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• 14:47, 2 May 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法10.pdf
• 14:35, 30 April 2023 Roundgod talk contribs created page 组合数学 (Spring 2023)/第二次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 191220020 || 戴一帆 |- | 191220060 || 林荣恩 |- | 191250004 || 曹雨森 |- | 191250127 || 孙伟杰 |- | 191250145 || 王子鉴 |- | 191820255 || 臧正贻 |- | 191840186 || 彭昕昂 |- | 201220011 || 章正辉 |- | 201220035 || 丁天行 |- | 201220043 || 吕培锋 |- | 201220073 || 曹云帆 |- | 201220092 || 吴杰伦 |- | 201220098 || 杨林 |- | 20122010...")
• 15:53, 27 April 2023 Etone talk contribs created page 组合数学 (Fall 2023)/The probabilistic method (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...")
• 09:56, 24 April 2023 Zhangxy talk contribs created page 概率论与数理统计 (Spring 2023)/Problem Set 3 (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...")
• 16:05, 20 April 2023 Zouzongrui talk contribs created page 概率论与数理统计 (Spring 2023)/第二次作业提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211830008 || 缪天顺 |- | 211240066 || 肖雨辰 |- | 211250182 || 胡皓明 |- | 211240076 || 刘嘉欣 |- | 211250235 || 陈荣锴 |- | 211850008 || 林朗 |- | 211240059 || 孙骞 |- | 211250044 || 朱家辰 |- | 211240046 || 吴奕胜 |- | 211240045 || 杨镇源 |- | 211870257 || 黄泽方 |- | 211850020 || 王雷宇 |- | 211098336 || 王远博 |- | 211240040 |...")
• 06:51, 20 April 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法9.pdf
• 06:51, 20 April 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法9.pdf
• 06:50, 20 April 2023 Chenxiaoyu talk contribs uploaded a new version of File:计算方法 Numerical method (Spring 2023)-Assignments5.pdf
• 06:48, 20 April 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-Assignments5.pdf
• 06:48, 20 April 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-Assignments5.pdf
• 06:47, 20 April 2023 Chenxiaoyu talk contribs created page 计算方法 Numerical method (Spring 2023)/Homework4 提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211502020 || 周相羽 |- | 211502005 || 黄逸飞 |- | 211502013 || 张逸飞 |- | 211502016 || 谢模阳 |- | 211502003 || 郭引商 |- | 211502002 || 王文萱 |- | 211240009 || 陆一阳 |- | 211220038 || 胡文菁 |- | 201240012 || 尹安周 |- | 211220093 || 曹博晗 |- | 211240032 || 黄文橼 |- | 211502004 || 陈雨婷 |- | 211240066 || 肖雨辰 |- | 211502008 || 李...")
• 12:56, 18 April 2023 Etone talk contribs created page 组合数学 (Fall 2023)/Existence problems (Created page with "== Existence by Counting == === Shannon's circuit lower bound=== This is a fundamental problem in in Computer Science. A '''boolean function''' is a function in the form <math>f:\{0,1\}^n\rightarrow \{0,1\}</math>. [http://en.wikipedia.org/wiki/Boolean_circuit Boolean circuit] is a mathematical model of computation. Formally, a boolean circuit is a directed acyclic graph. Nodes with indegree zero are input nodes, labeled <math>x_1, x_2, \ldots , x_n</math>. A circuit h...")
• 11:44, 18 April 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/Threshold of k-clique in random graph (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）子图概...")
• 02:29, 18 April 2023 User account Hlx talk contribs was created by Liuexp talk contribs
• 18:17, 17 April 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/Weierstrass Approximation Theorem (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：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> 使得对于 <math>[a,b]</math>...")
• 14:58, 17 April 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/Two-point sampling (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...")
• 02:27, 17 April 2023 Xyfu talk contribs moved page File:计算方法 Numerical method (Spring 2023)-计算方法8.pdf.pdf to File:计算方法 Numerical method (Spring 2023)-计算方法8.pdf
• 02:03, 17 April 2023 Xyfu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法8.pdf.pdf
• 02:03, 17 April 2023 Xyfu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法8.pdf.pdf
• 12:46, 13 April 2023 Gispzjz talk contribs created page 组合数学 (Fall 2023)/Problem Set 2 (Created page with "Let <math>S=\{P_1,...,P_n\}</math> be a set of properties, and let <math>f_k</math> (respectively, <math>f_{\geq k}</math>) denote the number of objects in a finite set <math>U</math> that have '''exactly''' <math>k</math> (respectively, '''at least''' <math>k</math>) of the properties. Let <math>A_i</math> denote the set of objects satisfies <math>P_i</math> in <math>U</math>, for any <math>I\subseteq\{1,...,n\}</math>, we denote <math>A_I=\bigcap_{i\in I}A_i</math> wi...")
