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24 April 2024
- 03:0203:02, 24 April 2024 diff hist +1,091 组合数学 (Spring 2024) →Concepts current
- 02:5702:57, 24 April 2024 diff hist +27,151 N 组合数学 (Fall 2024)/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..." current
- 02:5702:57, 24 April 2024 diff hist +157 组合数学 (Spring 2024) →Lecture Notes
22 April 2024
- 03:1403:14, 22 April 2024 diff hist +5,139 N 概率论与数理统计 (Spring 2024)/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..." current
- 03:1303:13, 22 April 2024 diff hist +7,005 N 概率论与数理统计 (Spring 2024)/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..." current
- 03:1203:12, 22 April 2024 diff hist +8,968 N 概率论与数理统计 (Spring 2024)/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..." current
- 03:1203:12, 22 April 2024 diff hist +325 概率论与数理统计 (Spring 2024) →Lectures
15 April 2024
- 14:5814:58, 15 April 2024 diff hist +750 概率论与数理统计 (Spring 2024) →Concepts
- 14:5714:57, 15 April 2024 diff hist +155 概率论与数理统计 (Spring 2024) →Lectures
- 14:5514:55, 15 April 2024 diff hist 0 概率论与数理统计 (Spring 2024) →Lectures
- 14:5414:54, 15 April 2024 diff hist +189 概率论与数理统计 (Spring 2024) →Lectures
12 April 2024
- 09:0209:02, 12 April 2024 diff hist −1 组合数学 (Spring 2024) →Lecture Notes
- 09:0109:01, 12 April 2024 diff hist +186 组合数学 (Spring 2024) →Lecture Notes
9 April 2024
- 13:2713:27, 9 April 2024 diff hist +14,440 N 组合数学 (Fall 2024)/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..." current
- 13:2613:26, 9 April 2024 diff hist +17,231 N 组合数学 (Fall 2024)/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..." current
- 13:2613:26, 9 April 2024 diff hist +87 组合数学 (Spring 2024) →Lecture Notes
- 13:2413:24, 9 April 2024 diff hist +80 组合数学 (Spring 2024) →Lecture Notes
8 April 2024
- 08:4208:42, 8 April 2024 diff hist +985 概率论与数理统计 (Spring 2024) →Concepts
- 08:4108:41, 8 April 2024 diff hist +11,838 N 概率论与数理统计 (Spring 2024)/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..." current
- 08:4008:40, 8 April 2024 diff hist +126 概率论与数理统计 (Spring 2024) →Lectures
27 March 2024
- 04:3704:37, 27 March 2024 diff hist +78 组合数学 (Spring 2024) →Concepts
- 04:3604:36, 27 March 2024 diff hist +79 组合数学 (Spring 2024) →Concepts
- 04:3504:35, 27 March 2024 diff hist +274 组合数学 (Spring 2024) →Concepts
- 04:2804:28, 27 March 2024 diff hist +1,749 组合数学 (Spring 2024) →Concepts
- 04:2704:27, 27 March 2024 diff hist +19,696 N 组合数学 (Fall 2024)/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''..." current
- 04:2604:26, 27 March 2024 diff hist +105 组合数学 (Spring 2024) →Lecture Notes
26 March 2024
- 18:5518:55, 26 March 2024 diff hist +57 组合数学 (Spring 2024) →Lecture Notes
25 March 2024
- 09:5909:59, 25 March 2024 diff hist +2,781 概率论与数理统计 (Spring 2024) →Concepts
- 09:5809:58, 25 March 2024 diff hist 0 概率论与数理统计 (Spring 2024) →Lectures
- 09:5809:58, 25 March 2024 diff hist +140 概率论与数理统计 (Spring 2024) →Lectures
20 March 2024
- 02:4002:40, 20 March 2024 diff hist −4 Assignment 1, Spring 2024 No edit summary current
- 02:3802:38, 20 March 2024 diff hist +23 Assignment 1, Spring 2024 →Question #2
- 02:3802:38, 20 March 2024 diff hist +24 Assignment 1, Spring 2024 →Question #1
- 02:3102:31, 20 March 2024 diff hist 0 Assignment 1, Spring 2024 →Files to download
- 02:3002:30, 20 March 2024 diff hist +345 Assignment 1, Spring 2024 No edit summary
- 02:2602:26, 20 March 2024 diff hist −1 Assignment 1, Spring 2024 →Question #1
- 02:2602:26, 20 March 2024 diff hist +2 Assignment 1, Spring 2024 →Question #1
- 02:2602:26, 20 March 2024 diff hist +322 Assignment 1, Spring 2024 →Question #1
- 02:2102:21, 20 March 2024 diff hist +2,619 N Assignment 1, Spring 2024 Created page with "==Question #1== 请使用多年(>20年)的NCEP/NCAR月平均再分析资料,画出各季节(至少画出冬夏两季)纬向平均温度场、纬向平均纬向风场的高度-纬度剖面分布,并简述其分布特征和季节变化特征。 ==Question #2== 请使用多年(>20年)的NCEP/NCAR月平均再分析资料,画出各季节(至少画出冬夏两季)温度场、纬向风场在各高度(850、500、100 hPa, 对于温度场请再画..."
