4.MIT教材《Introduction to Statistical Physics》评介研究

合集下载

材料中的热力学与动力学1

��
17
The state of a System at Equilibrium: -Defined by the collection of all macroscopic properties that are described by State variables (p, n, T, V, …)
or

∆U=q+w
− ��= ��
7
2th Law:
Define Entropy: - Puts restrictions on useful conversion of q to w - Follows from observation of a directionality to natural or spontaneous processes - Provides a set of principles for - determining the direction of spontaneous change - determining equilibrium state of system
11
3th Law:
Corollary:
It’s impossible to decrease the temperature of any system to T=0K in a finite number of steps.
12
These laws are Universally Valid, they cannot be circumvented.
-For a one-component System, all that is required is “n” and 2 variables. All other properties then follow.

MIT-SCIENCE-Lectures-intro_sts_p12003

INTRODUCTION TO STATISTICS FOR POLITICAL SCIENCE:1.IntroductionStephen AnsolabehereDepartment of Political ScienceMassachusetts Institute of TechnologyFall,20031.IntroductionStatistical tools are essential for social scientists.Basic concepts of statistics,especially randomness and averaging,provide the foundations for measuring concepts,designing stud-ies,estimating quantities of interest,and testing theories and conjectures.People are not always good statisticians.It is hard to maintain discipline in observing the world.W e often learn from what is convenient-a violation of random sampling.We often do not calculate averages well.To learn these concepts with the depth associated with a graduate education-where you will have the facility to use these concepts in your own research and possibly contribute to the development of statistical models that others may use-requires some mathematics.We will use,repeatedly,three sorts of functions-polynomials(especially quadratics),exponentials, and logarithms.We will also use summation,as that is necessary for the calculation of averages,and summation comes in two forms-discrete and continuous(or integration).We will use di®erencing and di®erentiation(the continuous version of di®erencing).Finally,we will use probability a special branch of mathematics designed to study uncertainty.This course is designed to be a self-contained introduction not only to the concepts but also to the tools of statistics for social sciences.At the beginning of this course I will review the basic mathematical tools used in statistics.As a result we will study calculus and probability theory.Much of the basic mathematics that social scientists use in statistical analyses and in formal modeling comes from the calculus,especially limits,derivatives,and integrals.Probability provides a theory of uncertainty,and is thus the essential tool of statistics.1.Two core ideas in statistics.A.AveragingStatistics involves studying the frequencies of events and behaviors.W e assume that every event has its own likelihood of occurence,such as the likelihoodof the birth of a boy or girl.The long-run average is a measure of that frequency.One important law of statistics is the Law of Large Numbers.If we observe the repetition of a certain trial or experiment or event,such as birth,the long-run frequency with which one outcome or another happens,such as a boy or a girl is born,is extremely close to the true frequency of that outcome.A second important law of statistics is the Central Limit Theorem,which states that the frequency of possible outcomes of a sum of variables follows a bell-shaped(or normal)curve.We will make both of these laws more precise later in the course.B.RandomnessProbability is the study of randomness and chance.The systematic study of probability emerged as an important mathematical subject of study in the18th Century.In the late 18th and19th Centuries the application of probability spread beyond games of chance to the study of physical and social behavior.And in the20th Century researchers realized that one could use randomness to increase the e±ciency with which we learn.That is perhaps the most surprising and counter intuitive aspect of statistics{randomness is useful.Two core applications of this idea are(1)random sample surveys and(2)randomized experiments.1.Random Sample Surveys:How can we learn about100million people with just1000?Random sample surveys are the most widely used tool for measuring quantities of interest in all of the social sciences.Nearly all government data are collected using random sample surveys-including measures of the economic and social conditions of the nation,ranging from crime to in°ation to income and poverty to public health.Random sample surveys are staples of political organizations and academics interested in understanding national opinion about important public policies and public o±cials.How do random sample surveys work?A relatively small group of people are chosen at random and interviewed.The average answer to a particular question in a random sample istaken to represent or measure the average answer to that question in the entire population from which the sample is taken.How many people are to be interviewed and what they are to be asked is a matter of choice for the social scientist.But,the power of the random sample survey is that random choice of individuals gives the researcher leverage-allowing for great economy in the study of populations.2.Randomized ExperimentsPeople have conducted controlled experiments for centuries,especially using physical ob-jects.Controls involving creating conditions in which all other factors are held constant. Even with the best controlled experiments,it is possible to leave some potentially important factor uncontrolled.Such uncontrolled factors might create spurious relations or mask im-portant e®ects.Perhaps the most profound contribution of probability theory to scienti¯c study of social and physical behavior is the notion that random assignment of individuals to di®erent experimental conditions(such as receiving a drug or receiving a placebo)can reduce or even eliminate the threat of spurious e®ects.2.Fundamentals of Research MethodsA.Measurement and Estimation1.Concepts and Variables{the constructs or behavior we wish to understand.A good example is\inequality."Exercise:De¯ne inequality.2.Measures{the mathematical representation of the concept.For example,the income distribution in a society might be used to measure inequality.Exercise:devise a measure of the total amount of income inequality in a country.3.Measurement Theory{what requirements do we impose on our measurement device.(i)accuracy(with enough observations we would arrive at the correct answer),(ii) precision(low noise),(iii)reliability(can replicate).B.Model Building1.E®ects and Behavioral RelationshipsSocial scientists freqently want to measure the e®ect of one factor on another.There are many such examples.What is the e®ect of police on crime?What is the e®ect of additional military force on the probability of winning a battle or war?How does class size a®ect educational performance?How do electoral rules,such as single member districts,translate votes into legislative seats?In each case,there is one factor whose levels or values we would like to vary,such as the number of police,in order to observe changes in a second factors,such as the crime rate. The¯rst factor we call an independent variable,and the second factor,a dependent variable.2.AccountingWe seek to make a complete accounting of behavior.In this respect we value models in which a set of variables has high explanatory power.W e also demand parsimony:simpler is better.Example.Housing sales prices can be predicted very well as a function of list prices.In a normal market sales prices are92percent of list prices,and the¯t is extremely good.3.Equilibrium ConceptsMany ideas and conjectures about how social relations produce outcomes:maximizing behavior,dynamic adjustment,e±cient markets,or natural selection.The forces that cre-ate social outcomes make it di±cult to give causal interpretations to observed e®ects or relationships.C.InferenceA fundamental methodological problem is knowing when you should go with one argu-ment or idea or a competing argument or idea.When we measure phenomena,we often thenuse the measurements to draw inferences about di®erent ideas.Are data consistent with an argument or idea?What conclusions can we draw about theories from data?In the end, then,statistics involves a bit of decision theory.Predictions of a theory or conjectures about the world are called hypotheses.When specifying hypotheses it is important to be clear about all of the possible values.In a court of criminal law,hypotheses are questions of guilt or innocence.In medicine,hypotheses are about the condition of the patient,such as whether a cancer is benign or malignant or whether a woman is pregnant or not.In the scienti¯c method generally,the question is whether an conjecture is true or not.Unfortuantely,we never observe the truth.We use data to make decisions about hy-potheses.The evidence brought to a trial are data.A series of test are data.An academic study generates data.The problem of inference is how to use data to make decisions about hypotheses.Ultimately,that will depend on the value we place on di®erent sorts of outcomes from our decisions.However,we can formulate the problem we face quite simply.We want to make the correct decision,and we can make a correct decision one of two ways.First,we may decide,using the data,that the hypothesis is true and the state of the world is such that it is true.Second,we may decide,using the data,that the hypothesis is not true and the state of the world is such that the hypothesis is not true.W e may also make errors two ways.W e may decide that the hypothesis is true when it is in fact false or we may decided that the hypothesis is false when it is infact true.One a central objective of researchers is to avoid either of the two sorts of errors.Sta-tistical design is fundamentally about how to minimize the chances of making a mistaken judgment.。