• 11:36, 13 April 2023 Etone talk contribs created page 组合数学 (Fall 2023)/Cayley's formula (Created page with "== Cayley's Formula == We now present a theorem of the number of labeled trees on a fixed number of vertices. It is due to [http://en.wikipedia.org/wiki/Arthur_Cayley Cayley] in 1889. The theorem is often referred by the name [http://en.wikipedia.org/wiki/Cayley's_formula Cayley's formula]. {{Theorem|Cayley's formula for trees| : There are <math>n^{n-2}</math> different trees on <math>n</math> distinct vertices. }} The theorem has several proofs, including the bijectio...")
• 13:06, 12 April 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/Average-case analysis of QuickSort (Created page with "[http://en.wikipedia.org/wiki/Quicksort '''快速排序'''（'''Quicksort'''）]是由Tony Hoare发现的基于比较的（comparison-based）排序算法。该算法的伪代码描述如下（为方便起见，假设数组元素互不相同——更一般情况的分析易推广得到）： '''''QSort'''''(A): 输入A[1...n]是存有n个不同数字的数组 if n>1 then '''pivot''' = A[1]; 将A中<pivot的元素存于数组L，将>pivot的元素存于...")
• 05:48, 11 April 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法7.pdf
• 05:48, 11 April 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法7.pdf
• 02:22, 6 April 2023 Chenxiaoyu talk contribs created page 计算方法 Numerical method (Spring 2023)/Homework3 提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211240009 || 陆一阳 |- | 211502020 || 周相羽 |- | 211502005 || 黄逸飞 |- | 211240066 || 肖雨辰 |- | 211502025 || 吴文翔 |- | 211502016 || 谢模阳 |- | 211098322 || 陈思翔 |- | 211220009 || 韦玮 |- | 211850020 || 王雷宇 |- | 211240032 || 黄文橼 |- | 211098324 || 肖卓凡 |- | 211220038 || 胡文菁 |- | 211240090 || 林锟珉 |- | 211502014 || 刘奕...")
• 02:16, 6 April 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-Assignments4.pdf
• 02:16, 6 April 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-Assignments4.pdf
• 15:05, 1 April 2023 Liuexp talk contribs created page File:计算方法6.pdf
• 15:05, 1 April 2023 Liuexp talk contribs uploaded File:计算方法6.pdf
• 14:25, 29 March 2023 Etone talk contribs created page 组合数学 (Fall 2023)/Pólya's theory of counting (Created page with "== Groups == A group <math>(G,\cdot)</math> is set <math>G</math> along with a binary operator <math>\cdot</math> which satisfies the following axioms: * ''closure'': <math>\forall g,h\in G, g\cdot h \in G</math>; * ''associativity'': <math>\forall f,g,h\in G, f\cdot(g\cdot h)=(f\cdot g)\cdot h</math>; * ''identity'': there exists a special element <math>e\in G</math>, called the '''identity''', such that <math>e\cdot g=g</math> for any <math>g\in G</math>; * ''inverse''...")
• 10:29, 27 March 2023 Zhangxy talk contribs created page 概率论与数理统计 (Spring 2023)/Problem Set 2 (Created page with "== Problem 1 (Warm-up problems) == <ul> <li>[<strong>Function of random variable (I)</strong>] Let [math]X[/math] be a random variable and [math]g:\mathbb{R} \to \mathbb{R}[/math] be continuous and strictly increasing. Show that [math]Y = g(X)[/math] is a random variable.</li> <li>[<strong>Function of random variable (II)</strong>] Let [math]X[/math] be a random variable with distribution function [math]\max(0,\min(1,x))[/math]. Let [math]F[/math] be a distribution func...") Tag: Visual edit: Switched
• 09:08, 27 March 2023 Roundgod talk contribs created page 组合数学 (Spring 2023)/第一次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 191220020 || 戴一帆 |- | 191220060 || 林荣恩 |- | 191250004 || 曹雨森 |- | 191250127 || 孙伟杰 |- | 191250145 || 王子鉴 |- | 191820255 || 臧正贻 |- | 201180088 || 陈浩楠 |- | 201220011 || 章正辉 |- | 201220035 || 丁天行 |- | 201220043 || 吕培锋 |- | 201220073 || 曹云帆 |- | 201220092 || 吴杰伦 |- | 201220098 || 杨林 |- | 20122010...")
