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15:5415:54, 3 October 2022 diff hist +217 高级算法 (Fall 2022) →Lecture Notes
15:5115:51, 3 October 2022 diff hist +97 高级算法 (Fall 2022) →Lecture Notes
15:4915:49, 3 October 2022 diff hist +5,755 N 高级算法 (Fall 2022)/Basic tail inequalities Created page with "=Markov's Inequality= One of the most natural information about a random variable is its expectation, which is the first moment of the random variable. Markov's inequality draws a tail bound for a random variable from its expectation. {{Theorem |Theorem (Markov's Inequality)| :Let <math>X</math> be a random variable assuming only nonnegative values. Then, for all <math>t>0</math>, ::<math>\begin{align} \Pr[X\ge t]\le \frac{\mathbf{E}[X]}{t}. \end{align}</math> }} {{Proo..." current
15:4815:48, 3 October 2022 diff hist +25,717 N 高级算法 (Fall 2022)/Hashing and Sketching Created page with "=Distinct Elements= Consider the following problem of '''counting distinct elements''': Suppose that <math>\Omega</math> is a sufficiently large universe. *'''Input:''' a sequence of (not necessarily distinct) elements <math>x_1,x_2,\ldots,x_n\in\Omega</math>; *'''Output:''' an estimation of the total number of distinct elements <math>z=|\{x_1,x_2,\ldots,x_n\}|</math>. A straightforward way of solving this problem is to maintain a dictionary data structure, which costs..." current
15:4715:47, 3 October 2022 diff hist +1 高级算法 (Fall 2022)/Limited independence →2-universal hash families current
15:4515:45, 3 October 2022 diff hist +8,181 高级算法 (Fall 2022)/Balls into bins No edit summary current
15:4515:45, 3 October 2022 diff hist +1 高级算法 (Fall 2022)/Balls into bins →2-universal hash families
15:3915:39, 3 October 2022 diff hist +13,598 高级算法 (Fall 2022)/Balls into bins No edit summary
15:3815:38, 3 October 2022 diff hist +5,762 高级算法 (Fall 2022)/Balls into bins →Coupon Collector
15:3615:36, 3 October 2022 diff hist +157 高级算法 (Fall 2022) →Lecture Notes

08:2108:21, 30 September 2022 diff hist +121 General Circulation(Fall 2022) →Course Slides

04:1504:15, 29 September 2022 diff hist +9 Assignment 1, Fall 2022 →下载区 current
02:5602:56, 29 September 2022 diff hist +21 General Circulation(Fall 2022) No edit summary

13:3913:39, 28 September 2022 diff hist +7 General Circulation(Fall 2022) →Course Slides
13:3813:38, 28 September 2022 diff hist +71 General Circulation(Fall 2022) →Course Slides
13:3713:37, 28 September 2022 diff hist +21 General Circulation(Fall 2022) →Course Slides

08:5408:54, 26 September 2022 diff hist +175 General Circulation(Fall 2022) →Assignments
08:5308:53, 26 September 2022 diff hist 0 General Circulation(Fall 2022) →Assignments
08:3308:33, 26 September 2022 diff hist +407 General Circulation(Fall 2022) →Course Slides
08:2808:28, 26 September 2022 diff hist +3 Assignment 1, Fall 2022 →Bonus Question
08:2808:28, 26 September 2022 diff hist +228 Assignment 1, Fall 2022 No edit summary
08:1308:13, 26 September 2022 diff hist +6 Assignment 1, Fall 2022 →On the netcdf file
08:0908:09, 26 September 2022 diff hist −17 Assignment 1, Fall 2022 →下载区
08:0808:08, 26 September 2022 diff hist +2,560 N Assignment 1, Fall 2022 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..."
08:0708:07, 26 September 2022 diff hist −24 General Circulation(Fall 2021) No edit summary current
08:0508:05, 26 September 2022 diff hist +5,196 General Circulation(Fall 2022) No edit summary
08:0408:04, 26 September 2022 diff hist +1,062 General Circulation(Fall 2022) No edit summary
08:0308:03, 26 September 2022 diff hist +2,249 N General Circulation(Fall 2022) 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..."
08:0208:02, 26 September 2022 diff hist +99 Main Page No edit summary Tag: Visual edit: Switched

