I*********t
发帖数: 5258 | 1 其实你可以“证明”1+1=2的
http://mathforum.org/library/drmath/view/51551.html
The proof starts from the Peano Postulates, which define the natural numbers
N. N is the smallest set satisfying these postulates:
P1. 1 is in N.
P2. If x is in N, then its "successor" x' is in N.
P3. There is no x such that x' = 1.
P4. If x isn't 1, then there is a y in N such that y' = x.
P5. If S is a subset of N, 1 is in S, and the implication
(x in S => x' in S) holds, then S = N.
Then you have to defi... 阅读全帖 |
|
t******n
发帖数: 2939 | 2 ☆─────────────────────────────────────☆
firearasi (firearasi) 于 (Thu May 23 18:10:13 2013, 美东) 提到:
1. 假设p1=2,p2=3,...,pn 是全部的素数...
2. 令 N=p1*p2*...*pn+1, 显然 N比 p1,p2,...,pn都大,因此不再p1,p2,..,pn,中, 所
以根据1, N是一个合数.
3. N是合数,那么必然能够被一个素数整除, 根据1, 所有的素数是p1,..., pn, 所以必
然有其中之一, 比如pj, 能整除N, 特别的, N 除以pj余数为0
4. N= pj*(p2*...*pn 括号内排除pj)+1=pj*something+1, 因此, N除以pj余数为1
5. 3 和 4 矛盾,N不能同时除以pj余0,而且余1.
现在有几种推理方法
6(I), 3和4矛盾, 矛盾的根源在于 假设1 是完全错误的, 于是 证毕,素数无穷 Q.E.D
或者走下列路线(l63路线)
6(II), 3和4矛盾的一个最近的根源来自于第3部的N是合数, ... 阅读全帖 |
|
d**********o
发帖数: 1321 | 3 针峰相对(6)
老师讲完No Free Lunch Theorem，已经到了四月下旬。
接下来周一的课（ 04、21、2014 ），代课老师又重复了那“Kolmogov Complexity”
，和Schema Theorem / Building Block Hypothesis, Deceptive Problems.
The complexity of a thing is defined by the smallest program that will
generate it.
How complex is the "source code" to generate? Kolmogov Complexity says
Program A cannot generate a program more complex than itself.
For Deceptive problems, Deception can be used to measure problem difficulty.
这堂课结束前，老师举一个什么例子的时候，居然说到来自非洲等穷困国家、地方的孩
子撒傻... 阅读全帖 |
|
d**********o
发帖数: 1321 | 4 针峰相对(6)
老师讲完No Free Lunch Theorem，已经到了四月下旬。
接下来周一的课（ 04、21、2014 ），代课老师又重复了那“Kolmogov Complexity”
，和Schema Theorem / Building Block Hypothesis, Deceptive Problems.
The complexity of a thing is defined by the smallest program that will
generate it.
How complex is the "source code" to generate? Kolmogov Complexity says
Program A cannot generate a program more complex than itself.
For Deceptive problems, Deception can be used to measure problem difficulty.
这堂课结束前，老师举一个什么例子的时候，居然说到来自非洲等穷困国家、地方的孩
子撒傻... 阅读全帖 |
|
y*f
发帖数: 2202 | 5 Infinite monkey theorem
From Wikipedia, the free encyclopedia
Given enough time, a chimp punching at random on a typewriter would almost
surely type out all of Shakespeare's plays.
The infinite monkey theorem states that a monkey hitting keys at random on a
typewriter keyboard for an infinite amount of time will almost surely type
a given text, such as the complete works of William Shakespeare. |
|
A******u
发帖数: 1279 | 6 The problem, as I see it, is that entropy is well defined in classical
mechanics. But the Boltzmann equation implicitly involves non-integrability
in the "Stosszahlansatz". So Boltzmann's H-theorem is a bit problematic. But
Gibbs did have a cleaner proof of the entropy theorem from a statistical
viewpoint. Simply put, in the classical realm the time is arrowed.
It is difficult in the quantum world. Von Neumann had a definition of
entropy for a quantal system based on density matrix. It has the a... 阅读全帖 |
|
d********f
发帖数: 43471 | 7 http://www.cnn.com/2016/03/16/europe/fermats-last-theorem-solve
It was a problem that had baffled mathematicians for centuries -- until
British professor Andrew Wiles set his mind to it.