- 01:3901:39, 20 March 2024 diff hist +2 General Circulation(Spring 2024) →Assignments current
- 01:3701:37, 20 March 2024 diff hist +2 General Circulation(Spring 2024) No edit summary
19 March 2024
- 16:0216:02, 19 March 2024 diff hist −12 General Circulation(Spring 2024) No edit summary
- 16:0116:01, 19 March 2024 diff hist +669 General Circulation(Spring 2024) No edit summary
- 15:5715:57, 19 March 2024 diff hist −42 General Circulation(Spring 2024) No edit summary
- 15:5515:55, 19 March 2024 diff hist +2,005 N General Circulation(Spring 2024) Created page with "{{Infobox |name = Infobox |bodystyle = |title = 大气环流 <br> General Circulation of the Atmosphere |titlestyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =Instructor |label1 = |data1 = |header2 = |label2 = |data2 = 张洋 |header3 = |label3 = Email |data3 = yangzhang@nju.edu.cn |header4 = |label4= office |data4= 仙林大气楼 B410 |header5 = Class |label5 = |data5 = |hea..."
- 15:5315:53, 19 March 2024 diff hist +4 Main Page No edit summary current Tag: Visual edit: Switched
- 14:4414:44, 19 March 2024 diff hist +3 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →Karger算法的分析 current
- 14:4214:42, 19 March 2024 diff hist +1 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →Karger算法的分析
- 14:4214:42, 19 March 2024 diff hist +8 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →一个概率法推论
- 13:5013:50, 19 March 2024 diff hist −1 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →Karger算法
- 13:4813:48, 19 March 2024 diff hist 0 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →Karger算法
- 13:4613:46, 19 March 2024 diff hist +44 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm No edit summary
- 13:4413:44, 19 March 2024 diff hist −24 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →Karger算法
- 13:4413:44, 19 March 2024 diff hist +2 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →Karger算法
- 13:4213:42, 19 March 2024 diff hist −1 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →一个概率法推论
- 13:4113:41, 19 March 2024 diff hist +204 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →一个概率法推论
- 13:3913:39, 19 March 2024 diff hist +22 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →一个概率法推论
- 13:3813:38, 19 March 2024 diff hist −546 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →一个概率法推论
- 13:2413:24, 19 March 2024 diff hist +174 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →一个概率法推论
- 13:1913:19, 19 March 2024 diff hist +33 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →Karger算法的分析
- 13:1713:17, 19 March 2024 diff hist 0 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →Karger算法的分析
- 13:1713:17, 19 March 2024 diff hist −129 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →A Consequence of the Probabilistic Method
- 13:1213:12, 19 March 2024 diff hist +6 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →Karger算法的分析
- 13:1213:12, 19 March 2024 diff hist +49 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →Karger算法的分析
- 13:1013:10, 19 March 2024 diff hist −1,961 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →Analysis of Karger's Algorithm
- 12:0512:05, 19 March 2024 diff hist +9 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →Karger算法
- 12:0412:04, 19 March 2024 diff hist −830 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm →Karger算法
- 10:3710:37, 19 March 2024 diff hist −526 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm No edit summary
- 09:5109:51, 19 March 2024 diff hist +33,970 N 组合数学 (Fall 2024)/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..." current
- 09:5009:50, 19 March 2024 diff hist +68 组合数学 (Spring 2024) →Lecture Notes
- 09:4409:44, 19 March 2024 diff hist +179 概率论与数理统计 (Spring 2024) →Lectures
18 March 2024
- 15:5115:51, 18 March 2024 diff hist +15,498 N 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm Created page with "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 :<math>C=E(S,T..."
