This is intended for storing my drafts of my works. It is messy and will never be organised or documented. Feel free to subscribe to it:

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Note: The note is written on the basis of my knowledge. Therefore, sometime I might assume the the reader has already be familiar with special knowledge. For example, I might add something from condensed matter physics to notes in topology. I might also be too tacit because I have already been familiar with other similar concepts. For example, I might be too tacit about homology group in topology because I have already learnt cohomology groups in Cech Cohomology.

That said, if there is really trouble in reading these notes, feel free to email me.

I am so sorry that this is becoming so unexpectedly messy that I sometimes cannot find useful information here. A clean up is in schedule. Before that take place, please use SEARCH to find anything.

Here in this folder, are notes that are considered finished and are not likely to be updated, unless to correct spelling, grammar, etc.

• Light Harvesting Course Note

    Notes taken when I was attending the course *An Introduction to 
    Light Harvesting in Bacteria and Plants*.
  

• Notes of Lectures on the Frontiers of Physics, a course designed for professors to introduce their own fields.

• Notes of Physical Challenges of Quantum Computation, the dissertation of professor MH. Wong. Although I did not finish it, I may not read it anymore.

1. Complex Geometry - index of ...

   This is intended for keeping a index of notation of the course Introduction to Algebraic Geometry (which actually teaches Complex Geometry) as well as its textbook Introduction to Complex Geometry.

   1.1. Complex Geometry - misc

    Here are some miscellaneous things related to the same book.
    For example, my homeworks and some related exercises.
   

2. draft.pdf

   This is a general purpose draft. It contains currently:

   • Problems in Bernevig’s Topological .... This is a draft for my solution to that.

   • Some notes about superconductors. Written when I am preparing for the Solid State Theory's final exam.

   • Why 0/0 is undefined? My opinion

   • Preface of BSCS. My notes about the preface of a book. It is very interesting.

   • Some notes on solving systems of ODE equations.

   • notes on Quantum Statistical Mechanics.

   • The Mathematical Theory of Communication

     This is Shannon's landmarking paper on Information Theory. I read only a part of it to try to grasp the connotation of the trendy phrase information entropy.

   • Quantum Field Theory

     Notes for the book The Quantum Theory of Fields by Weinberg.

3. Useful (anit)Commutative relationships

4. feynman diagram (in dormant state, perhaps I will not update it).

   Notes for studying Feynman diagram. Currently stopped at defining Green function.

5. Note of Sheaf Theory (in dormant state, perhaps I will not update it).

   Notes taken to understand sheaf cohomology. (Scattered and incomplete.)

6. Algebra (in dormant state, perhaps I will not update it).

   • Noetherian Ring

     Introduces Noetherian module and Noetherian ring. From S.Lang's Algebra.

7. Quantum Field Theory in a Nutshell (inside QFT) (in dormant state, perhaps I will not update it).

   Notes for the book Quantum Field Theory in a Nutshell by A. Zee.

8. Quantum Field Theory in Condensed Matter Physics (inside QFT) by Nagaosa

9. Quantum Information (in dormant state, perhaps I will not update it).

   Here is the notes of Preskill's Quantum Computation course in Caltech. It is very ineresting. I focus on the part of quantum Information theory.

10. Group Theory in Physics (in dormant state, perhaps I will not update it).

    Here is the course taught by Professor Fei Ye, about group theory's application in physics. This course, although is targeted at graduate level, is quite elemetary from a mathematical perspective. However, my notes will contain the occasional sparking intuition that I got from Fei Ye's lecture, which is certainly not contained in the textbook.

11. Programs

    Here store various small programs/scripts for expedate calculation using computer's power.

12. Notes for Advanced Quantum Mechanics

    The notes for Advanced Quantum Mechanics, tought by Professor MH. Yong. Also due to the level of graduates here, the class is targeted not at too high a level.

13. Notes about Bernevig's book

    Topological Insulators and Superconductors, by Bernevig.

    • Chapter 2 Berry Phase

    • Notes about TR Symmetry (Chapter 4)

      This is notes I wrote when I read the third chapter of Bernevig's book Introduction to Topological Insulator and Superconductors. It also contains a summary of result about spins (or in general, Rotations in quantum mechanics), which is quite useful for studying other quantum mechanical properties.

14. General Physics Formula

    This file stems from my preparation notes for GRE physics test. It contains several useful physics formulae, with links to their sources.

15. Latex Packages

    The packages I write to speed out latex writting.

16. Gravity and Entanglement [dead]

    Notes about a lecture. However, this note may not be updated in the future.

17. Lattice Green function [dead]

    Notes for calculating lattice Green function. However, this not is unlikely to be updated in the future.

18. Notes of Connecting Few-body and Many-body Pictures of Fractional Quantum Hall Physics [dead]

    Notes about a conference named just like above. The detailed link can be found inside the note.

19. Notes of Various papers.

20. Useful (anti)Commutative Relationships

21. UltiSnips

    Snippets to speed up typing, using UltiSnips plugin for Vim.

22. Fun facts

    Interesting facts that may or maynot be useful. About physics and mathematics.

23. Basic Topology Notes

    From definition of topological space, to simplicial homology, use Armstrong's text.

24. Condensed Matter Field Theory note

    The textbook Condensed Matter Field Theory by Atland and B.Simons. A really good one.

25. Conference OR Schools

26. Dirac Hamiltonian

27. Short Notes

    Some short notes about premature ideas.

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