"There are no whole number solutions to the equation xn + yn = zn when n is
greater than 2."
Otherwise known as "Fermat's Last Theorem," this equation was first posed by
French mathematician Pierre de Fermat in 1637, and had stumped the world's
brightest minds for over 300 years.
难怪这题能成为民科最爱 |
|
n********n
发帖数: 8336 | 8 The existence of God using logical absolutes
This is an attempt to demonstrate the existence of God using logical
absolutes. The oversimplified argument, which is expanded in outline form
below, goes as follows: Logical absolutes exist. Logical absolutes are
conceptual by nature--are not dependent on space, time, physical properties,
or human nature. They are not the product of the physical universe (space,
time, matter) because if the physical universe were to disappear, logical
absolutes w... 阅读全帖 |
|
x*******i
发帖数: 59 | 9 Please read the novel first. Not only for understanding the dark forest
conjecture, but also for enjoying the nice story.
The dark forest conjecture tries to answer a question "if there are a lot of
civilizations in the space, why we haven't received any type of
communication signal". The dark forest conjecture says it is because the
civilizations are afraid of doing so.Why? because there will be a very high
probability that the civilization will be terminated if it tries to
broadcast signal.
Th... 阅读全帖 |
|
f***e
发帖数: 332 | 10 WEI ZHANG TO RECEIVE 2010 SASTRA RAMANUJAN PRIZE
http://www.math.ufl.edu/sastra-prize/2010.html
The 2010 SASTRA Ramanujan Prize will be awarded to Wei Zhang, who is now a
Benjamin Pierce Instructor at the Department of Mathematics, Harvard
University,
USA. This annual prize which was established in 2005, is for outstanding
contributions by very young mathematicians to areas influenced by the genius
Srinivasa Ramanujan. The age limit for the prize has been set at 32 because
Ramanujan achieved so ... 阅读全帖 |
|
AM
发帖数: 141 | 11 原文在这里，文章中的照片都贴不到版上，为啥？打倒老邢。
http://www.mysanco.com/wenda/index.php?class=discuss&action=que
张益唐和北大数学78级
作者：香港浸会大学 --- 汤涛
--- 谨以此文纪念陈景润诞辰80周年；他影响了那个难忘的时代
2013年是北京大学数学系成立100周年。百年大庆，作为校友，总觉得应该写点什么作
为纪念。
1904年，清政府颁布的《钦定学堂章程》规定“高等算学”隶属格致科（现在称理科）
，并且规定了算学门的课程。辛亥革命后，京师大学堂于1912年5 月1日改名为国立北
京大学。同年公布的“民国元年所订之大学学制及其学科”中格致科改名为理科，其中
包括数学门。1913年秋，北京大学数学门招收新生，标志着中国现代第一个大学数学系
正式开始教学活动。北大数学的早期学生张国焘因为后期的政治生涯为数学系增添了些
许传奇。
北大数学的一百年培养了大量的人才，先后培养出6000多名本科生、1000多名硕士、博
士毕业生，一大批优秀的数学家和其他方面的专家分布在各行业， 许多人成绩斐然，
得到社会各界的高度评价... 阅读全帖 |
|
g*****g
发帖数: 34805 | 12 我看你还是再读一遍CAP theorem吧。NoSQL如果完全支持ACID，就跟RDBMS的属性一样
了，那还叫
NoSQL干啥。NoSQL就是跟ACID不兼容的。Berkeley DB能支持ACID本质上是因为是单机
系统，你来个多机的Berkeley DB还能支持ACID我就服。
RDBMS支持ACID，是CA系统，NoSQL可以是CP或者AP，两者在CAP theorem下是互补的，
不是冲突的。 |
|
b*******g
发帖数: 603 | 13 是你提出这个傻逼言论我才友善提示你击败了 CAP theorem. 这之前你连这个名词都没
听说过。
没听说过 CAP theorem对高并发必然是外行， period. |
|
a*****g
发帖数: 19398 | 14 Number of legal Go positions
The 361 points on a 19x19 Go board can be colored empty, black, or white.