• 04:03, 26 March 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法5.pdf
• 04:03, 26 March 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法5.pdf
• 07:30, 24 March 2023 Zouzongrui talk contribs created page 概率论与数理统计 (Spring 2023)/第一次作业提交名单 (submission_list) Tag: Visual edit
• 06:56, 17 March 2023 Xyfu talk contribs moved page File:计算方法4.pdf to File:计算方法 Numerical method (Spring 2023)-计算方法4.pdf
• 06:46, 17 March 2023 Xyfu talk contribs created page File:计算方法4.pdf
• 06:46, 17 March 2023 Xyfu talk contribs uploaded File:计算方法4.pdf
• 12:45, 16 March 2023 Etone talk contribs created page 组合数学 (Fall 2023)/Sieve methods (Created page with "== Principle of Inclusion-Exclusion == Let <math>A</math> and <math>B</math> be two finite sets. The cardinality of their union is :<math>|A\cup B|=|A|+|B|-{\color{Blue}|A\cap B|}</math>. For three sets <math>A</math>, <math>B</math>, and <math>C</math>, the cardinality of the union of these three sets is computed as :<math>|A\cup B\cup C|=|A|+|B|+|C|-{\color{Blue}|A\cap B|}-{\color{Blue}|A\cap C|}-{\color{Blue}|B\cap C|}+{\color{Red}|A\cap B\cap C|}</math>. This is illu...")
• 07:00, 16 March 2023 Roundgod talk contribs created page 组合数学 (Fall 2023)/Problem Set 1 (Created page with "== Problem 1 == Fix positive integers <math>n</math> and <math>k</math>. Let <math>S</math> be a set with <math>|S|=n</math>. Find the number of <math>k</math>-tuples <math>(T_1,T_2,\dots,T_k)</math> of subsets <math>T_i</math> of <math>S</math> subject to each of the following conditions separately. Briefly explain your solution. * <math>T_1\subseteq T_2\subseteq \cdots \subseteq T_k.</math> * The <math> T_i</math>s are pairwise disjoint. * <math> T_1\cup T_2\cup \cdot...")
• 16:10, 15 March 2023 Chenxiaoyu talk contribs created page 计算方法 Numerical method (Spring 2023)/Homework2 提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211240009 || 陆一阳 |- | 211240066 || 肖雨辰 |- | 211502005 || 黄逸飞 |- | 211220118 || 刘艺葳 |- | 211502013 || 张逸飞 |- | 211220009 || 韦玮 |- | 201180132 || 徐宸宇 |- | 211502014 || 刘奕 |- | 211502020 || 周相羽 |- | 211502008 || 李诚希 |- | 211220093 || 曹博晗 |- | 211220121 || 唐周旋 |- | 211220018 || 陈润涛 |- | 211240019 || 姜宇翔 |...")
• 11:18, 15 March 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-Assignments3.pdf
• 11:18, 15 March 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-Assignments3.pdf
• 17:35, 11 March 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/Karger's min-cut algorithm (Created page with "= Graph Cut = Let <math>G(V, E)</math> be an undirected graph. A subset <math>C\subseteq E</math> of edges is a '''cut''' of graph <math>G</math> if <math>G</math> becomes ''disconnected'' after deleting all edges in <math>C</math>. Let <math>\{S,T\}</math> be a '''bipartition''' of <math>V</math> into nonempty subsets <math>S,T\subseteq V</math>, where <math>S\cap T=\emptyset</math> and <math>S\cup T=V</math>. A cut <math>C</math> is specified by this bipartition as...")
• 16:43, 11 March 2023 Etone talk contribs created page 概率论与数理统计 (Spring 2023)/Polynomial identity testing (Created page with "=Polynomial Identity Testing (PIT) = The '''Polynomial Identity Testing (PIT)''' is such a problem: given as input two polynomials, determine whether they are identical. It plays a fundamental role in ''Identity Testing'' problems. First, let's consider the univariate ("one variable") case: * '''Input:''' two polynomials <math>f, g\in\mathbb{F}[x]</math> of degree <math>d</math>. * Determine whether <math>f\equiv g</math> (<math>f</math> and <math>g</math> are identica...")
• 06:12, 10 March 2023 Chenxiaoyu talk contribs created page File:计算方法 Numerical method (Spring 2023)-计算方法3.pdf
• 06:12, 10 March 2023 Chenxiaoyu talk contribs uploaded File:计算方法 Numerical method (Spring 2023)-计算方法3.pdf
• 15:25, 3 March 2023 Zhangxy talk contribs created page 概率论与数理统计 (Spring 2023)/Problem Set 1 (Created page with "*目前作业非最终版本。 *每道题目的解答都要有<font color="red" size=5>完整的解题过程</font>。中英文不限。 *我们推荐大家使用LaTeX, markdown等对作业进行排版。 Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\mathbf{Pr})<\math>. == Problem 1 ==")
• 08:31, 3 March 2023 Etone talk contribs created page 组合数学 (Fall 2023)/Generating functions (Created page with "== Generating Functions == In Stanley's magnificent book ''Enumerative Combinatorics'', he comments the generating function as "the most useful but most difficult to understand method (for counting)". The solution to a counting problem is usually represented as some <math>a_n</math> depending a parameter <math>n</math>. Sometimes this <math>a_n</math> is called a ''counting function'' as it is a function of the parameter <math>n</math>. <math>a_n</math> can also be tre...")
• 08:17, 3 March 2023 User account Zouzongrui talk contribs was created by Liuexp talk contribs