## Rational Points of Elliptic Curves

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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.

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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.

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

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Rephrase the chess picking problem in a more formal way.

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Misc things that are taught in class but not written in the note of MATH 210.

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

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Rephrase the chess picking problem in a more formal way.

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Discuss POJ3557 Map Generator and its variants.

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This post discusses Longest Increasing Subsequence (LIS) and network flow problem.

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When solving a problem, it is common that we have two different strategies that fit in different cases. For example, one algorithm may have a better time complexity but uses more memory than the other. Or, one is fast when there are only a few of large objects, but the other works better when there are many small objects. However, I found that there usually exists a solution which is a naive mixture of the two strategies, and its performance will be the sqrt of the two.

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Service invocation is tricky. The protocol itself seems to be super simple: we call a function, and it returns. But the problem is, when the function is on another machine, how we know the state of that machine / the whole system. The developers of the caller do not want to care, so we protocol designers should care for them. But trying to make everyone happy is so tough here.

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TL; DR: Reflection should be used for encoding or serilization.

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

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Rephrase the chess picking problem in a more formal way.

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Discuss POJ3557 Map Generator and its variants.

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This post makes notes on residue theorem and its application, since most non-mathematicians only need to remember this after learning complex analysis. Some definitions may be not defined very rigorously from a complex analysis view.

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This post discusses Longest Increasing Subsequence (LIS) and network flow problem.

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This post makes notes on residue theorem and its application, since most non-mathematicians only need to remember this after learning complex analysis. Some definitions may be not defined very rigorously from a complex analysis view.

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

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

** Published:**

When solving a problem, it is common that we have two different strategies that fit in different cases. For example, one algorithm may have a better time complexity but uses more memory than the other. Or, one is fast when there are only a few of large objects, but the other works better when there are many small objects. However, I found that there usually exists a solution which is a naive mixture of the two strategies, and its performance will be the sqrt of the two.

** Published:**

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

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In this post I want to analyze the stability of Dledger, a DAG-based distributed logging system.

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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.

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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.

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Service invocation is tricky. The protocol itself seems to be super simple: we call a function, and it returns. But the problem is, when the function is on another machine, how we know the state of that machine / the whole system. The developers of the caller do not want to care, so we protocol designers should care for them. But trying to make everyone happy is so tough here.

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There is always a need for service discovery and load balancing, but no universal solution. Sometimes naive ways may satisfy most needs.

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I find that some terms are confusing.

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TL; DR: Reflection should be used for encoding or serilization.

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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.

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This post discusses Longest Increasing Subsequence (LIS) and network flow problem.

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

** Published:**

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.

** Published:**

There is always a need for service discovery and load balancing, but no universal solution. Sometimes naive ways may satisfy most needs.

** Published:**

Service invocation is tricky. The protocol itself seems to be super simple: we call a function, and it returns. But the problem is, when the function is on another machine, how we know the state of that machine / the whole system. The developers of the caller do not want to care, so we protocol designers should care for them. But trying to make everyone happy is so tough here.

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I find that some terms are confusing.