Only some of the 3^361 possible positions are legal, namely those where
every group of connected stones of the same color has an empty point
adjacent to it. In the position above, black stones at E18 and N9 lack such
``liberties'', making the position illegal. Due to its capture rule, the
positions that can arise in a game of Go are exactly the legal positions. On
Jan 20, 2016, the number of le... 阅读全帖 |
|
j***b
发帖数: 5901 | 15 documentclass是roport,分若干章，每章若干节。
定理编号想要得是带章节号的，比如Theorem 2.1.3等等，
结果总是显示成Theorem 2.13，也就是节号和定理好之间
没有点。这是怎么回事呢？ |
|
w****h
发帖数: 212 | 16 如果定义定理定义如下：
\newtheorem{Theorem}{Theorem}[section]
\newtheorem{Definition}{Definition}
\newtheorem{Assumption}{Assumption}
\begin{Definition} \label{T:defgms} xxxx
\end{Definition}
结果显示的definition为斜体、非粗，我想要正体、粗体格式，该如何设置？ |
|
s****u
发帖数: 5 | 17 \newtheorem{Theorem}{Theorem}[section]
\theoremstyle{definition}
\newtheorem{Definition}{Definition}
这样，定理是斜体的，定义是正体的，但是一般不会粗体的吧 |
|
w****h
发帖数: 212 | 18 如何给\newtheorem{Theorem}{Theorem}[section]
\theoremstyle{definition}
\newtheorem{Definition}{Definition}添加\bf?在哪里添加？ |
|
w****h
发帖数: 212 | 19 你可以看看如下：
\documentclass[10pt,conference,letterpaper,twocolumn]{IEEEtran}
\usepackage{amsfonts}
\pagestyle{plain}
\pagenumbering{arabic}
\usepackage{amsmath,multirow} % for subequations
\usepackage{subfigure,graphics,psfig,epsfig,wrapfig}
\newtheorem{Theorem}{Theorem}
\newtheorem{Definition}{Definition}
\newtheorem{Assumption}{Assumption}
\newtheorem{Corollary}{Corollary}
显示的是斜体、非粗；
奇怪的是，但我在\documentclass[a4paper, 12pt]{article}下面，就能够显示正常的
粗体、正体定理、定义。
我不会change the definition of the class |
|
w******n
发帖数: 430 | 20 多谢，我google搞定了lemma和corollary，但是definition要跟他们混合编号没搞定，
我尝试：
\newtheorem{definition}{Definition}[section]
好像没什么用，然后
\newtheorem{definition}[theorem]{Definition}
编译报错，不知道如何让definition和theorem一起编号。 |
|
a**e
发帖数: 5794 | 21 我估计definition环境在别的地方已经定义过了，你可以试试下面两种方法
1. \renewtheorem{definition}[theorem]{Definition}[chapter]
或者
2. \newtheorem{mydef}[theorem]{Definition}[chapter]
然后你就用mydef |
|
z***c
发帖数: 2959 | 22 要求theorem header全部upper case，如下，怎么设置？多谢
THEOREM
PROPOSITION |
|
p***c
发帖数: 2403 | 23 我有一个定理Theorem xxx
我下面紧接着有个定理，还是想标成Theorem xxx (cont'd)这样应该怎么写啊？ |
|
t******y
发帖数: 147 | 24 update一下，我改用
begin{theorem}
..............................
begin{minipage}[t]{linewidth}
begin{itemize}
item ........................
end{itemize}
end{minipage}
..............................
end{theorem}
这下iteminze中的文字和公式都没有超过rightmargin，但是minipage之前的文字被
stretch到整行了。有什么命令可以防止文字被full stretch吗？ |
|
y***i
发帖数: 11639 | 25
,
statistically
from
theorem
results.
请注意这一句，repast的说法看来很准确
"The t-test ....require normality of the sample means.....in addition that
the sample variance follows a scaled Χ2distribution....Normality of the
individual data values is not required if these conditions are met."
而且 "However, if the sample size is large Slutsky's theorem implies that
the distribution of the sample variance has little effect on the
distribution of the test statistic."
