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03:5603:56, 5 April 2025 概率论与数理统计 (Spring 2025)/Problem Set 3 (hist | edit) [6,583 bytes] Zouzongrui (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== Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\mathbf{Pr})</math>. Without further notice, we assume that the expectation of random variables are well-defined. The term <math>\log</math> used in this context refers to the natural l...")

05:0805:08, 2 April 2025 计算方法 Numerical method (Spring 2025)/Homework3 提交名单 (hist | edit) [1,495 bytes] Houzhe (talk | contribs) (Created page with "<center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 221220090 || 周思桥 |- | 221240002 || 季悦宁 |- | 221240040 || 郑雯琪 |- | 231098068 || 戎昱 |- | 231098091 || 刘棣文 |- | 231098166 || 陈展 |- | 231200035 || 葛翰飞 |- | 231220006 || 陆华均 |- | 231220036 || 周楚函 |- | 231220049 || 张泽宇 |- | 231220065 || 劳汉显 |- | 231220067 || 黄裕书琪 |- | 231220071 || 吴江涛 |- | 231220122 || 安琦煜 |- | 231220132 ||...")

10:3310:33, 1 April 2025 概率论与数理统计 (Spring 2025)/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...")
10:3310:33, 1 April 2025 概率论与数理统计 (Spring 2025)/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...")
10:3210:32, 1 April 2025 概率论与数理统计 (Spring 2025)/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...")

07:2307:23, 31 March 2025 概率论与数理统计 (Spring 2025)/第二次作业提交名单 (hist | edit) [1,338 bytes] Zouzongrui (talk | contribs) (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 231840166 || 赵少凡 |- | 231200035 || 葛翰飞 |- | 231240011 || 陈力琰 |- | 231840058 || 王润希 |- | 231880123 || 陆博文 |- | 231240005 || 王甚易 |- | 231880394 || 翟笑晨 |- | 231240047 || 姜淮仁 |- | 231880152 || 李佳骏 |- | 231240015 || 邱文宣 |- | 231240002 || 余孟凡 |- | 231098046 || 李方泽 |- | 231240060 || 侯佳松 |- | 23124...")

09:5809:58, 26 March 2025 组合数学 (Fall 2025)/Existence problems (hist | edit) [14,440 bytes] Etone (talk | contribs) (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...")
09:5609:56, 26 March 2025 组合数学 (Fall 2025)/Cayley's formula (hist | edit) [17,231 bytes] Etone (talk | contribs) (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...")

10:0310:03, 21 March 2025 概率论与数理统计 (Spring 2025)/Average-case analysis of QuickSort (hist | edit) [11,838 bytes] Etone (talk | contribs) (Created page with "[http://en.wikipedia.org/wiki/Quicksort '''快速排序'''（'''Quicksort'''）]是由Tony Hoare发现的排序算法。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A中>pivot的元素存于数组R; \\保持内部元素之...")
09:5809:58, 21 March 2025 组合数学 (Fall 2025)/Pólya's theory of counting (hist | edit) [19,696 bytes] Etone (talk | contribs) (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''...")

03:1203:12, 19 March 2025 计算方法 Numerical method (Spring 2025)/Homework2 提交名单 (hist | edit) [1,497 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 |- | 221220090 || 周思桥 |- | 221240002 || 季悦宁 |- | 221240040 || 郑雯琪 |- | 231098068 || 戎昱 |- | 231098091 || 刘棣文 |- | 231098166 || 陈展 |- | 231200035 || 葛翰飞 |- | 231220006 || 陆华均 |- | 231220036 || 周楚函 |- | 231220049 || 张泽宇 |- | 231220065 || 劳汉显 |- | 231220067 || 黄裕书琪 |- | 231220071 || 吴江涛 |- | 23122012...")

14:5314:53, 16 March 2025 组合数学 (Spring 2025)/Problem Set 1 (hist | edit) [2,757 bytes] Gispzjz (talk | contribs) (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 numbers 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 answer. * <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 \cdots...")

14:5514:55, 13 March 2025 概率论与数理统计 (Spring 2025)/Problem Set 2 (hist | edit) [12,336 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== Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\mathbf{Pr})</math>. Without further notice, we assume that the expectation of random variables are well-defined. The term <math>\log</math> used in this context refers to the natural l...")