13 March 2024
- 16:0416:04, 13 March 2024 diff hist +101 概率论与数理统计 (Spring 2024) →Lectures
12 March 2024
- 02:5602:56, 12 March 2024 diff hist +24,945 N Quantum Created page with "= 量子算法与物理实现研讨会= ==时间地点 == *'''<font size=4> 2019年10月19、20日: 9 am--5 pm.</font>''' * <font size=4> 南京大学 计算机科学与技术系 (南京大学仙林校区常州楼)111报告厅</font> [http://map.baidu.com/?l=&s=s%26wd%3D南京仙林大道163号++南京大学(仙林校区)计算机系楼 在线地图] ==联系人与联系方式 == * 姚鹏晖 pyao@nju.edu.cn * 张利剑 lijian.zhang@nju.edu.cn ==会议主旨..." current
6 March 2024
- 11:4211:42, 6 March 2024 diff hist +1 组合数学 (Spring 2024) →Lecture Notes
- 11:4111:41, 6 March 2024 diff hist +25,549 N 组合数学 (Fall 2024)/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..." current
- 11:4111:41, 6 March 2024 diff hist +229 组合数学 (Spring 2024) →Lecture Notes
4 March 2024
- 08:5208:52, 4 March 2024 diff hist +125 概率论与数理统计 (Spring 2024) →Lectures
27 February 2024
- 10:5210:52, 27 February 2024 diff hist +44 Main Page →Home Pages for Courses and Seminars
- 10:3910:39, 27 February 2024 diff hist +39,712 N 组合数学 (Fall 2024)/Basic enumeration 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..." current
- 10:3710:37, 27 February 2024 diff hist +76 组合数学 (Spring 2024) →Lecture Notes
- 07:4407:44, 27 February 2024 diff hist −153 概率论与数理统计 (Spring 2023) →Assignments current
26 February 2024
- 09:3609:36, 26 February 2024 diff hist +49 概率论与数理统计 (Spring 2024) →Course info
- 09:3509:35, 26 February 2024 diff hist +12 概率论与数理统计 (Spring 2024) No edit summary
- 09:3409:34, 26 February 2024 diff hist +1 概率论与数理统计 (Spring 2024) No edit summary
- 09:3409:34, 26 February 2024 diff hist +1,010 概率论与数理统计 (Spring 2024) →Concepts
- 09:3109:31, 26 February 2024 diff hist +50 概率论与数理统计 (Spring 2024) →Lectures
18 February 2024
- 07:4007:40, 18 February 2024 diff hist +1,438 N 组合数学 (Spring 2024)/Course materials 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..." current
- 07:3907:39, 18 February 2024 diff hist −4 组合数学 (Spring 2024) →Course info Tag: Manual revert
- 07:3907:39, 18 February 2024 diff hist +4 组合数学 (Spring 2024) →Course info Tag: Reverted
- 07:3807:38, 18 February 2024 diff hist +4,631 N 组合数学 (Spring 2024) Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>组合数学 <br> Combinatorics</font> |titlestyle = |image = |imagestyle = |caption = |captionstyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =Instructor |label1 = |data1 = |header2 = |label2 = |data2 = 尹一通 |header3 = |label3 = Email |data3 = yinyt@nju.edu.cn |header4 = |label4= office |data4=..."
- 07:3407:34, 18 February 2024 diff hist +4 概率论与数理统计 (Spring 2024) →Course info
- 07:3307:33, 18 February 2024 diff hist +6,287 N 概率论与数理统计 (Spring 2024) Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>'''概率论与数理统计'''<br> '''Probability Theory''' <br> & '''Mathematical Statistics'''</font> |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..."
- 07:2307:23, 18 February 2024 diff hist +123 Main Page →Home Pages for Courses and Seminars Tag: Visual edit: Switched
3 December 2023
- 12:4112:41, 3 December 2023 diff hist +13 高级算法 (Fall 2023) →Lecture Notes
- 12:4012:40, 3 December 2023 diff hist +14 高级算法 (Fall 2023) →Lecture Notes
- 12:3912:39, 3 December 2023 diff hist +64 高级算法 (Fall 2023) →Lecture Notes
- 12:3212:32, 3 December 2023 diff hist 0 高级算法 (Fall 2023) →Lecture Notes
29 November 2023
- 16:3316:33, 29 November 2023 diff hist +2,459 N Assignment 4, Fall 2023 Created page with "在第四章中,我们从准地转近似下的纬向平均风场、温度场的趋势方程出发,定义了E-P通量。但是该定义下的E-P通量并没有考虑到大气湿过程的影响。如果从第三章介绍的水汽方程出发,我们可以按照以下步骤定义出一个包含大气大尺度运动中湿过程作用的广义的E-P通量。 1)在准地转近似下,如果我们按照对热力学方程的简化方法,将比湿(specific humidity..." current
- 16:3316:33, 29 November 2023 diff hist +54 General Circulation(Fall 2023) →Assignments current