所以说，对大样本数ttest完全成立。ttest远比一般的理解更powerful。现在问题是 |
|
p*****m
发帖数: 7030 | 26 你这么着照抄wiki是不行的。。刚才那几位讨论的都是有些理论基础的至少
,
statistically
from
theorem
results.
请注意这一句，repast的说法阿其实很准确
"The t-test ....require normality of the sample means.....in addition that
the sample variance follows a scaled Χ2distribution....Normality of the
individual data values is not required if these conditions are met."
而且 "However, if the sample size is large Slutsky's theorem implies that
the distribution of the sample variance has little effect on the
distribution of the test statistic."
所以说，对大样本数t |
|
F*Q
发帖数: 3259 | 27 【 以下文字转载自 Mathematics 讨论区 】
发信人: fullmath (风之子), 信区: Mathematics
标 题: 菲尔兹奖得主Donaldson揭田刚学术剽窃
发信站: BBS 未名空间站 (Sun Nov 24 11:38:48 2013, 美东)
国际顶尖数学家唐纳森教授等再揭田刚学术剽窃
作者：东闲
近日伦敦皇家学院首席教授唐纳森，美国纽约石溪大学教授陈秀雄等学者联
名公开发文，揭露田刚的又一起剽窃丑闻。唐纳森是国际顶尖数学家，曾获得菲
尔兹奖、克劳福特奖、邵逸夫数学奖等众多国际数学最高奖。陈秀雄是国际著名
几何学家，曾在国际数学家大会上做过邀请报告。
文章以十页的篇幅逐条列举了田刚在长达1年多时间里多次抄袭、公然抢夺
唐纳森教授等学术成果的来龙去脉。事实清楚，证据确凿。唐纳森教授作为国际
顶尖学者，发长文公开指责田刚抄袭，说明事态已经到了非常严重的程度。
这已经不是田刚第一次被揭发学术不端了。国际顶尖数学家丘成桐，萧荫堂
等都曾多次指出田刚自从读博士起就存在剽窃、夸大等学术不端行为。
唐纳森教授等文章链接
Xiuxiong C... 阅读全帖 |
|
G****n
发帖数: 145 | 28 But Andrei Shleifer, who won the clark medal is the real deal!
The law and economics of self-dealing[PDF] from uva.nl…, R La Porta, F
Lopez-de-Silanes, A Shleifer - 2005 - nber.org
... Andrei Shleifer Department of Economics Harvard University Littauer
Center M-9 Cambridge,
MA 02138 and NBER a*******[email protected] Page 3. 1 1. Introduction. Over the
last twenty
years, both academic and practical approaches to corporate ...
Cited by 462 - Related articles - Library Search - BL Direct - All 71
vers... 阅读全帖 |
|
c********a
发帖数: 23 | 29 You are right. Since lots of the textbooks use
the low pass signal to explain the sampling theorem.
That is why 抽样定理说的是至少是该信号最高频率的两倍.
However, it is not true for band pass or high pass signals.
Acctually, we should use sampling rate >= 2* bandwidth to
define the sampling theorem. |
|
G*****s
发帖数: 664 | 30 。。。
你不知道Shannon Limit？
这个才是Shannon的主要贡献之一啊，信息论的基础之一
Sampling Theorem虽然对Signal Processing和Communications都很重要，但算不得
Information Theory的基础吧，而且Sampling Theorem历史上独立给出的人很多，不单
单我前面提到的这几个人
Shannon在Information Theory上的那些定理才是有划时代意义的
我还以为Shannon Limit被打破了呢。。 |
|
G*****s
发帖数: 664 | 31 。。。
你不知道Shannon Limit？
这个才是Shannon的主要贡献之一啊，信息论的基础之一
Sampling Theorem虽然对Signal Processing和Communications都很重要，但算不得
Information Theory的基础吧，而且Sampling Theorem历史上独立给出的人很多，不单
单我前面提到的这几个人
Shannon在Information Theory上的那些定理才是有划时代意义的
我还以为Shannon Limit被打破了呢。。 |
|
r*********n
发帖数: 4553 | 32 Totally disagree with: A theory is already done. Most network information
theory problems are open。The insufficiency of the random coding argument
methods used in Shannon's point-to-point channel capacity theorem becomes
more and more apparent when one tries to directly extension the results to a
network. The building block of wireless networks is no longer point-to-
point channels,but rather BC,MAC,IC,RC etc. If poin-to-point channel
theorems are applied without discretion to wireless networks, |
|
g****t
发帖数: 31659 | 33 凡是theorem这个词儿用的多的文章,都很可疑.
