Learning Notes

Abstract Algebra (2022 Fall)

These Chinese notes were taken when I attended the Tsinghua course lectured by Prof. Minxian Zhu in 2022 Fall.

• Group theory
• Ring theory
• Field theory

Measures and Integral (2023 Spring)

These were solutions to Stein’s book on Real Analysis written by me when I attended the Tsinghua course lectured by Prof. Yong Lin in 2023 Spring.

• Chp2. Integration Theory
• Chp3. Differentiation and Integration
• Chp4. Hilbert Space
• Chp6. Abstract Measure and Integration Theory
• final exam

Selected Topics in Computational Quantum Physics (2023 Fall)

Course description, Notes and Codes

• see this page

Numerical Analysis (2023 Fall)

Notes and Codes

• see this page

Methods of Discrete Mathematics (2024 Spring)

This course contains two parts: graph theory and combinatorics. These notes were taken in Chinese.

• 1. Introductory Concepts in Graph Theory

• 2. Trees and Spanning Trees

• 3. Euler Problems and Hamiltonian Problems

• 4. Matchings

• 5. Planarity

• 6. Colorings

• 7. Introduction to Extremal Graph Theory

• 8. Introduction to Spectral Graph Theory

• 9. Binomial Coefficients, The Principle of Inclusion and Exclusion, The Pigeonhole Principle and Ramsey Theory

• 10. Recurrence, Generating Functions and Inversion Formulae

• 11. Pólya’s Theory of Counting

Quantum Inequalities (2025 Spring)

These notes were taken when I attended the Tsinghua course lectured by Prof. Jinsong Wu (BIMSA) in 2025 Spring.

Other Reading Topics

• Linear response theory and density functional perturbation theory

• Kreiss matrix theorem

• Log-Sobolev inequalities for quantum Markovian semigroups on finite dimensional spaces, see also Eric Carlen’s notes

• Conditional expectations onto *-subalgebras and convexity inequalities

• Convergence of Fourier series

法华山在会稽南四十里。晋义熙十三年，僧昙翼栖此，诵《法华经》，颇有灵感。晋贤见，乃置寺，因以为名。梁天鉴中，昭明太子送金缕袈裟，红银缾、瑠璃钵各一副至会昌寺，废大中复兴，改寺额曰“天衣山”。有十峯双涧，崷崪澄澈，颇快登览，古今多有纪咏云。——《会稽掇英总集》

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