MIT 教授为博一新生讲授的Stata编程专题英文版---lecture5

• Lots of “if” and “in” commands could slow things down
• Create “1% sample” to develop and test code (to prevent unanticipated crashes after code has been running for hours)
Precision issues in Mata
Large data sets in Stata
• Computer architecture overview
– CPU: executes instructions – RAM (also called the “memory”): stores frequentlyaccessed data – DISK (“hard drive”): stores not-as-frequently used data
Precision issues in Mata
Precision issues in Mata
Mata r = c = 0 A = (1e10, 2e10 \ 2e-10, 3e-10) A rank(A) luinv(A, 1e-15) _equilrc(A, r, c) A r c rank(A) luinv(A) c’:*luinv(A):*r’ end
Overview
• This lecture is part wrap-up lecture, part “tips and tricks” • Focus is on dealing with large data sets and on numerical precision • Numerical precision

国外通信类经典书籍介绍

国外通信类经典书籍1、《Linear Systems and Signals》——thi这本书个人觉得很不错，是一本线性系统和信号的入门好书。

可以适用于通信、电路、控制等专业。

虽说是入门的好书，但是本书的编排是内容由浅入深，讲述可是深入浅出。

我通读全书后，觉得深有体会，看这本书就像在看小说一般，对于一个话题的介绍，往往从其历史发展说起，让你知道其来龙去脉。

不像国内的书，一上来就是定理、定律。

同时，书中每讲完一个知识点，都会有适当的例题让你加深理解。

本书给我的一种感觉就是，作者将一种菜吃透了，消化了，而且掌握了作者这种菜的方法，然后把这种做法告诉你，然你自己去做菜，做出来的菜可能不一样，但是方法你是掌握了。

最根本的你掌握了，做什么菜是你自己的发挥了。

不像国内的教科书，就要你做出一样的菜才是学会了做菜。

这本书讲述了线性系统的一般原理，信号的分析处理，例Fourier变换、Laplace变换、z变换、Hilbert变换等等。

从连续信号说到离散信号，总之是一气呵成，中间似乎看不出什么突变。

对于初学者，这是一本很好的入门书，对于深入者，这又是一本极好的参考书。

极力推荐。

实话说，Lathi的书每看一回都会有新的感觉，常看常新。

2、《Fundamentals of Statistical Signal Processing,Volume I: Estimation Theory》——Steven M. Kay3、《Fundamentals of Statistical Signal Processing,Volume II: Detection Theory》——Steven M. Kay这两本书是Kay的成名作。

