Solved Difficulty: D2C 思考题 inspired by Saionji Video Channel Eastmost Eki There are n points on a 2D plane. You can select any real point as pivot in the rectangle bounded by (a,b) and (c,d) and rotate the entire plane by d degree clockwis……

思考题 inspired by car lanes Car Lane In Ryuto the capital of the Dragon Kingdom, there is an intersection with k+1 exits. On one lane of one exit, there is a queue of n cars. The i-th car in the queue wants to go in the direction d_i (1\leq d_i\le……

Solved Difficulty: D2C-D2D 思考题 inspired by Create Mod Assembly Line There is an assembly line consisting of n machines. The i-th machine on the line holds an infinitely long input queue and a processing time of t_i seconds. The machines wo……

short 思考题 A^B Problem Given two pattern strings A and B that consists of lower-case letters, ? (match a single character) and * (match one or more characters) For example, abc?d*e matches abcfdppe and abcgde but not ae or abcdde. Find a string t……

funny problem from model theory problem sheet 题面 Let L be a countable language, T a theory. Let c_1,c_2,... be new constants, L'=L\cup\lbrace c_1,...\rbrace, and let X be the set of all complete theories of L' with T\subset t. Enumerate the L' se……

Rotman algebraic topology上的题, 个人认为出的非常好, 极大增进了读者对\pi_1(S^1)计算过程的理解. 题面 A group G which is also a topology space is called a topological group if \mu:G\times G\to G:(x,y)\mapsto xy and i:G\to G:x\mapsto x^{-1} are contin……

思考题 featuring Hikari again! Guess the string Hikari and her master Ninetail are playing a game. Hikari thinks of a string S with lower-case letters, and Ninetail asks her to make q modifications one by one. Each modification can only be one of t……

Dieudonne的题, 真实难度不好说, 回顾一下发现其实挺简单的. 题面 Let E be a Hilbert space, F a dense linear subspace of E, distinct from E. (For example E space of l^2 sum of a suitable countable linear independent set and F space of finite sum of thi……

题目背景 为证一个非零吃大师 题面 Assuming AC, prove that for a integral domain R, if any nonzero prime ideal P contains a nonzero prime (p), R is UFD. 先想再看提示哦 提示 Let S be the set of elements that are prime factori……

概括 原文为英文，本文是回忆版，具体数据可能有误。考完收试卷、草稿纸。可以携带一张A4手写笔记。不可以带计算器。 期中传送门 120分钟5题. P1 有一根长为2a的均匀杆子竖立在光滑水平面上，由于扰动开始倒下，问： 快接触地面时的角速度 快接触地面时的质心速度 P……