提醒：本游记体量较大，字数约15000，图片数量超过100，可以考虑在WiFi环境下阅读）   “我的梦想就是生活在一个滨海城市，有一个家，养两只猫，在慢节奏的海风中悠闲地生活。现在，就只差一只猫了。” ——厦门地铁树洞投稿   厦门是改革开放早期的经济特区之一，如……

水水文章。 笔者和HDD 292在寒假时一起游玩了 Create Arcane Engineering 整合包。由于笔者手头拮据，并无多余的资金购置服务器，于是探索了几种常见的服务器平替和端口映射方法，现比较： Essential Essential是国外大佬团队开发的游戏内社交平台mod，支持好友、聊……

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 完整题解来自ox帅气lecturer, 我只能证明F<\mathbb C的情况 ;( ;( ;() 题面 V是域F上的一个线性空间, \dim V=n, 且有T\in L(V). 现取\lambda_1,...,\lambda_n\in F两两不等, 且任意\lambda_i都不是T的特征值. 试证明存在\alpha_1,...,\alpha_n\in F使得 \……

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……