16:0716:07, 12 March 2025 组合数学 (Fall 2025)/Sieve methods (hist | edit) [33,970 bytes] Etone (talk | contribs) (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...")

12:0912:09, 10 March 2025 概率论与数理统计 (Spring 2025)/第一次作业提交名单 (hist | edit) [1,455 bytes] Zouzongrui (talk | contribs) (Created page with "如有错漏邮件请及时联系助教。 <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 231200035 || 葛翰飞 |- | 231880394 || 翟笑晨 |- | 231840166 || 赵少凡 |- | 231880123 || 陆博文 |- | 231840058 || 王润希 |- | 231240002 || 余孟凡 |- | 231240060 || 侯佳松 |- | 231240055 || 魏全烨 |- | 231098046 || 李方泽 |- | 231240015 || 邱文宣 |- | 231240011 || 陈力琰 |- | 231240038 || 肖金宇 |- | 231230102 || 庄铸锴 |-...")

04:2204:22, 5 March 2025 计算方法 Numerical method (Spring 2025)/Homework1 提交名单 (hist | edit) [1,668 bytes] Houzhe (talk | contribs) (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 221180168 || 聂超 |- | 221220090 || 周思桥 |- | 221240002 || 季悦宁 |- | 221240040 || 郑雯琪 |- | 221504031 || 刘鸿嘉 |- | 231098068 || 戎昱 |- | 231098091 || 刘棣文 |- | 231098166 || 陈展 |- | 231200035 || 葛翰飞 |- | 231220006 || 陆华均 |- | 231220019 || 何云天 |- | 231220036 || 周楚函 |- | 231220049 || 张泽宇 |- | 231220065 ||...") originally created as "Homework1 提交名单"

07:2707:27, 3 March 2025 概率论与数理统计 (Spring 2025)/Entropy and volume of Hamming balls (hist | edit) [3,052 bytes] Etone (talk | contribs) (Created page with "在求解抛掷公平硬币（fair coin）的尾概率时，我们经常会需要分析如下二项式系数求和： :<math>\sum_{k=0}^r{n\choose k}</math>，对于某个<math>1\le r\le n</math> 这其实等价与求一个 <math>n</math> 维汉明空间中半径为 <math>r</math> 的球的体积。 :{|border="2" width="100%" cellspacing="4" cellpadding="3" rules="all" style="margin:1em 1em 1em 0; border:solid 1px #AAAAAA; border-collapse:collapse;empty-cells:show;" | :'...")

12:0912:09, 25 February 2025 组合数学 (Fall 2025)/Generating functions (hist | edit) [25,549 bytes] Etone (talk | contribs) (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...")

12:0412:04, 19 February 2025 概率论与数理统计 (Spring 2025)/Problem Set 1 (hist | edit) [10,255 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 1== Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\mathbf{Pr})</math>. <h2 id="problem-2-principle-of-inclusion-and-exclusion">Problem 1 (Principle of Inclusion and Exclusion)</h2> Let <math>n\ge 1</math> be a positive integer and <math>A_1,A_...")