我只读过第一卷，因为图书馆只有第一卷:p这两本书比Van Trees的书成书要晚，所以内容比较新。

作者的作风很严谨，书中的推导极其严密。

不失为一位严谨的学者的作风！虽说推导严密，但是本书也不只是单纯讲数学的，与工程应用也很贴近。

introduction to mathematical statistics

which is 1 − (5/6)18 − 18(1/6)(5/6)17 − 153(1/6)2(5/6)16 = 0.60.
Chapter 3
29
3.2.8
The number of missile hits on the plane is binomial with n = 6 and p = 0.2. The probability that the plane will crash is the probability that k ≥ 2. This event is the complement of the event that k = 0 or 1, so the probability is
Probabilities for the second system are binomial with n = 100 and p = 0.02. The probability that k ≥ 1 is 1 − (0.98)100 = 1 − 0.133 = 0.867
System 2 is superior from a bulb replacement perspective.
∑ service =
k
3 =0
⎛10
⎜ ⎝
k
⎞⎟(0.05)k ⎠
(0.95)10−k
= 0.599 + 0.315 + 0.075 + 0.010 = 0.999
3.2.6
Probabilities for the first system are binomial with n = 50 and p = 0.05. The probability that k ≥ 1 is 1 − (0.95)50 = 1 − 0.077 = 0.923.

U5P1_lhospitals-rule-and-improper-integrals

x→ 0
lim
− sin x − cos x = lim . x→0 2x 2
All together, the calculation looks like: lim cos x − 1 x2 = = = = − sin x 2x − cos x lim x→0 2 − cos 0 2 1 − . 2
1
Repeating L’Hˆ opital’s Rule
This example illustrates the superiority of Version 1 of l’Hˆ opital’s rule; it works even if g � (a) = 0. In this case, f (x) = cos x − 1, g (x) = x2 , and a = 0. We’re trying to ﬁnd: cos x − 1 . x→ 0 x2 lim We can easily verify that f (a) = g (a) = 0. We apply l’Hˆ opital’s rule: lim cos x − 1 − sin x = lim . x→0 x2 2x
Introduction to L’Hˆ opital’s Rule
In this ﬁnal unit we tie up some loose ends related to calculus and limits. Our ﬁrst topic is L’Hˆ opital’s rule, which is useful for understanding multiplication and division by inﬁnity. L’Hˆ opital’s rule is also known as L’Hospital’s rule; the circumﬂex accent indicates that the letter S has been omitted, so the two spellings are equivalent. The two spellings are pronounced identically, with a long O and silent S. L’Hˆ opital’s rule is used to calculate limits of expressions like: x ln x xe−x ln x x as x → 0+ , as x → ∞, as x → ∞.

T.W. ANDERSON (1971). The Statistical Analysis of Time Series. Series in Probability and Ma

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理论物理电子书

理论物理电子书理论物理-电子书0000理论物理基础彭桓武Simons B. Concepts in theoretical physics (Cambridge lecture notes, 2002)(T)(273s)Principles of Modern Physics-N E I L A S H B Y-S T A N L E Y C . M I L L E R-University of ColoradoFUNDAMENTALS OF physics-J. Richard Christman0-mathematical physics李代数李超代数及在物理学中的应用孙洪洲群论.及其在粒子物理学中的应用,.高崇寿.1992群论及其在固体物理中的应用【徐婉棠,喀兴林】群论及其在物理中的应用(马中骐)群论习题精解+(马中骐)群论与量子力学物理系群论讲义物理学中的群论(上册).陶瑞宝物理学中的群论基础 A W 约什Geometry_Topology_and Physics-NakaharaGeometry+and+Physics+(Jürgen Jost)Lee J.M. Differential and physical geometry (draft)(721s)数学物理中的微分几何与拓扑学_汪容.浙大版.1998Differential Geometry, Analysis and Physics 。

