Xiaoshuo Lin
School of Mathematical Sciences
University of Science and Technology of China
Hefei 230026, Anhui Province, P. R. China
About Me
Education
Sep 2022 – Jun 2026 (Expected): Undergraduate, Hua Loo-Keng Talent Program in Mathematics, School of Mathematical Sciences, University of Science and Technology of China.
Sep 2019 – Jun 2022: Senior High School, The Affiliated High School of South China Normal University.
Research Interests
Geometric Analysis
Algebraic Topology
Teaching Assistant
Course Resources
All works created by me are licensed under CC BY-NC-SA 4.0
Mathematical Analysis
Real Analysis
Honors Real Analysis Homework Assignments PDF
Complex Analysis
Honors Complex Analysis Homework Assignments PDF
Errata to Complex Analysis by Stein and Shakarchi PDF
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
Costa’s Minimal Surface — Asymptotics of the Ends and Symmetry of the Surface Slides
Functional Analysis
Differential Equations
Notes (on ODEs) and Homework Assignments PDF
Handwritten Notes on PDEs PDF
Errata to Partial Differential Equations by Lawrence C. Evans PDF
Linear Algebra
Abstract Algebra
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
“Commutative Algebra” by Richard E. Borcherds Videos
Homological Algebra
“Introduction to Homological Algebra” by Richard E. Borcherds Videos
Lie Groups and Lie Algebras
Combinatorics
“Extremal Combinatorics” by Jonathan Noel Videos
Probability Theory
Notes and Homework Assignments Part 1 Part 2 with Guide on Exercises
Stochastic Processes
Applied Stochastic Processes (Spring 2024)
Selected Solutions to Stochastic Processes by Sheldon M. Ross PDF
Handwritten notes on Chapters 4–8 PDF
Foundations of Geometry
Lecture Notes on Foundations of Geometry PDF
General Topology
Honors Topology Homework Assignments PDF
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
Honors Differential Geometry Homework Assignments PDF
Hints and Extensions to Chapters 1–5 by Rui Xiong PDF
Smooth Manifolds
Differentiable Manifolds (MATH5003P) Homework Assignments PDF
Corrections to Lee’s Introduction to Smooth Manifolds PDF
“Manifolds and Geometry” by Jiaqiang Mei Videos
Riemannian Geometry
Riemannian Geometry Homework Assignments PDF
Corrections to Lee’s Introduction to Riemannian Manifolds PDF
Riemannian Geometry @PKU Videos
Algebraic Topology
Algebraic Topology Homework Assignments PDF
Videos available online Seminar NTU NCTS Nankai Andrews Univ.
Characteristic Classes
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Characteristic Classes by J. W. Milnor and J. D. Stasheff PDF (adapted from the original LaTeX project by the TeXromancers)
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
“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
Asymptotics and Numerical Approximation of the Riemann \(\zeta\) Function Slides
Scientific Programming with Python
A Python Project for Random String Plucking and Overtone Generation PDF
General Physics
- Short notes Mechanics Thermotics Electromagnetism 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