[Everyday Mathematics]20150122
设 $f:[0,1]\to [0,1]$.(1). 若 $f$ 连续, 试证: $\exists\ \xi\in [0,1],\st f(\xi)=\xi$.(2). 若 $f$ 单调递增, 试证: $\exists\ \xi\in [0,1],\st f(\xi)=\xi$.(3). 若 $f$ ...
[Everyday Mathematics]20150224
设 $A,B$ 是 $n$ 阶实对称矩阵, 它们的特征值 $>1$. 试证: $AB$ 的特征值的绝对值 $>1$.[Everyday Mathematics]20150224的更多相关文章[Everyday Mathematics]2015030...
[Everyday Mathematics]20150228
试证: $$\bex \int_0^\infty \sin\sex{x^3+\frac{\pi}{4}}\rd x =\frac{\sqrt{6}+\sqrt{2}}{4}\int_0^\infty e^{-x^3}\rd x. \eex$$[Everyday Mathematics]2015022...
[Everyday Mathematics]20150226
设 $z\in\bbC$ 适合 $|z+1|>2$. 试证: $$\bex |z^3+1|>1. \eex$$[Everyday Mathematics]20150226的更多相关文章[Everyday Mathematics]20150304证明...
[Everyday Mathematics]20150227
(Marden's Theorem) 设 $p(z)$ 是三次复系数多项式, 其三个根 $z_1,z_2,z_3$ 不共线; 再设 $T$ 是以 $z_1,z_2,z_3$ 为顶点的三角形. 则存在唯一的一个内切于 $T$ 的椭圆, 使得切点为 $T$ 各边的中点, 椭圆的的两焦点为 $p'(z)$...
[Everyday Mathematics]20150303
设 $f$ 是 $\bbR$ 上的 $T$ - 周期函数, 试证: $$\bex \int_T^\infty\frac{f(x)}{x}\rd x\mbox{ 收敛 } \ra \int_0^T f(x)\rd x=0. \eex$$[Everyday Mathematics]20150303的更多...
[Everyday Mathematics]20150301
设 $f(x)$ 在 $[-1,1]$ 上有任意阶导数, $f^{(n)}(0)=0$, 其中 $n$ 是任意正整数, 且存在 $C>0$, $$\bex |f^{(n)}(x)|\leq C^nn!,\quad \forall\ n\in\bbN,\quad \forall\ x\in[-1...
[Everyday Mathematics]20150225
设 $f:\bbR\to\bbR$ 二次可微, 适合 $f(0)=0$. 试证: $$\bex \exists\ \xi\in\sex{-\frac{\pi}{2},\frac{\pi}{2}},\st f''(\xi)=f(\xi)(1+2\tan^2\xi). \eex$$[Everyday M...
[Everyday Mathematics]20150302
$$\bex |p|<\frac{1}{2}\ra \int_0^\infty \sex{\frac{x^p-x^{-p}}{1-x}}^2\rd x =2(1-2p\pi \cot 2p\pi). \eex$$[Everyday Mathematics]20150302的更多相关文章&...
[Everyday Mathematics]20150215
设 $n,k$ 是正整数, 使得 $x^{2k}-x^k+1$ 整除 $x^{2n}+x^n+1$. 试证: $x^{2k}+x^k+1$ 整除 $x^{2n}+x^n+1$.[Everyday Mathematics]20150215的更多相关文章[Everyday Math...
Mathematics | Mean, Variance and Standard Deviation
Mean is average of a given set of data. Let us consider below exampleThese eight data points have the mean (average) of 5:Variance is sum of squares o...
How do I learn mathematics for machine learning?
https://www.quora.com/How-do-I-learn-mathematics-for-machine-learning HowdoIlearnmathematicsformachinelearning?PromotedbyTimeDoctorSoftwareforproducti...
How to Be Good at Mathematics
HowtoBeGoodatMathematicsCommunityQ&ASometimes,thehardestsubjectforsomepeopleismathematics.Therearesomanyformulas,equations,andpartsofmathtoknow,it...
[Everyday Mathematics]20150304
证明:$$\bex\frac{2}{\pi}\int_0^\infty\frac{1-\cos1\cos\lm-\lm\sin1\sin\lm}{1-\lm^2}\cos\lmx\rd\lm=\sedd{\ba{ll}|\sinx|,&-1<x<1,\\\frac{1}{2}|\...
How to do Mathematics
著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。作者：匿名用户链接：http://www.zhihu.com/question/30087053/answer/47815698来源：知乎Benson Farb：晨兴通俗报告How to do Mathematics文稿(z)晨兴通...
Mathematics for Computer Graphics数学在计算机图形学中的应用 [转]
最近严重感觉到数学知识的不足！http://bbs.gameres.com/showthread.asp?threadid=10509[译]MathematicsforComputerGraphicsMathematicsforComputerGraphics数学在计算机图形学中的应用GregTur...
Principles and strategies for mathematics study
MakemathematicsstudyahabitwithdoggedperseveranceDon'tbuildmansionontopofloosesand.Concreteasolidfoundationbyallocatingatleastonehourformathstudyeveryd...
What Is Mathematics?
WhatIsMathematics?TheNationalCouncilofTeachersofMathematics(NCTM),theworld'slargestorganizationdevotedtoimprovingmathematicseducation,isdevelopingaset...
Consideration about improving mathematics study
Inthisarticle,I’llpresentmyideasabouthowtoimprovemathematicsstudy,whicharetheforewordsofmyhandwritingnotesonRoyden’s“RealAnalysis”.Fromnowon,Iwillprac...
吴恩达机器学习笔记43-SVM大边界分类背后的数学（Mathematics Behind Large Margin Classification of SVM）
假设我有两个向量，吴恩达机器学习笔记43-SVM大边界分类背后的数学（MathematicsBehindLargeMarginClassificationofSVM）的更多相关文章[吴恩达机器学习笔记]12支持向量机3SVM大间距分类的数学解释12.支持向量机...