Jeffrey M. Lee微分几何学及其在物理学中的应用物理学家用微分几何-侯伯宇-侯伯元物理中的张量孙志铭Arnold vol1，2A Guided Tour Of Mathematical Physics (By Roel Snieder, Department Of Geophysics, Utrecht UniversAbramovitz M., Stegun I.A. (eds.) Handbook of mathematical functions (10ed., NBS, 1972)(T)(1037s)Academic Press, Methods of Modern Mathematical Physics -- Vol. 1, Functional AnCourant, Hilbert - Methods of Mathematical Physics Vol. 1 ENG (578p)Introduction+to+Applied+Mathematics-GilbertStrangIntroduction+to+Mathematical+Physics+(Laurie+Cosse y)Math_method_for_Phy_Ken Riley, Michael Hobson and Stephen Bence Cambridge, 1997Szekeres, Peter - A Course in Modern Mathematical Physics - Groups, Hilbert Spaces and Differenti数学物理方法梁昆淼数学物理方法（R.+柯朗、D.+希尔伯特）数学物理方法吴崇试数学物理学中的微分形式数学物理中的几何方法(B·F·舒茨)特殊函数概论王竹溪物理学中的非线性方程刘式适物理学中的数学方法（李政道）1-Classical Mechanics and Fluid MechanicsClassical Mechanics - Goldstein古典力学(戈德斯坦)Hand, Finch Analytical Mechanics (Cup, 1998)(T)(590S)Structure and Interpretation of Classical Mechanics-Gerald Jay Sussman and Jack Wisdom with Meinhard E. Mayer -MIT Press经典力学张启仁2-Statistical And Thermal Physics理论物理学基础教程丛书统计物理学(苏汝铿)量子统计力学 by 张先蔚量子统计物理学(北京大学物理系)统计物理现代教程（上、下册）(雷克)统计物理中的蒙特卡罗模拟方法（含有热力学，难度适中）Reif. Fundamentals of Statistical And Thermal PhysicsBratteli O , Robinson D W Vol 1 Operator Algebras And Quantum Statistical Mechanics (2Ed , SpringHuang K. Statistical mechanics (2ed., Wiley, 1987)(T)(506s)Reichl L.E. A modern course in statistical physics (2ed, Wiley, 1998)(T)(840s)3-Electrodynamics赵凯华-电磁学上宇宙电动力学_阿尔芬引力论和宇宙论：广义相对论的原理和应用-温伯格相对论物理宇宙学讲义俞允强天体物理学【李宗伟、肖兴华】+时空的大尺度结构（原版）- 霍金简明天文学手册-刘步林广义相对论引论广义相对论dirac广义相对论（刘辽）大众天文学【法】弗拉马利翁Jackson J.D. Classical electrodynamics (3ed., Wiley,1999)(ISBN 047130932X)(600dpi)(K)(T)(833s).d（研究生程度的必读教材）JACKSON经典电动力学（上册）（经典之作）J.A.Wheeler E.F.Taylor Spacetime_PhysicsHerbert Neff - Introductory ElectromagneticsElectromagnetics (Rothwell & Cloud, 2001 CRC Press)Electricity+and+Magnetism-MITcourseCohen-Tannoudji Introduction to quantum electrodynamicsBuch_John Wiley. Sons_An Introduction to Modern Cosmology4-Optics（光学经典，全面、很厚，很难）光学原理上册、下册(m.玻恩 e.沃耳夫)Bass M , Et Al (Eds) Osa Handbook Of Optics, Vol 1 (Mgh, 1995)(1606s)Goodman - Geometrical Optics--p1628 - cambridgeWiley,.Modern.Nonlinear.Optics.Part.I.Advances.in. Chemical.Physics.Volume.119.(2001),.2Ed5-Quantum MechanicsClassical and Quantum ChaosCohen-Tannoudji Quantum Mechanics, Vol 1Galindo A., Pascual P. Quantum mechanics I (Springer,1990)(ISBN 0387514066)(T) (431s)量子系统中的几何相位-A.Bohm等Jack_Simons_-_Quantum MechanicsJohn_Norbury_-_Quantum_Mechanics_for_Undergraduate sMathematics+of+Quantum+Computation-Goong.ChenModern Quantum Mechanics And Solutions For The Exercices (J J Sakurai)Nuclear And Particle Physics-NielsWaletPhillips.-.Introduction.to.quantum.mechanics.(2003 )(T)(284s)Quantum Mechanics - Concepts and Applications-Tarun.BiswasShankar-Principles Of Quantum Mechanics 2nd EditionThe Basic Tools Of Quantum MechanicsThe+Physics+of+Phase+Transitions-P. Papon J. Leblond P.H.E. MeijerLecture Notes in Physics-Time+in+Quantum++Mechanics+1J.G. Muga.R. Sala Mayato?I.L. Egusquiza (Eds.)Zaarur E. Schaum's Outline of Quantum Mechanics.. Including Hundreds of Solved Problems (Schaum,1喀兴林-高等量子力学席夫量子力学-繁体中文版量子力学(Messiah)Vol1量子力学（卷I）.曾谨言量子力学“天龙八部”-张永德量子力学+(苏汝铿)量子力学Fermi量子力学讲义（张永德）量子力学原理(狄拉克)量子论的物理原理量子论与原子结构-吴大遒量子物理学导论(MIT)物理学引论Vol4-A.P.French By Tsungp Lee量子物理-赵凯华高等量子力学-张永德6-Field theory量子场论-温伯格1,2,3An Introduction to Quantum FieldTheory(Peskin,Schroeder)(full and revised)Banks,Modern+Quantum+Field+Theory--A+Concise+Intro ductionField.theory,.Roman.S..(2ed.,.Springer,.2005)Giachetta,Advanced+Classical+Field+Theory经典场论Kleinert H. Quantum field theory and particle physicsItep-PARTICLE-PHYSICS-and-field-theory场论I-M.A.ShifmanQuantum Field Theory R ClarksonQuantum+Field+Theory+(M.Srednicki) Quantum+Field+Theory-David McMahon Sundaresan. Handbook of particle physics (CRC, 2001)(T)(439 Tong-Quantum Field Theory Zinn-Justin. Quantum field theory and critical phenomena (1ed., 1989)(K)(150dpi)(T)(924s) 北大2005量子场论讲义（赵光达）量子场论-清华王青讲义规范场论（胡瑶光）粒子和场【卢里着,董明德等译】量子场论(上)【依捷克森,祖柏尔着,杜东生等译】量子场论A.Zee量子场论F.Mandl-G.Shaw量子场论LEWIS-H.RYDER实时统计场论-徐宏华统计物理学中的量子场论方法-Abrikosov微分几何-统一场论超弦理论导论Elias-Kiritsis张秋光《场论》上册朱洪元+量子场论On Wittens 3-manifold Invariants-Kevin WalkerLectures on Topological Quantum Field Theory-J. M. F. Labastidaa-Carlos LozanobGEOMETRY OF 2D TOPOLOGICAL FIELD THEORIES-Boris DUBROVIN-SISSA, TriesteDunne(1999)-Aspects of Chern-Simons Theorylabastida(1998)-Chern-Simons Gauge Theory-- Ten Years After7-Solid state physics（非常好的书）固体物理学（黄昆）固体物理导论C.KittelMechanics Of Solids-Bela I. Sandor-University of Wisconsin-MadisonKleinert H. Gauge fields in condensed matter physics part1(T)(252s)Ashcroft, Neil W, Mermin, David N - Solid State PhysicsAltland & Simons - Concepts Of Theoretical Solid State Physics。

