Landscape [landscape]

These are my mathematical writings.

JK 也能聽懂的理論物理 [theo]

這些筆記源於我早些時候不成熟的思考,雖然並不存在重大謬誤,但觀點顯得過於淺顯了。 –20.06.2025

我和相關專業不怎麼沾邊,但綜合受到的普通物理學教育,乘著突然興起的念頭,總想寫點什麼,特別是關於如何正確簡潔地給大眾介紹「深奧」的理論物理。

本文以下內容要求完全的初中物理知識和一定的數學基礎。

參考資料

  1. J. Schwichtenberg, Physics from Symmetry(2nd Edition), Springer, 2018.
  2. Prof Kenneth Young on A Special Lecture: Principle of Least Action, The Chinese University of Hong Kong.
  3. 林琦焜, 最小作用量原理, 數學傳播 35卷1期, 2009.
  4. Ghirardi, Giancarlo and Angelo Bassi, Collapse Theories, The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.)
  5. J.S. Bell, Against ‘Measurement’, reprinted in Speakable and Unspeakable in Quantum Mechanics, 2nd edn. (Cambridge University Press, Cambridge, 2004)
  6. J.N. Shutt, Determinism, locality, and meta-time, 2008
  7. T. Norsen, Foundations of Quantum Mechanics, (Springer, 2017)
  8. J. Baez, Getting to the Bottom of Noethers Theorem, 2018.
  9. D. Stretch, Emmy Noether: Against the odds, 2000.

Reinforcement learning for finding counterexamples in graph theory [rl4fc]

This is a report for HEGL Praktikum in SoSe 2023. This is a multi-author article, I wrote it with my groupmates and post it here now as a reference.

Exercise session of differential geometry 1 [diffgeo]

This page is reserved for the course “Grundlagen der Geometrie und Topologie” taught in SS2025 in Heidelberg. I will upload my notes for the exercise sessions here. All these notes are not official and written by my own. They should only be considered as the supplementary material for the preparation of exams.

1. Week 0: Point-set topology [diffgeo-w0]

In the 0th week we have reviewed some concepts of basic point-set topology, especially the notion of product topology and compactness.

2. Week 1: Topological and smooth manifolds [diffgeo-w1]

In the 1st week we have seen more examples of manifolds, talked about the orientability, filled the gap of the rank theorem in the lecture and studied the smooth group actions on manifolds.

3. Week 2 [diffgeo-w2]

Cancelled due to public holidays.

4. Week 3: Tangent spaces and vector bundles [diffgeo-w3]

This week is mainly about an important construction in differential geometry: the vector bundles. A special case is the tangent bundle of a smooth manifold, and we explained some geometric intuition of this object.

5. Week 4: Metrizable manifolds and distributions [diffgeo-w4]

We give a geometric intuition of how distributions look like and explore the two theorems of Frobenius. In the second part we prove that every manifold is metrizable, which is a very useful fact.

6. Week 5: Partition of unity [diffgeo-w5]

We prove the Tietze extension theorem and existence of partition of unity on manifolds, both using the beautiful Urysohn’s lemma. Partition of unity is indeed a highlight of differential geometry, to make many things on manifolds possible.

7. Week 6 + 7: Lie groups and Lie algebras [diffgeo-w6w7]

[In preparation] We cover some important examples of Lie groups and Lie algebras, together with some themes that is not covered in the lecture, including Lie group representations and Baker-Hausdorff formula.