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- 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...")
- 13:27, 9 April 2024 组合数学 (Fall 2024)/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...")
- 13:26, 9 April 2024 组合数学 (Fall 2024)/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...")
- 13:33, 8 April 2024 概率论与数理统计 (Spring 2024)/第一次作业提交名单 (hist | edit) [1,975 bytes] Zouzongrui (talk | contribs) (Created page with "<center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 221240092 || 杨煜申 |- | 221240007 || 郭宇轩 |- | 221180115 || 黄文睿 |- | 221900051 || 吴子奕 |- | 221900156 || 韩加瑞 |- | 221900332 || 王卫东 |- | 221240068 || 周凡淇 |- | 221240093 || 陈力峥 |- | 221240035 || 李想 |- | 线上 || 仇嘉明 |- | 221900500 || 李亦非 |- | 221240087 || 顾鹏 |- | 221870066 || 陶心悦 |- | 221240066 || 张植翔 |- | 215220012 || 吕茄...")
- 08:41, 8 April 2024 概率论与数理统计 (Spring 2024)/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...")
- 13:44, 3 April 2024 计算复杂性 (Spring 2024)/第一次作业提交名单 (hist | edit) [885 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 |- | 201502003 || 丁显浓 |- | 201840009 || 田永上 |- | 211250001 || 鞠哲 |- | 211502001 || 任楷文 |- | 211502005 || 黄逸飞 |- | 211502008 || 李诚希 |- | 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 |- | 221840...")
- 05:05, 27 March 2024 计算方法 Numerical method (Spring 2024)/Homework2 提交名单 (hist | edit) [2,225 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 |- | 221840201 || 钟锦立 |- | 221240027 || 唐诗博 |- | 221220067 || 刘思远 |- | 221502009 || 李嘉洲 |- | 221220118 || 但佳霖 |- | 221502005 || 王昕浩 |- | 221870052 || 吴隽雨 |- | 221220146 || 王浩然 |- | 221502001 || 赵子轩 |- | 221220029 || 陈俊翰 |- | 221240093 || 陈力峥 |- | 221502006 || 张文权 |- | 221502016 || 张晓言 |- | 221220...")
- 04:27, 27 March 2024 组合数学 (Fall 2024)/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''...")
- 02:21, 20 March 2024 Assignment 1, Spring 2024 (hist | edit) [3,330 bytes] Etone (talk | contribs) (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...")
- 15:55, 19 March 2024 General Circulation(Spring 2024) (hist | edit) [2,624 bytes] Etone (talk | contribs) (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...")
- 12:42, 19 March 2024 组合数学 (Fall 2024)/Problem Set 1 (hist | edit) [1,789 bytes] Gispzjz (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...")
- 09:51, 19 March 2024 组合数学 (Fall 2024)/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...")
- 05:30, 19 March 2024 概率论与数理统计 (Spring 2024)/Problem Set 1 (hist | edit) [12,854 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 1== <p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\mathbf{Pr})</math>.</p> <h2 id="problem-2-principle-of-inclusion-and-exclusion">Problem 1 (Principle of Inclusion and Exclusion)</h2> <p>Let <math>n\ge 1</math> be a positive integer and <math>A_1,A_2...")
- 15:51, 18 March 2024 概率论与数理统计 (Spring 2024)/Karger's min-cut algorithm (hist | edit) [12,035 bytes] Etone (talk | contribs) (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...")
- 06:52, 13 March 2024 计算方法 Numerical method (Spring 2024)/Homework1 提交名单 (hist | edit) [2,364 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 |- | 211240035 || 王祉天 |- | 221220158 || 颜伟坤 |- | 221870199 || 黄一凡 |- | 221502010 || 梁志浩 |- | 221220118 || 但佳霖 |- | 221502009 || 李嘉洲 |- | 221870222 || 刘烨 |- | 221240092 || 杨煜申 |- | 221220019 || 洪观澜 |- | 221220034 || 王旭 |- | 221502016 || 张晓言 |- | 221502001 || 赵子轩 |- | 221502005 || 王昕浩 |- | 221220067 |...")
- 02:56, 12 March 2024 Quantum (hist | edit) [24,945 bytes] Etone (talk | contribs) (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...")
- 11:41, 6 March 2024 组合数学 (Fall 2024)/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...")