超详细MIT线性代数公开课笔记_完整版

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3 倍这一过程。E21 的第二行使矩阵 A 的行向量进行前述的线性组合，而其它两行
为了保持与原矩阵相同，采用同阶单位阵 I 的行向量。左乘的这个矩阵为“初等矩
阵”（Elementary Matrix），因此记做 E。我以为是消元矩阵，所以记做 E 呢。因
为所乘行向量的倍数-3 出现在 E 矩阵的第二行第一列，因此将之标注为 21。完成
回代 Back-Substitution
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做方程的高斯消元时，需要对等式右侧的 b 做同样的乘法和加减法。手工计算时比较有效率的方法是应用“增广矩阵”（augmented matrix），将 b 插入矩阵 A
之后形成最后一列，在消元过程中带着 b 一起操作。（Matlab 是算完系数矩阵再处
理 b 的。）
0 0 1 0 0 1 0 0 1
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第 03 讲矩阵的乘法和逆矩阵 Multiplication & inverse matrices
矩阵乘法 Matrix multiplication
我们通过四种方法讨论如何使矩阵 A 与 B 相乘得到矩阵 C。其中 A 为 mn（m
行 n 列）矩阵，而 B 为 np 矩阵，则 C 为 mp 矩阵，记 cij 为矩阵 C 中第 i 行第 j
1 2 3 6
方程组列图像为 x 2
y
5 z 2 4
6 3 1 2
如果改变等号右侧的 b 的数值，那么对于行图像而言三个平面都改变了，而对
于列图像而言，三个向量并没有发生变化，只是需要寻找一个新的组合。
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那么问题来了，是否对于所有的 b，方程 Ax=b 都有解？从列图像上看，问题转化为“列向量的线性组合是否覆盖整个三维空间？” 反例：若三个向量在同一平面内——比如“列 3”恰好等于“列 1”加“列 2”，而若 b 不在该平面内，则三个列向量无论怎么组合也得不到平面外的向量 b。此时矩阵 A 为奇异阵或称不可逆矩阵。在矩阵 A 不可逆条件下，不是所有的 b 都能令方程 Ax=b 有解。对 n 维情形则是，n 个列向量如果相互独立——“线性无关”，则方程组有解。否则这 n 个列向量起不到 n 个的作用，其线性组合无法充满 n 维空间，方程组未必有解。从行图像的角度来看，三元方程组是否有解意味着什么？当方程所代表的三个平面相交于一点时方程有唯一解；三个平面中至少两个平行则方程无解；平面的两两交线互相平行方程也无解；三个平面交于一条直线则方程有无穷多解。都是示意图，来看看 GS 和 Lay 的作图差异有多大吧……

概率论与统计书目推荐

好，现在终于到了与Econ，Finance 关系最紧密的概率统计部分。

关于概率统计的重要性我实在不想再强调了，不过需要再说一句的是，很多同学觉得学计量，学Finance很多东西看不懂，迷茫，那就是因为你概率统计没学好；甚至还有很多论调说什么Idea最重要，数学不重要，对于这种说法，我想说，别说Econ，Finance，连数学都是Idea最重要，任何学科都是Idea最重要的，但是你连基本的知识，研究工具都没掌握，都一窍不通，何来资本去讨论什么Idea？？好了，语调有点激烈，不想多说了，这个问题说多了没意思！下面我概率统计分开讲。

1概率：Basic Probability Theory这个很重要，虽然不是基于Measure-Theory的，但是是你明白概率是什么东西的基础。

国内数学系本科一学期的概率论的内容基本跟这边Undergraduate的Honors Course for Probability差不多，但问题是很多学校的老师不怎么认真在讲的时候。

比如我所在学校的数学系，当时那个老师真是不咋地，上课光在那闲扯淡，证明一点都不讲，而且课堂过大，整个数学院所有不同专业的学生一起在上课，起码100多号人，效果可想而知。

