology of China Hefei, Anhui Province, P.R.China E-mail:

About Me

2022.9-Present: Undergraduate, in the Hua Loo-Keng Talent Program in Mathematics, School of Mathematical Sciences, University of Science and Technology of China.
2019.9-2022.6: Senior High School, The Affiliated High School of South China Normal University.

Lecture Materials

Some course materials that may be helpful :)

Mathematical Analysis 数学分析

• Notes [pdf]

• Mathematical Analysis (A3) Homework Assignments [pdf]

Real Analysis 实分析

• Real Analysis (Honor) Homework Assignments [pdf]

• Real Analysis by Terence Tao @UCLA

• Real Analysis 2023 Spring

Complex Analysis 复分析

• Lecture Notes on Complex Analysis (Honor) [pdf]

• Complex Analysis (Honor) Homework Assignments + Solutions to Stein & Shakarchi's Complex Analysis [pdf]

  Unofficial Errata for the Book (Chapters 6, 7, 9, 10) [pdf]

• Complex Mapping Visualizer [1] [2]

• A second course in complex analysis based on Stein & Shakarchi's book, Chapters 6~10 @CUHK

• A Beautiful Group, SL₂(ℤ)

Special Functions 特殊函数

• NIST Digital Library of Mathematical Functions

• Some notes on several special functions by Michael Taylor

• Costa's Minimal Surface - Asymptotics of the Ends and Symmetry of the Surface [pdf]

Functional Analysis 泛函分析

• Functional Analysis @PKU

Linear Algebra 线性代数

• Lecture Notes on Linear Algebra [pdf]

• Notes and Homework Assignments[pdf]

Modern Algebra 近世代数

• Notes and Homework Assignments [pdf]

• Group Names

• Group Explorer

• Number of Small Groups

• Abstract Algebra @BSU

• Solutions to exercises from Abstract Algebra by Dummit & Foote

Commutative Algebra 交换代数

• Commutative Algebra by Richard E. Borcherds

• Class Notes on Commutative Algebra @RPTU

Probability Theory 概率论

• Notes and Homework Assignments [pdf]

• Guide on exercises [pdf]

• Extended Lectures in Probability Homework Assignments [pdf]

• Univariate Distribution Relationships

• Probability @PKU

Applied Stochastic Processes 实用随机过程

• Slides -- 2024 Spring

  1. Preliminaries [pdf]

  2. The Poisson Process [pdf]

  3. Renewal Theory [pdf]
  4. Markov Chains [pdf]
  5. Continuous-Time Markov Chains [pdf]
  6. Martingales [pdf]
  7. Random Walks [pdf]
  8. Brownian Motion and Other Markov Processes [pdf]

• Selected Solutions to Sheldon M. Ross's Stochastic Processes [pdf]

• Reference notes for Chapters 4~8 [pdf]

• Homework with Hints and Supplements @Columbia

• Applied Probability and Stochastic Modeling @UMich

• Applied Stochastic Processes @PKU

Introduction to Differential Equations 微分方程引论

• Notes and Homework Assignments [pdf]

• 2023 Fall Course Homepage

• More Lyapunov Theory @Stanford

• Errata in Differential Equations, Dynamical Systems, and an Introduction to Chaos

Foundations of Geometry 几何学基础

• Lecture Notes on Foundations of Geometry [pdf]

Differential Geometry 微分几何

• Differential Geometry (Honor) Homework Assignments [pdf]

• Chapter 1~5 with Hints and Supplements [pdf]

• Reference for Global Differential Geometry

• 2023 Fall Differential Geometry (H) course video

General Topology 拓扑学

• Topology (Honor) [2020 Spring] [2022 Spring]

• Corrections to Introduction to Topological Manifolds [GTM 202]

