Local vs Global seems to be one of the most important philosophies behind math. People in some fields call it "compactness", others don't. In short, it says that the property of an object is related to the property of every smaller subobject.

In this post, I list some results I know, basically for personal notes. But there are way more theories related or inspired by this idea.

This post briefly proves why the rational points of an elliptic curve is a group. The proof idea comes from MATH 214B, but I tried to use classical language.

This posts briefly introduced what I learned on C++ 20 coroutine mechanism after I used it to imitate Python generator and ayncio. REPO

This posts discusses the relation between two's complement and 2-adic integer in math. I want to show what operations we can have if we ignore overflow.

George is a fantastic teacher with very attractive lectures. I think his secret sauces include the following:

• Look at everything from different views: Zoe (ζωή, big picture) versus Bios (βίος, details).
• Selectively focus on the most important techniques and examples, ignoring unnecessary points. Students can feel that they learned a lot without remembering too much boring concepts.
• Have his own methodologies on creative process. Students can experience those "Aha" times when following his introduction.

The trade-offs may be as follows: (very biased personal view, don't take it serious)

• (+) Attending lectures is always pleasant.
• (+) Students can learn things quickly and apply to his own research.
• (-) His lectures may give the false image that creating things is as easy as the fusion of ideas. This is not true because one must have a broad view to know what to borrow, and there are boring times such as trials and errors, non-trivial adoptation and modification of existing methods. He omitted these in his lecture.

I would strongly recommend everyone interested in networking try his 216 and 219.

In this post I won't put all Bia unless interesting. Using those well-defined mathematical terms, Zoai are quite easy to state and thus very short.

Authentication (AuthN, 認証) and authorization (AuthZ, 承認) are important pieces in system security. In one word, AuthN verifies the identity of the requester, and AuthZ decides whether a specific operation is allowed.

This is a review and summary for course MATH 220BC, given by Professor Artem Chernikov and Andrew Marks.

In this post, I listed important theorems (in my mind) like a dictionary, so I can recall what I learnt when I read this in future. Only the overview and summary may be useful to other people.

This is a review and summary for course MATH 206A Combinatorics at UCLA, given by Prof. Igor Pak.

I try to make the flow more naturally, but also want to include brief description of important theorems.

This post introduces some tricks on polynomials widely used in ICPC. I will try to practice algebraic knowledge as well.

Rephrase the chess picking problem in a more formal way.