我不知道别的学校情况咋样，但是我本科所在学校的数学系还是国内比较不错的，连这里况且如此，很多地方可能也好不到哪去。

当然，这只是我个人的瞎猜想，没有任何证据。

这门课的主要教材是名家Durrett的《The essentials of Probability 》，我想很多人都知道他的另外一本Graduate Probability教材《Probability：Theory and Examples》，现在美国这边的学校几乎都用这本书作为Math PHD Probability课的教材。

顺便说一句，Durrett是超级牛人钟开莱（中国人，虽然是美国公民）的学生，好像我记得他在一本书里管钟开莱叫做Academic Godfather，真是牛到无极限啊。

中山大学心理统计学课件Lecture1

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Statistical methods play a critical role in most types of psychological research. For example, suppose you wanted to known whether a glass of warm milk at bedtime will help insomniacs(” š ‡ ö) get to sleep faster. In this case, you don’t expect the warm milk to knock out(¦\Z) any of the subjects, or even to help every one of them.
‘§¶¡: %nÚOÆ Ç‘ “: dÍ, ù“
þ‘žm: (Ïo3-5! þ‘/:: C403 áµ Barry H.Cohen Explaining Psychological Statistics, 3rd Edition. John Wiley & Sons, Inc. 2008.
Lecture 1: Introduction to psychological statistics
2
Lecture 1: Introduction to psychological statistics
%nÚOÆ(Statistics Methods for Psychology)
What is(are) statistics?
1
What is statistics? or What are statistics? Statistics are observations organized into numerical form. (Ú Oêâ) Statistics refers to a branch of mathematics that is concerned with methods for understanding and summarizing collections of numbers. (ÚOÆ) There is a third meaning for the term statistics, which distinguishes a statistic from a parameter. (ÚOþ)

博士必读数学

博士必读数学前面几篇谈了一些对数学的粗浅看法。

其实，如果对某门数学有兴趣，最好的方法就是走进那个世界去学习和体验。

这里说说几本我看过后觉得不错的数学教科书。

1. 线性代数(Linear Algebra)：我想国内的大学生都会学过这门课程，但是，未必每一位老师都能贯彻它的精要。

这门学科对于Learning 是必备的基础，对它的透彻掌握是必不可少的。

我在科大一年级的时候就学习了这门课，后来到了香港后，又重新把线性代数读了一遍，所读的是Introduction to Linear Algebra (3rd Ed.) by Gilbert Strang.这本书是MIT的线性代数课使用的教材，也是被很多其它大学选用的经典教材。

它的难度适中，讲解清晰，重要的是对许多核心的概念讨论得比较透彻。

我个人觉得，学习线性代数，最重要的不是去熟练矩阵运算和解方程的方法——这些在实际工作中MATLAB可以代劳，关键的是要深入理解几个基础而又重要的概念：子空间(Subspace)，正交(Orthogonality)，特征值和特征向量(Eigenvalues and eigenvectors)，和线性变换(Linear transform)。

（如果你能理解傅立叶变化究竟做了一件什么事情，你才能说你知道了子空间！学线性代数一定要理解MATLAB能为你做的事情之外其他的东西，这才是精髓。

而很遗憾，很多高校的线性代数考试只测试学生的计算能力。

有几个数学老师能告诉学生：我们为什么要计算特征值？）从我的角度看来，一本线代教科书的质量，就在于它能否给这些根本概念以足够的重视，能否把它们的联系讲清楚。

Strang 的这本书在这方面是做得很好的。

而且，这本书有个得天独厚的优势。

书的作者长期在MIT讲授线性代数课(18.06)，课程的video在MIT 的Open courseware网站上有提供。

有时间的朋友可以一边看着名师授课的录像，一边对照课本学习或者复习。

物理学经典教材

考研差不多在大学四年级上学期结束的时候，1月份。

因此目前为止你有大约16个月的学习时间。

根据你的现状，开始学习的策略，分为三点一是读书，掌握基础知识二是选择将来的方向三是提前联系学校和联系老师关于读书，最后面开的书单花费的时间周期过长，且英语要求并不适合。

