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- 01:39, 21 May 2024 概率论与数理统计 (Spring 2024)/第三次作业提交名单 (hist | edit) [2,002 bytes] Zouzongrui (talk | contribs) (Created page with " 如有错漏邮件请联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 221900059 || 王齐剑 |- | 221240007 || 郭宇轩 |- | 221240068 || 周凡淇 |- | 221240092 || 杨煜申 |- | 221240035 || 李想 |- | 221240087 || 顾鹏 |- | 221240027 || 唐诗博 |- | 221240065 || 何俊渊 |- | 221240023 || 蒋耀瑾 |- | 201850051 || 李轲楠 |- | 221240070 || 汪宗元 |- | 221900332 || 王卫东 |- | 221240073 || 李恒济 |- | 221098038 |...")
- 09:48, 20 May 2024 组合数学 (Fall 2024)/Extremal set theory (hist | edit) [51,460 bytes] Etone (talk | contribs) (Created page with "== Sunflowers == An set system is a '''sunflower''' if all its member sets intersect at the same set of elements. {{Theorem|Definition (sunflower)| : A set family <math>\mathcal{F}\subseteq 2^X</math> is a '''sunflower''' of size <math>r</math> with a '''core''' <math>C\subseteq X</math> if ::<math>\forall S,T\in\mathcal{F}</math> that <math>S\neq T</math>, <math>S\cap T=C</math>. }} Note that we do not require the core to be nonempty, thus a family of disjoint sets is...")
- 16:06, 14 May 2024 计算方法 Numerical method (Spring 2024)/Homework5 提交名单 (hist | edit) [2,091 bytes] Kvrmnks (talk | contribs) (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 191240047 || 孙宇飞 |- | 201240036 || 钱儒凡 |- | 211240013 || 李昀芃 |- | 211240020 || 朱睿骐 |- | 211240035 || 王祉天 |- | 211294003 || 倪昀 |- | 221180133 || 黄可唯 |- | 221220002 || 沈均文 |- | 221220003 || 林涵坤 |- | 221220019 || 洪观澜 |- | 221220027 || 蒋宇阳 |- | 221220029 || 陈俊翰 |- | 221220033 || 孙一鸣 |- | 22122003...")
- 15:55, 14 May 2024 组合数学 (Spring 2024)/Problem Set 3 (hist | edit) [2,925 bytes] Gispzjz (talk | contribs) (Created page with "== Problem 1 == Solve the following two existence problems: * You are given <math>n</math> integers <math>a_1,a_2,\dots,a_n</math>, such that for each <math> 1\leq i\leq n</math> it holds that <math>i-n\leq a_i\leq i-1</math>. Show that there exists a '''nonempty''' subsequence (not necessarily consecutive) of these integers, whose sum is equal to <math> 0 </math>. (Hint: Consider <math> b_i=a_i-i </math>) * You are given two '''multisets''' <math> A </math> and <ma...")
- 13:06, 14 May 2024 组合数学 (Spring 2024)/Problem Set 2 (hist | edit) [5,164 bytes] Roundgod (talk | contribs) (Created page with "== Problem 1 == Count the number of lattice paths from <math>(0, 0)</math> to <math>(n, n)</math> with steps up and to the right, when two paths are considered equal if one can be moved on top of the other by a rotation or reflection. For example: center|frameless (Hint: Represent a path as a sequence of <math>0</math>s and <math>1</math>s and determine the group that acts on these sequences.) == Problem 2 == Suppose we are given <math>m</math> <math>n<...")
- 13:05, 14 May 2024 组合数学 (Spring 2024)/Problem Set 1 (hist | edit) [1,789 bytes] Roundgod (talk | contribs) (Created page with "== Problem 1 == How many <math>n\times m</math> matrices of <math>0</math>'s and <math>1</math>'s are there, such that every row and column contains an even number of <math>1</math>'s? An odd number of <math>1</math>'s? == Problem 2 == * There is a set of <math>2n</math> people: <math>n</math> male and <math>n</math> female. A good party is a set with the same number of male and female. How many possibilities are there to build such a good party? * Try to express the a...")
- 09:38, 14 May 2024 组合数学 (Fall 2024)/Extremal graph theory (hist | edit) [18,939 bytes] Etone (talk | contribs) (Created page with "== Forbidden Cliques == Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" === Mantel's theorem === We consider a typical extremal problem for graphs: the largest possible number of edges of '''triangle-free''' graphs, i.e. graphs contains no <math>K_3</math>. {{Theorem|Theorem (Mantel 1907)| :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <m...")