这个词儿本身是数学家用来表示:"A和B是同义反复" 的.
话说香农,Kalman,这样的,一篇文章才几个theorem阿.
现在的文章......
看看paper就知道了 |
|
B*B
发帖数: 87 | 34 一个麦克斯韦方程解的存在性和唯一性的问题。
需要证明三维空间里面partial differential equations形式的Maxwell equations的
解的existence and uniqueness。给定初始条件initial condition,对t=0时的E和H的
值作为initial condition。求解t为任意时刻的E和H的值。
然后这是一个Cauchy problem of Maxwell equations。
我不求解Boundary condition问题，只是求解Cauchy问题。
要证明这个existence和uniqueness需要怎么做？
我看了一些PDE的书，都是介绍用Cauchy－Kowalevski theorem或者Holmgren theorem。
但是怎么应用这定理完全没有溉念。
因为看到PDE书基本上都是介绍通用的PDE，没有专门对maxwell equations的。
求教这个证明的思路，感觉对PDE的人来说应该不困难。
但是就是找不到相关的文献或者书本具体针对maxwell equations 讨论的。
真心求高人指教。 |
|
l***u
发帖数: 1 | 35 1. Fourier Inversion Theorem
Th: If \int_{-\inf}^{\inf} \abs(g_{X}(t))dt <\inf, then X is absolutely
continuous with density
f(x)=1/(2*pi) \int_{\-inf}^{\inf} exp(-itx) g(t)dt
2. The Ch. f. of Laplace distribution, which has density is 1/2*exp(-\abs(x)),
is
g(t)=1/(1+t^2)
This is easy to verify by standard calculation.
3. So, by Fourier Inversion Theorem,
1/2*exp(-\abs(x))=1/(2*pi) \int_{\-inf}^{\inf} exp(-itx)*1/(1+t^2) dt
=1/(2*pi) \int_{\-inf}^{\inf} exp(itx)*1/(1+t^2) dt
|
|
s***t
发帖数: 113 | 36 Godel's theorem suggests Fermat's last theorem may not be provable. |
|
d********f
发帖数: 8289 | 37 F(p) = int_0^\infty e^{pt} f(t) dt
the initial value and final value theorem say
pF(p) -> f(0) as p -> \infty
pF(p) -> f(\infty) as p ->0
but in the proof, f is assume to be differentiable,
I was wondering if we only assume f is continuous,
do the two theorems still hold?
how to prove them? |
|
W**********d
发帖数: 15 | 38 I have a good (maybe) idea. Why don't mathematicians establish a hypertext,
cross-refered, online encyclopaedia of all definitions, lemmas and theorems?
Does there exist any similar project? If you know it please tell me. (I
know wikipedia and mathworld.)
By the deduction nature of mathematics, it is the ideal subject to establish
such a system. We can use XML and database techniques to describe every
single entry of it. For example, an entry for a theorem can be consisted of
the following parts |
|
a***n
发帖数: 40 | 39 【 以下文字转载自 Statistics 讨论区 】
发信人: alvin (al), 信区: Statistics
标 题: a question about least favorable prior
发信站: BBS 未名空间站 (Tue May 29 23:34:29 2007)
Can a least favorable prior be an improper prior? My impression is that it
can, but it seems not true from the proof of the following theorem.
The theorem is: if Delta0 is a Bayes rule w.r.t. proper prior Pi0, and R(
theta, Delta0) <= r(Pi0, Delta0) for any theta. Then Pi0 is least favorable.
One of the steps of the proof is: integral of "R(delta0, the |
|
p*********g
发帖数: 5964 | 40 hehe,你说的这个收缩是指graph minor吧，Robertson–Seymour theorem你可以再wikipedia上搜索以下Robertson–Seymour theorem就知道planar graph是minor closed得 |
|
i********e
发帖数: 31 | 41 Yes.