• Math 544 Homework Assignments by John M. Lee

• π-Base, a community database of topological counterexamples

• Dan Ma's Topology Blog, expository articles in general topology

Algebraic Topology 代数拓扑

• Algebraic Topology @Andrews University

• Algebraic Topology by Roman Sauer

• Algebraic Topology (H)

Differentiable Manifolds 微分流形

• Corrections to Introduction to Smooth Manifolds [GTM 218]

• Differentiable Manifolds [2023 Fall] [2024 Fall, Course Homepage]

• Manifolds and Geometry by Jiaqiang Mei

Algebraic Geometry 代数几何

• Algebraic Geometry @Berkeley [I: Varieties] [II: Schemes] [Extra Topics]

• Algebraic Curves @BIMSA

• Class Notes on Plane Algebraic Curves @RPTU

• Class Notes on Algebraic Geometry @RPTU

• The Stacks project: an open source textbook and reference work on algebraic geometry

• The Rising Sea: Foundations of Algebraic Geometry Notes

Freshman Seminar “科学与社会”研讨课

• Asymptotics and Numerical Approximation of the Riemann Zeta Function [pdf]

Fundamentals of Scientific Programming with Python 科学计算基础

• My project [pdf]

Mechanics 力学

• Reference notes [pdf]

Thermotics 热学

• Reference notes [pdf]

Optics 光学

• Reference notes [pdf]

Atomic Physics 原子物理

• Reference notes [pdf]

Useful Links

@USTC

• USTC WebVPN

• 中国科学技术大学综合教务系统

• 中国科学技术大学教务处

• 中国科学技术大学研究生学期课程表查询

• 中国科学技术大学几何与物理研究中心

• 中国科学技术大学中法数学中心

• 中国科学技术大学国际合作与交流部暨港澳台事务办公室

• 中国科大全球化学习平台

• USTC邮件系统

• 瀚海教学网

• 睿客网

• USTC评课社区

• USTC学习资料

• USTC飞跃网站

@Maths

• Mathematics Stack Exchange

• MathOverflow

• Approach Zero, a math-aware search engine

• Math Solves Everything

• Library Genesis (.is) (.li)

• Wikipedia

• Banana Space

• Wolfram MathWorld

• arXiv

• Mathematical Communication @BIMSA

• Curriculum Guide to Majors in the Mathematical Sciences

• An Infinitely Large Napkin

• PKUSMS-UndergradGuide

• The Legacy of FDUer

• Sequence Machine

• Discrete Differential Geometry @CMU

• Computer Graphics @CMU

• Functional Analysis @IMPA

• Riemannian Geometry @PKU

@LaTeX

• Overleaf - Online LaTeX Editor

• TeX Stack Exchange

• TeX to Unicode

• Create LaTeX Tables

• Figure out LaTeX commands for symbols by drawing the symbol here

• TikZiT

• The TeXromancers - a group that TeX's up old book and modernizes notation in them

@English

• Corpus of Contemporary American English

• The Free Dictionary

• TED

@Physics

• The Feynman Lectures on Physics

• Electromagnetism 1

• Electromagnetism 2

Useful Tools

• ChatGPT

• AI: Talk to Claude

• GPTZero: AI Detection

• Documents Transfer

• Screen Mirroring App [Receiver] [Sender]

• DjVu to PDF

• Bibliography Generator

• Uncertainty Calculator

• Toolight

• Code in Word

Others' Homepages

• 王作勤

• 陈小伍

• 刘世平

• 梁永祺

• 刘利刚

• 李文威

• 肖梁

• 刘思齐

• 陈童

• 谢启鸿

• 陳誼廷

• 王金龍

• 熊锐 [Blog] [GitHub Page]

• 李卫雨

• 孙天阳

• 任宣霏

• 郑滕飞

• John W. Milnor

• J.S. Milne

• John M. Lee

• Allen Hatcher

• Rick Durrett

• Richard E. Borcherds

• Michael Taylor

• Claudio Landim

• Matt Salomone

• Dexter Chua

• Sheldon Axler