11:4811:48, 21 September 2022 diff hist +15,811 N 高级算法 (Fall 2022)/Limited independence Created page with "= <math>k</math>-wise independence = Recall the definition of independence between events: {{Theorem |Definition (Independent events)| :Events <math>\mathcal{E}_1, \mathcal{E}_2, \ldots, \mathcal{E}_n</math> are '''mutually independent''' if, for any subset <math>I\subseteq\{1,2,\ldots,n\}</math>, ::<math>\begin{align} \Pr\left[\bigwedge_{i\in I}\mathcal{E}_i\right] &= \prod_{i\in I}\Pr[\mathcal{E}_i]. \end{align}</math> }} Similarly, we can define independence between..."
11:4811:48, 21 September 2022 diff hist +75 高级算法 (Fall 2022) →Lecture Notes
11:4711:47, 21 September 2022 diff hist +11,376 N 高级算法 (Fall 2022)/Balls into bins Created page with "=Balls into Bins= Consider throwing <math>m</math> balls into <math>n</math> bins uniformly and independently at random. This is equivalent to a random mapping <math>f:[m]\to[n]</math>. Needless to say, random mapping is an important random model and may have many applications in Computer Science, e.g. hashing. We are concerned with the following three questions regarding the balls into bins model: * birthday problem: the probability that every bin contains at most one..."
11:4711:47, 21 September 2022 diff hist +61 高级算法 (Fall 2022) →Lecture Notes
11:4611:46, 21 September 2022 diff hist 0 高级算法 (Fall 2022) →Lecture Notes
11:4611:46, 21 September 2022 diff hist −122 高级算法 (Fall 2022) →Lecture Notes
11:4611:46, 21 September 2022 diff hist +371 高级算法 (Fall 2022) →Lecture Notes

12:2312:23, 18 September 2022 diff hist +14 高级算法 (Fall 2022) No edit summary
12:2212:22, 18 September 2022 diff hist 0 高级算法 (Fall 2022) →Course info

08:0708:07, 13 September 2022 diff hist −71 高级算法 (Fall 2022) →Lecture Notes
05:4305:43, 13 September 2022 diff hist +6,210 N 高级算法 (Fall 2022)/Finite Field Basics Created page with "=Field= Let <math>S</math> be a set, '''closed''' under binary operations <math>+</math> (addition) and <math>\cdot</math> (multiplication). It gives us the following algebraic structures if the corresponding set of axioms are satisfied. {|class="wikitable" !colspan="7"|Structures !Axioms !Operations |- |rowspan="9" style="background-color:#ffffcc;text-align:center;"|'''''field''''' |rowspan="8" style="background-color:#ffffcc;text-align:center;"|'''''commutative<br>rin..." current
05:4305:43, 13 September 2022 diff hist +30,540 N 高级算法 (Fall 2022)/Fingerprinting 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..." current
05:4205:42, 13 September 2022 diff hist +73 高级算法 (Fall 2022) →Lecture Notes
05:4205:42, 13 September 2022 diff hist +134 高级算法 (Fall 2022) →Lecture Notes

09:1109:11, 6 September 2022 diff hist 0 高级算法 (Fall 2022) →Lecture Notes
09:0909:09, 6 September 2022 diff hist +184 高级算法 (Fall 2022) →Lecture Notes

07:3107:31, 5 September 2022 diff hist +17,328 N 高级算法 (Fall 2022)/Probability Basics Created page with "=Probability Space= The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one of the greatest mathematician of the 20th century, who advanced various very different fields of mathematics. {{Theorem|Definition (Probability Space)| A '''probability space''' is a triple <math>(\Omega,\Sigma,\Pr)</math>. *<math>\Omega</math> is a set, called the '''sample space'''. *<math>\Sigma\subseteq 2^{\Omega}</math> is the..." current

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