Solved! Difficulty: Div2C :O 竟然有60期了！！ 本期题目来源于Group Theory作业，，，难度不高 Congratulations on the 60th entry!! This problem is from my Group Theory homework (not very hard). Z(Sym(n))=ONE In the world of MATHS, a permutation i……

题目背景 证明连续性时缩放水平哈哈了(sweatgrinning) 题面 f is a nonconstant holomorphic function on a region \Omega_1 and g is defined on f(\Omega_1). Prove that if h=g\circ f is holomorphic, then so is g. 先想再看提示哦 提……

Note: This is a April Fools' Joke Introduction Nowadays, as most programming languages are built on top of English grammar and syntax, it is sometimes difficult for Latin, Spanish or French speakers to get used to the syntax in programming. Insprie……

思考题 aimed for inexperienced participants? Silenced! Ookami and her teammates are taking an English class. The team has n people(animals?) in total. Initially, each person can raise his/her hand and speak freely. However, once a student has raise……

Solved! Difficulty: Div2 C 思考题 in mid autumn LianLi Branches Wulpit has drawn n nodes(indexed from 1 to n) and n-m edges on paper for homework assignments. They form m rooted trees (aka a forest). However, when she went to the toilet, Fely……

题目背景 人见人爱的代数小题 :] 惊人的是竟然在Hungerford II.2.8.9才出现, 还标了名字 😮 题面 A^ * is a normal subgroup of A, B^ * is a normal subgroup of B. Prove that: (i) A^ *(A\cap B^ *) is a normal subgroup of A^ *(A\cap B) (ii) B^ *(A^ *\cap B) i……

题目背景 本题竟然与xgn目前正在学习的序数有关, 真是可喜可贺!(crim boi在thu里有包含序数的课程吗?) 题面 If you don't remember what a topology is, please refer to this passage. Preliminary: Open sets in \mathbb R are just union (can be infinite) of som……

Solved! Difficulty: Div2B 1 problem for div3 participants. Beautiful Dice Painting When Epis is bored, she will draw dices. The canvas contains n*n dots. Initially they are all white. You need to paint exactly v dots black so that the final c……

题目背景 Rudin Real and Complex Analysis第一题, 真是开门红. 题面 We call a pairing (X,\mathfrak{M}) \sigma-algebra if \mathfrak{M} is a subset of P(X) satisfying the three properties below: (1) X\in\mathfrak{M} (2) If A\in\mathfrak{M}, A^c\in\mathf……

trivial 思考题 I am Banach This is a classic problem by Banach nearly without any change. There are N boys and M girls. Each boy loves a single girl and each girl loves a single boy. Your task is to divide the boys into two groups A_0 and A_1 and t……