Matrix Analysis: Roger A. Horn, Charles R. Johnson - Google Books Result
by Roger A. Horn, Charles R. Johnson - 1985 - Science - 561 pages
"The following result, an immediate corollary of Weyl's theorem known as the
monotonicity theorem, says that all the eigenvalues of a Hermitian matrix .
.."
books.google.com/books?isbn=0521386322... |
|
Q***5
发帖数: 994 | 42 Of cause, "现代西方数学不过是把俄罗斯数学不为人之的定理用英语写出来而已" is
just meant to be an exageration, I doubt even the one who said it seriously
believed it.
I heard another side of the story: some Math professor in US complaint that
Russian Math historians had such a huge vanity that they named every big
math theorem after some Russian mathematician, even when there was no solid
evidence that the mathematician in question deserved it -- and what was more
annoying: the date they claimed that the theorem was proved by |
|
Q***5
发帖数: 994 | 43 Of cause, "现代西方数学不过是把俄罗斯数学不为人之的定理用英语写出来而已" is
just meant to be an exageration, I doubt even the one who said it seriously
believed it.
I heard another side of the story: some Math professor in US complaint that
Russian Math historians had such a huge vanity that they named every big
math theorem after some Russian mathematician, even when there was no solid
evidence that the mathematician in question deserved it -- and what was more
annoying: the date they claimed that the theorem was proved by ... 阅读全帖 |
|
g****t
发帖数: 31659 | 44 苏联人确实更早证明过很多东西。
Of cause, "现代西方数学不过是把俄罗斯数学不为人之的定理用英语写出来而已" is
just meant to be an exageration, I doubt even the one who said it seriously
believed it.
I heard another side of the story: some Math professor in US complaint that
Russian Math historians had such a huge vanity that they named every big
math theorem after some Russian mathematician, even when there was no solid
evidence that the mathematician in question deserved it -- and what was more
annoying: the date they claimed that the theor... 阅读全帖 |
|
a***s
发帖数: 616 | 45 Under certain conditions, this may be true. Try Berry-Esseen Theorem, which
gives the rates of convergence of the cdf. From that, we see that F_n conver
ges to F uniformly. You may prove that f_n converges to f for almost all x i
n R (not necessary all x). But Berry-Esseen Theorem has some assumptions.
N) |
|
R********n
发帖数: 519 | 46 太赞了！谢谢大牛，呵呵，我刚google到了这个Tubular neighborhood theorem
我想要这个结论的出发点是因为一个猜测，本来也不知道对不对，但感觉有了你说的这
个theorem，应该是对的？:-)
对于一个属于R^D的smooth Riemannian manifold M，如果我们以某个分布 P 在M上面
sampling点得到x，然后对x加上R^D空间各向同性的正态噪声e，得到y=x+e
另一方面，如果在M上以另一个分布P'在M上sampling点得到x'，然后对x'加上在x'的
normal space里的各项同性的正态噪声e'，得到y'=x'+e'
猜测是，如果正态噪声e的方差不是太大，我们通过选择分布P'和e'的方差，
可以使得y和y'的在R^D空间的分布是一样的
exsit) |
|
l*******t
发帖数: 3 | 47 来自主题: Mathematics版 - 关于不等式 如何用Farkas Lemma推Gordan's theorem
Gordan's theorem: Either Ax < 0 has a solution x, or ATy = 0 has a nonzero
solution y with y ≥ 0.
严格不等号怎么处理呢？ |
|
n*********y
发帖数: 54 | 48 WEI ZHANG TO RECEIVE 2010 SASTRA RAMANUJAN PRIZE
http://www.math.ufl.edu/sastra-prize/2010.html
The 2010 SASTRA Ramanujan Prize will be awarded to Wei Zhang, who is now a
Benjamin Pierce Instructor at the Department of Mathematics, Harvard
University, USA. This annual prize which was established in 2005, is for
outstanding contributions by very young mathematicians to areas influenced
by the genius Srinivasa Ramanujan. The age limit for the prize has been set
at 32 because Ramanujan achieved so ... 阅读全帖 |
|