09:2809:28, 18 February 2025 组合数学 (Spring 2025)/Course materials (hist | edit) [1,438 bytes] Gispzjz (talk | contribs) (Created page with "== Textbooks == {|border="2" cellspacing="4" cellpadding="3" rules="all" style="margin:1em 1em 1em 0; border:solid 1px #AAAAAA; border-collapse:collapse;empty-cells:show;" |border|100px |width="100%"| :J. H. van Lint and R. M. Wilson. ''A course in Combinatorics, 2nd Edition.'' Cambridge University Press, 2001. |- |border|100px|| :S. Jukna. ''Extremal Combinatorics: With Applications in Computer Science, 2nd Edition...")
09:2309:23, 18 February 2025 组合数学 (Spring 2025)/Basic enumeration (hist | edit) [39,712 bytes] Gispzjz (talk | contribs) (Created page with "== Basic Enumeration == The three basic rules for enumeration are: *'''The sum rule''': for any '''''disjoint''''' finite sets <math>S</math> and <math>T</math>, the cardinality of the union <math>|S\cup T|=|S|+|T|</math>. *'''The product rule''': for any finite sets <math>S</math> and <math>T</math>, the cardinality of the Cartesian product <math>|S\times T|=|S|\cdot|T|</math>. *'''The bijection rule''': if there exists a bijection between finite sets <math>S</math> a...")
09:2109:21, 18 February 2025 组合数学 (Fall 2025)/Basic enumeration (hist | edit) [39,712 bytes] Gispzjz (talk | contribs) (Created page with "== Basic Enumeration == The three basic rules for enumeration are: *'''The sum rule''': for any '''''disjoint''''' finite sets <math>S</math> and <math>T</math>, the cardinality of the union <math>|S\cup T|=|S|+|T|</math>. *'''The product rule''': for any finite sets <math>S</math> and <math>T</math>, the cardinality of the Cartesian product <math>|S\times T|=|S|\cdot|T|</math>. *'''The bijection rule''': if there exists a bijection between finite sets <math>S</math> a...")
09:1809:18, 18 February 2025 组合数学 (Spring 2025) (hist | edit) [11,483 bytes] Gispzjz (talk | contribs) (Created page with " This is the webpage for the ''Combinatorics'' class of Spring 2024. Students who take this class should check this page periodically for content updates and new announcements. = Announcement = = Course info = * '''Instructor ''': 尹一通 ([http://tcs.nju.edu.cn/yinyt/ homepage]) :* '''email''': yinyt@nju.edu.cn :* '''office''': 计算机系 804 * '''Teaching assistant''': ** [https://lhy-gispzjz.github.io/ 刘弘洋] ([mailto:liuhongyang@smail.nju.edu.cn liuhongy...") Tag: Visual edit

07:3007:30, 16 February 2025 计算方法 Numerical method (Spring 2025) (hist | edit) [5,910 bytes] Kvrmnks (talk | contribs) (create page) Tag: Visual edit: Switched
07:3007:30, 16 February 2025 概率论与数理统计 (Spring 2025) (hist | edit) [19,684 bytes] Zhangxy (talk | contribs) (Created page with "{{Infobox |name = Infobox |bodystyle = |title = '''概率论与数理统计''' '''Probability Theory''' & '''Mathematical Statistics''' |titlestyle = |image = |imagestyle = |caption = |captionstyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =Instructor |label1 = |data1 = |header2 = |label2 = |data2 = '''尹一通''' |header3 = |label3 = Em...")

11:4311:43, 14 February 2025 计算复杂性 (Spring 2025) (hist | edit) [3,036 bytes] Roundgod (talk | contribs) (Created page with "{{Infobox |name = Infobox |bodystyle = |title = 计算复杂性 Computational Complexity |titlestyle = |image = |imagestyle = |caption = |captionstyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 = Instructor |label1 = |data1 = |header2 = |label2 = |data2 = 姚鹏晖 |header3 = |label3 = Email |data3 = pyao@nju.edu.cn |header4 = |label4= Off...")

04:4804:48, 12 January 2025 高级算法 (Fall 2024)/Final提交名单 (hist | edit) [1,275 bytes] Zhangyiyao (talk | contribs) (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211220076 || 杨景越 |- | 211220152 || 吴振宇 |- | 211250001 || 鞠哲 |- | 211250044 || 朱家辰 |- | 211250182 || 胡皓明 |- | 211502020 || 周相羽 |- | 211820282 || 彭钰朝 |- | 211830008 || 缪天顺 |- | 221220002 || 沈均文 |- | 221502010 || 梁志浩 |- | 221840188 || 谭泽晖 |- | 502023330043 || 吕铸恒 |- | 502024330003 || 陈思睿 |- | 5020...")

19:1219:12, 6 January 2025 高级算法 (Spring 2025) (hist | edit) [6,786 bytes] Liumingmou (talk | contribs) (Created page with "{{Infobox |name = Infobox |bodystyle = |title = 高级算法 Advanced Algorithms |titlestyle = |image = |imagestyle = |caption = |captionstyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =任课教师 |label1 = |data1 = |header2 = |label2 = |data2 = '''刘明谋''' |header3 = |label3 = 电子邮件 |data3 = lmm@nju.edu.cn |header4 = |label4=...")

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