但是你可以从另一个角度开始考研的理论部分考试是各类专业里水分最小的，所以必须要彻底拿下。

除了数学政治英语，物理课可以分为普通物理+数理方法+四大力学几个部分，需要从普物开始击破。

普物的教材，清华张三慧编写的是比较简单也全面的，让你了解物理学的基本的面貌，每册都不厚，力，热，电，光，量子，在清华工科是两个学期的课程。

里面有习题和思考题，如果自己思考并且做出来，就能达到普物的要求。

数学物理方法的要求就高一些。

主要是复变函数和偏微分方程。

如果时间不够，可以放弃复变函数，但是数理方程是必要的。

《数学物理方程与特殊函数》，王元明著是最薄的一本书，也是这一个领域最低的要求。

此外是四大力学。

电动力学可以用俞允强写的《电动力学简明教程》，统计力学用汪志诚的《热力学与统计物理》，分析力学可以跳过去不学，量子力学可以用曾谨言，周世勋的书合用。

一定要解题，解题是考察自己是否真的理解的一个必要过程。

可以做一下往届的考研试题。

有了这些基础，就可以考虑方向和选择学校了。

方向太多，热门的竞争也会比较激烈，数理要求也比较高。

多问问吧，光学，凝聚态，量子计算都很热门，但是国内差距还是很大。

关于学校，国内比较好的有北京大学，中科院物理所，清华大学，南京大学。

联系老师是必要的环节，也从某种角度是一种必要的礼貌，毕竟老师没有理由只有成绩高，其他一无所知的学生。

很多笔试出色的学生会落榜也是这个道理。

如果有可能，可以物理系的课程都选了，或者旁听。

如果有机会，可以考虑出国读物理。

报名GRE sub物理考试，大约在每年11月，要提前很久报名。

题目并不难，都是选择题，且比普通物理高一点点。

这是美国各大学物理系的必要的考试。

MIT 教授为博一新生讲授的Stata编程专题英文版---lecture3

– Stata knows how to choose a good “h” and in general it gets it right
• Stata updates its parameter guess using the numerical derivatives as follows (i.e. it takes a “Newton” step):
From “lf” to “d0”, “d1”, and “d2”
• In some (rare) cases you will want to code the gradient (and possibly) the Hessian by hand. If there are simple analytic formulas for these and/or you need more speed and/or the numerical derivatives are not working out very well, this can be a good thing to do.
clear set obs 1000 set seed 12345 gen x = invnormal(uniform()) gen y = (0.5 + 0.5*x > invnormal(uniform())) ml model lf myprobit_lf (y = x) ml maximize probit y x
What’s going on in the background?
• We just wrote a 3 (or 5) line program. What does Stata do with it? • When we call “ml maximize” it does the following steps:

MIT本科计算机教材

30 教材名称: COMPUTER SIMULATION OF LIOUIDS
作者: ALLEN
31 教材名称: CONTROL OF UNCERTAIN SYSTEMS
作者: DAHLEH
32 教材名称: CONTROL SYSTEM DESIGN
作者: FRIEDALND
作者: PERLMAN
62 教材名称: INTRO TO ALGORITHMS
作者: CORMEN
63 教材名称: INTRO.TO FORTRAN 90 F/ENGRS.+SCI.
作者: NYHOFF
64 教材名称: INTRO.TO MATLAB F/ENGRS+SCI.
作者: HOWE
76 教材名称: MICROSOFT ACCESS 2000 BIBLE
作者: PRAGUE
77 教材名称: MICROSYSTEM DESIGN
作者: SENTURIA
78 教材名称: MICRSFT,VISUAL BASIC:PROGRAMMER'S GDE
作者: MENEZES
59 教材名称: HOW COMPUTERS WORK,MILLENIUM ED.-W/CD
作者: WHITE
60 教材名称: HOW TO SET UP+MAINTAIN A WEB SITE-W/CD
作者: STEIN
61 教材名称: INTERCONNECTIONS:BRIDGES,ROUTERS…
作者: HERTZ
68 教材名称: Introduction to Random Signals & Applied Kalman Filtering 3/E (With Matlab Exercise & Solutions )

书籍——自然语言处理、计算语言学与中文信息处理

1、Speech and Language Processinga) 作者: Daniel Jurafsky / James H. Martinb) 副标题: An Introduction to Natural Language Processing, Computational Linguistics and Speech Recognitionc) ISBN: 9780130950697d) 定价: USD 97.00e) 出版社: Prentice Hallf) 装帧: Paperbackg) 第一版出版年: 2000-01-26；第二版出版年：2006h) 相关网站：/~martin/slp.htmli) 英文简介：This book takes an empirical approach to language processing, based on applying statistical and other machine-learning algorithms to large corpora.Methodology boxes are included in each chapter. Each chapter is built around one or more worked examples to demonstrate the main idea of the chapter. Covers the fundamental algorithms of various fields, whether originally proposed for spoken or written language to demonstrate how the same algorithm can be used for speech recognition and word-sense disambiguation. Emphasis on web and other practical applications. Emphasis on scientific evaluation. Useful as a reference for professionals in any of the areas of speech and language processing.j) 中文译名：自然语言处理综论k) 译者: 冯志伟/ 孙乐m) 页数: 588 页n) 出版社: 电子工业出版社o) 定价: 78.0p) 装帧: 平装q) 出版年: 2005r) 中文简介：本书是一本全面系统地讲述计算机自然语言处理的优秀教材。

MIT牛人解说数学体系(增加部分英文翻译和备注)

在过去的一年中，我一直在数学的海洋中游荡，research进展不多，对于数学世界的阅历算是有了一些长进。

为什么要深入数学的世界作为计算机的学生，我没有任何企图要成为一个数学家。

我学习数学的目的，是要想爬上巨人的肩膀，希望站在更高的高度，能把我自己研究的东西看得更深广一些。

说起来，我在刚来这个学校的时候，并没有预料到我将会有一个深入数学的旅程。

我的导师最初希望我去做的题目，是对appearance 和motion建立一个unified的model。

这个题目在当今Computer Vision中百花齐放的世界中并没有任何特别的地方。

事实上，使用各种Graphical Model把各种东西联合在一起framework，在近年的论文中并不少见。

我不否认现在广泛流行的Graphical Model是对复杂现象建模的有力工具，但是，我认为它不是panacea（万应灵药），并不能取代对于所研究的问题的深入的钻研。

