风车问题
IMO 2011 年的第 2 题： 设 $S$ 是平面上包含至少两个点的有限点集，并且其中任意三点不共线。定义一个「风车」过程：直线 $l$ 从 $S$ 中一点 $P$ 开始，绕 $P$ 顺时针旋转，...
Math
使用对偶图证明欧拉公式
使用 dual graph 证明欧拉公式：$V-E+F=2$ 对于一个 connected planar graph $G$，如下图蓝色部分所示，其所对应的 dual graph $G^*$ 则为红色部分： $G^*$ 的每个顶点对应 $G$ 中的每个面...
Interesting Problems
一些有趣的数学、物理、计算机问题 ...
Nonlinear Optimization
EN553.762 Review. Based on Numerical Optimization Book ...
一个计数谜题的意外答案
问题： 想象光滑的地面有两个静止的小滑块，左面有一堵质量无穷大的墙。左边的小滑块质量为 $1$。此时给右边的小滑块一个向左的速度，假设所有的碰撞...
Matrix Derivatives
Notes on doing derivatives w.r.t. matrix/vector ...
Convex Optimization
AA/EE/ME 578 Review ...
Linear Algebra Review
From ME 510 & AMATH 584 ...
Shortest Path Problem
Finding the best route between two cities, given a complicated road network; or transmitting a message between two computers along a network of hundreds of computers, are all classified as the shortest path problem. ...
The Assignment Problem
Given $n$ workers and $n$ jobs, and the cost $c_{ij}$ to train the $i$-th worker for the $j$-th job, find an assignment of one worker to each job which minimized the total training cost. ...