- 12:00, 8 May 2024 计算复杂性 (Spring 2024)/第二次作业提交名单 (hist | edit) [827 bytes] Roundgod (talk | contribs) (Created page with "如有错漏请邮件联系助教。 <center> {| class="wikitable" style="text-align:center" |- ! 学号 !! 姓名 |- | 201502003 || 丁显浓 |- | 201840009 || 田永上 |- | 211250001 || 鞠哲 |- | 211502001 || 任楷文 |- | 211502005 || 黄逸飞 |- | 211502009 || 曲桐希 |- | 211502024 || 贺卓宇 |- | 211502025 || 吴文翔 |- | 211840112 || 聂易辰 |- | 211840292 || 窦若庭 |- | 211850106 || 杨林峰 |- | 221180115 || 黄文睿 |- | 221840186...")
- 11:17, 6 May 2024 概率论与数理统计 (Spring 2024)/第二次作业提交名单 (hist | edit) [2,025 bytes] Zouzongrui (talk | contribs) (Created page with " 如有错漏请联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 221240092 || 杨煜申 |- | 221240083 || 陈正佺 |- | 221240007 || 郭宇轩 |- | 221900059 || 王齐剑 |- | 221240035 || 李想 |- | 221240009 || 冯雨桐 |- | 221240068 || 周凡淇 |- | 211240020 || 朱睿骐 |- | 221240093 || 陈力峥 |- | 221240066 || 张植翔 |- | 201850051 || 李轲楠 |- | 221240041 || 周越洋 |- | 221240056 || 郭子良 |- | 221240047 ||...")
- 05:19, 5 May 2024 概率论与数理统计 (Spring 2024)/Problem Set 3 (hist | edit) [6,279 bytes] Zhangxy (talk | contribs) (Created page with "*每道题目的解答都要有完整的解题过程，中英文不限。 *我们推荐大家使用LaTeX, markdown等对作业进行排版。 == Assumption throughout Problem Set 3== <p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\mathbf{Pr})</math>.</p> <p>Without further notice, we assume that the expectation of random variables are well-defined.</p> <p>The term <math>\log</math> used in this context refers to the natural l...")
- 01:37, 2 May 2024 计算方法 Numerical method (Spring 2024)/Homework4 提交名单 (hist | edit) [2,065 bytes] Kvrmnks (talk | contribs) (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 191240047 || 孙宇飞 |- | 201240036 || 钱儒凡 |- | 211240013 || 李昀芃 |- | 211240020 || 朱睿骐 |- | 211240035 || 王祉天 |- | 211294003 || 倪昀 |- | 221180133 || 黄可唯 |- | 221220002 || 沈均文 |- | 221220003 || 林涵坤 |- | 221220019 || 洪观澜 |- | 221220027 || 蒋宇阳 |- | 221220029 || 陈俊翰 |- | 221220033 || 孙一鸣 |- | 22122003...")
- 18:45, 29 April 2024 组合数学 (Spring 2024)/第二次作业提交名单 (hist | edit) [1,218 bytes] Roundgod (talk | contribs) (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 201098313 || 杨文昊 |- | 201220011 || 章振辉 |- | 201220094 || 肖依博 |- | 201220179 || 阎子扬 |- | 201300026 || 高峰 |- | 201502003 || 丁显浓 |- | 201840009 || 田永上 |- | 201840058 || 蒋潇鹏 |- | 201840281 || 史成璐 |- | 211098220 || 付博 |- | 211220104 || 崔乐天 |- | 211220151 || 吴羽 |- | 211240012 || 陈宇宁 |- | 211240046 ||...")
- 02:57, 24 April 2024 组合数学 (Fall 2024)/The probabilistic method (hist | edit) [27,151 bytes] Etone (talk | contribs) (Created page with "== The Probabilistic Method == The probabilistic method provides another way of proving the existence of objects: instead of explicitly constructing an object, we define a probability space of objects in which the probability is positive that a randomly selected object has the required property. The basic principle of the probabilistic method is very simple, and can be stated in intuitive ways: *If an object chosen randomly from a universe satisfies a property with posi...")