如果统计学习包治百病，那么很多“下游”的学科也就没有存在的必要了。

事实上，开始的时候，我也是和Vision中很多人一样，想着去做一个Graphical Model——我的导师指出，这样的做法只是重复一些标准的流程，并没有很大的价值。

经过很长时间的反复，另外一个路径慢慢被确立下来——我们相信，一个图像是通过大量“原子”的某种空间分布构成的，原子群的运动形成了动态的可视过程。

微观意义下的单个原子运动，和宏观意义下的整体分布的变换存在着深刻的联系——这需要我们去发掘。

在深入探索这个题目的过程中，遇到了很多很多的问题，如何描述一个一般的运动过程，如何建立一个稳定并且广泛适用的原子表达，如何刻画微观运动和宏观分布变换的联系，还有很多。

在这个过程中，我发现了两个事情：我原有的数学基础已经远远不能适应我对这些问题的深入研究。

在数学中，有很多思想和工具，是非常适合解决这些问题的，只是没有被很多的应用科学的研究者重视。

mit phdeconomics 专业phd英文书单

mit phdeconomics 专业phd英文书单Here is an English essay with over 1000 words on the topic "MIT PhD in Economics Reading List":The MIT PhD in Economics program is one of the most prestigious and rigorous doctoral programs in the field of economics. As part of their studies, students are expected to engage with a vast and diverse body of literature spanning economic theory, empirical methods, and applied research. To provide a solid foundation for their academic training, the program curates a comprehensive reading list that covers the core areas of the discipline. This reading list serves as a guiding framework for incoming PhD students, ensuring they develop a deep understanding of the fundamental principles and ongoing debates within the field of economics.The reading list for the MIT PhD in Economics program is divided into several core areas, each of which reflects the program's emphasis on a well-rounded education. The first section focuses on microeconomic theory, which forms the bedrock of economic analysis. Students are expected to familiarize themselves with seminal works such as "Microeconomic Theory" by Andreu Mas-Colell, Michael Whinston, and Jerry Green, which provides acomprehensive and rigorous treatment of consumer theory, producer theory, and general equilibrium analysis. Additionally, students are encouraged to delve into more specialized areas of microeconomic theory, such as game theory, contract theory, and information economics, through the works of scholars like John Nash, Oliver Hart, and Joseph Stiglitz.The second major component of the reading list is macroeconomic theory, which examines the behavior of the economy as a whole. Students are expected to engage with classic texts like "A Monetary History of the United States, 1867-1960" by Milton Friedman and Anna Schwartz, which provides a comprehensive historical analysis of the role of monetary policy in economic fluctuations. Furthermore, students explore more contemporary macroeconomic theories, such as those developed by Robert Lucas, Edward Prescott, and Finn Kydland, which have significantly influenced our understanding of business cycles, economic growth, and the effects of policy interventions.In addition to the foundational theories of micro- and macroeconomics, the MIT PhD in Economics reading list also emphasizes the importance of empirical methods and applied research. Students are expected to familiarize themselves with seminal works in econometrics, such as "Econometric Analysis" by William Greene, which provides a thorough overview of statisticaltechniques for the analysis of economic data. Furthermore, students are encouraged to engage with cutting-edge empirical studies in various subfields of economics, such as labor economics, public finance, and development economics, to gain a deep understanding of the practical application of economic principles.One of the unique aspects of the MIT PhD in Economics reading list is its emphasis on the historical and institutional context of economic thought. Students are expected to delve into works that explore the evolution of economic ideas and the social, political, and cultural factors that have shaped the discipline over time. This includes readings from prominent economic historians like Robert Fogel, Douglass North, and Daron Acemoglu, who have shed light on the complex interplay between economic forces and broader societal changes.Moreover, the reading list recognizes the increasingly interdisciplinary nature of economics, with students expected to engage with relevant literature from fields such as psychology, sociology, and political science. This exposure to diverse perspectives is intended to broaden students' understanding of the complex and multifaceted nature of human behavior and decision-making, which are at the heart of economic analysis.As students progress through the MIT PhD in Economics program,they are expected to develop a deep and nuanced understanding of the core areas of the discipline, as well as the ability to critically engage with the latest research and debates in the field. The reading list serves as a gateway to this intellectual journey, providing a solid foundation upon which students can build their own research agendas and contribute to the ongoing advancement of economic knowledge.It is important to note that the reading list is not a static document, but rather a living, evolving resource that is regularly updated to reflect the changing landscape of economic research and the emerging areas of inquiry within the discipline. This ensures that the MIT PhD in Economics program remains at the forefront of the field, equipping students with the knowledge and critical thinking skills necessary to tackle the complex economic challenges of the 21st century.In conclusion, the MIT PhD in Economics reading list is a comprehensive and rigorous collection of works that form the core of the program's academic curriculum. By engaging with this extensive body of literature, students develop a deep understanding of economic theory, empirical methods, and applied research, positioning them to make significant contributions to the field and advance the frontiers of economic knowledge. The reading list serves as a testament to the program's commitment to excellence ineconomic education and research, and its enduring influence on the global landscape of the discipline.。