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.
Posts by Tags
algebra
Polynomial Algorithms
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This post introduces some tricks on polynomials widely used in ICPC. I will try to practice algebraic knowledge as well.
Chess Picking Problem
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Rephrase the chess picking problem in a more formal way.
Algebra Miscs
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Misc things that are taught in class but not written in the note of MATH 210.
algorithm
Polynomial Algorithms
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This post introduces some tricks on polynomials widely used in ICPC. I will try to practice algebraic knowledge as well.
Chess Picking Problem
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Rephrase the chess picking problem in a more formal way.
POJ3557 Map Generator
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Discuss POJ3557 Map Generator and its variants.
LIS and network flow
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This post discusses Longest Increasing Subsequence (LIS) and network flow problem.
The sqrt thesis of mixing strategies
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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.
api
Service Invocation: A Brief Survey
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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.
NDN API 1: Encoding
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TL; DR: Reflection should be used for encoding or serilization.
combinatorics
MATH 206A: Combinatorics - Course Review
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This is a review and summary for course MATH 206A Combinatorics at UCLA, given by Prof. Igor Pak.
Chess Picking Problem
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Rephrase the chess picking problem in a more formal way.
POJ3557 Map Generator
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Discuss POJ3557 Map Generator and its variants.
Residue Theorem and its Application
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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.
LIS and network flow
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This post discusses Longest Increasing Subsequence (LIS) and network flow problem.
complex analysis
Residue Theorem and its Application
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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.
course review
MATH 220BC: Mathematical Logic - Course Review
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This is a review and summary for course MATH 220BC, given by Professor Artem Chernikov and Andrew Marks.
MATH 206A: Combinatorics - Course Review
Published:
This is a review and summary for course MATH 206A Combinatorics at UCLA, given by Prof. Igor Pak.
data structure
The sqrt thesis of mixing strategies
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.
functional analysis
logic
MATH 220BC: Mathematical Logic - Course Review
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This is a review and summary for course MATH 220BC, given by Professor Artem Chernikov and Andrew Marks.
math
Stability of DLedger
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In this post I want to analyze the stability of Dledger, a DAG-based distributed logging system.
misc
Two’s complement and 2-adic number
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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.
ndn
Authentication and Authorization
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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.
Service Invocation: A Brief Survey
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.
Service Discovery: A Survey
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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.
Confusing Terms
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I find that some terms are confusing.
NDN API 1: Encoding
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TL; DR: Reflection should be used for encoding or serilization.
network
CS 219: Network Verification - Course Review
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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.
network flow
LIS and network flow
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This post discusses Longest Increasing Subsequence (LIS) and network flow problem.
programing language
Some Notes on Playing C++ Coroutine
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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
security
Authentication and Authorization
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.
service-dicvovery
Service Discovery: A Survey
Published:
There is always a need for service discovery and load balancing, but no universal solution. Sometimes naive ways may satisfy most needs.
service-invocation
Service Invocation: A Brief Survey
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.
term
Confusing Terms
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I find that some terms are confusing.