- 03:14, 22 April 2024 概率论与数理统计 (Spring 2024)/Weierstrass Approximation Theorem (hist | edit) [5,139 bytes] Etone (talk | contribs) (Created page with "[https://en.wikipedia.org/wiki/Stone%E2%80%93Weierstrass_theorem '''魏尔施特拉斯逼近定理''']（'''Weierstrass approximation theorem'''）陈述了这样一个事实：闭区间上的连续函数总可以用多项式一致逼近。 {{Theorem|魏尔施特拉斯逼近定理| :设 <math>f:[a,b]\to\mathbb{R}</math> 为定义在实数区间 <math>[a,b]</math> 上的连续实值函数。对每个 <math>\epsilon>0</math>，存在一个多项式 <math>p</math> 使得对...")
- 03:13, 22 April 2024 概率论与数理统计 (Spring 2024)/Threshold of k-clique in random graph (hist | edit) [7,005 bytes] Etone (talk | contribs) (Created page with "在 Erdős-Rényi 随机图模型 <math>G(n,p)</math> 中，一个随机无向图 <math>G</math> 以如下的方式生成：图 <math>G</math> 包含 <math>n</math> 个顶点，每一对顶点之间都独立同地以概率 <math>p</math> 连一条无向边。如此生成的随机图记为 <math>G\sim G(n,p)</math>。 固定整数 <math>k\ge 3</math>，考虑随机图 <math>G\sim G(n,p)</math> 包含 <math>K_k</math>（<math>k</math>-团，<math>k</math>-clique）子图...")
- 03:12, 22 April 2024 概率论与数理统计 (Spring 2024)/Two-point sampling (hist | edit) [8,968 bytes] Etone (talk | contribs) (Created page with "= 利用线性同余方程构造两两独立的随机变量 = 令<math>p</math>为一质数。考虑模<math>p</math>余数构成的集合<math>[p]=\{0,1,\ldots,p-1\}=\mathbb{Z}_p</math>。众所周知，当<math>p</math>为质数时，<math>\mathbb{Z}_p</math>为对模<math>p</math>加法和乘法运算闭合的'''有限域'''。 我们现在构造一系列值域为<math>[p]</math>的'''两两独立'''（'''pairwise Independent'''）且'''均匀分布'''（'''uniforml...")
- 11:07, 10 April 2024 组合数学 (Spring 2024)/第一次作业提交名单 (hist | edit) [1,274 bytes] Roundgod (talk | contribs) (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 201098313 || 杨文昊 |- | 201220005 || 左中铭 |- | 201220011 || 章振辉 |- | 201220013 || 王力 |- | 201220094 || 肖依博 |- | 201220179 || 阎子扬 |- | 201300026 || 高峰 |- | 201502003 || 丁显浓 |- | 201840009 || 田永上 |- | 201840058 || 蒋潇鹏 |- | 201840281 || 史成璐 |- | 211098220 || 付博 |- | 211220104 || 崔乐天 |- | 211220128 ||...")
- 18:33, 9 April 2024 组合数学 (Fall 2024)/Problem Set 2 (hist | edit) [5,164 bytes] Roundgod (talk | contribs) (Created page with "== Problem 1 == Count the number of lattice paths from <math>(0, 0)</math> to <math>(n, n)</math> with steps up and to the right, when two paths are considered equal if one can be moved on top of the other by a rotation or reflection. For example: center|frameless Hint: Represent a path as a sequence of <math>0</math>s and <math>1</math>s and determine the group that acts on these sequences. == Problem 2 == Suppose we are given <math>m</math> <math>n</m...")
- 16:32, 9 April 2024 计算方法 Numerical method (Spring 2024)/Homework3 提交名单 (hist | edit) [2,065 bytes] Kvrmnks (talk | contribs) (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 191240047 || 孙宇飞 |- | 201240036 || 钱儒凡 |- | 211240013 || 李昀芃 |- | 211240020 || 朱睿骐 |- | 211240035 || 王祉天 |- | 211294003 || 倪昀 |- | 221180133 || 黄可唯 |- | 221220002 || 沈均文 |- | 221220003 || 林涵坤 |- | 221220019 || 洪观澜 |- | 221220027 || 蒋宇阳 |- | 221220029 || 陈俊翰 |- | 221220033 || 孙一鸣 |- | 22122003...")
- 15:55, 9 April 2024 概率论与数理统计 (Spring 2024)/Problem Set 2 (hist | edit) [14,357 bytes] Zhangxy (talk | contribs) (Created page with "*每道题目的解答都要有完整的解题过程，中英文不限。 *我们推荐大家使用LaTeX, markdown等对作业进行排版。 == Assumption throughout Problem Set 2== <p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\mathbf{Pr})</math>.</p> <p>Without further notice, we assume that the expectation of random variables are well-defined.</p> <p>The term <math>\log</math> used in this context refers to the natural l...")
