必讀讀物
Snedecor, George W., and William G. Cochran. Statistical Methods. Ames, IA: Iowa State University Press, 1989. ISBN: 9780813815619.
Snedecor, George W., and William G. Cochran.《統計方法》，Ames：愛荷華州立大學出版社，1989. ISBN: 0813815614.
Bulmer, M. G. Principles of Statistics. New York, NY: Dover Publications, 1979. ISBN: 9780486637600.
Bulmer,M.G 《統計學原理》，紐約：多佛出版社，1979. ISBN: 0486637603.
Chiang, Alpha C. Fundamental Methods of Mathematical Economics. New York, NY: McGraw-Hill, 1984. ISBN: 9780070108134.
蔣中一.《數理經濟學的基本方法》，紐約：麥格羅.希爾，1984 .ISBN: 0070108137.
推薦讀物
Goldberg, Samuel. Probability: An Introduction. New York, NY: Dover Publications, 1987. ISBN: 9780486652528.
(Discrete Probability)
Goldberg, Samuel.《概率：導論》。紐約：多佛出版社，1979.ISBN：0486637603
Rice, John A. Mathematical Statistics and Data Analysis. Belmont, CA: Duxbury Press, 1994. ISBN: 9780534209346.
(Mathematical Statistics Course)
Rice, John A.《數學統計和資料分析》. Belmont, CA: Duxbury Press, 1995. ISBN: 0534209343. （數學統計課程）
數學工具的示例
立方法則
Edward R. Tufte. "The Relationship between Seats and Votes in Two-party Systems." The American Political Science Review 67, no. 2 (June, 1973): 540-554.
Edward R. Tufte.〈兩黨體制中席位和投票的關係〉，《美國政治學評論》67, no. 2 (June, 1973): 540-554.
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LEC #課 TOPICS 課程單元 READINGS 閱讀資料
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Part 1: Introduction: Research Methods and Challenges
第一部分：導論：研究方法與挑戰
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1
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Introduction 導論
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Part 2: Mathematical Tools
第二部分：數學工具
This section of the course reviews basic mathematical tools. You will also perform simple regression analyses using STATA® and we will use the functions that you estimate in the mathematics review.
此部分將討論基本的數學工具。你也將使用STATA®進行簡單的回歸分析，並且我們將使用數學討論中提及的函數。
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2
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Functions and Limits 函數與極限
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Chiang. Chaps. 2 and 6
《數理經濟學的基本方法》第2,6章
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3
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Derivatives 導數
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Chiang. Chap. 7
《數理經濟學的基本方法》第7章
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4
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Maximization 最大值
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Chiang. Chap. 9
蔣.《數理經濟學的基本方法》第9章
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5
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Sums and Integrals 和與積分
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Chiang. Chap. 13
蔣《數理經濟學的基本方法》第13章
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Part 3: Probability and Models of Data
第三部分：概率與資料模型
This section of the course develops the mathematical concepts used in statistics. Three ideas are essential: Random Variable, Density Functions, and Expectations.
此部分課程擴展了統計學中的基本數學概念。三個基本想法如下：隨機變數，密度函數與期望。
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6
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Random Variables, Populations and Samples 隨機變數，總體和例子
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Snedecor and Cochran. Chap. 1
《統計方法》第1章
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7
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Probability: Two Laws of Probability, Bayes Theorem 概率：概率二法則，貝葉斯定理
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8
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Probability Functions: Binomial, Bernoulli, Poisson
Uniform, Normal
概率函數：二項式，伯努利，泊松均勻分佈，正態分佈
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9
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Expected Value: Mean, Variance, Covariance
期望值：平均數，方差和協方差
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10
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Sums of Random Variables and Limit Theorems, Law of Large Numbers, Central Limit Theorem
隨機變數和與極限定理，大數法則與中央極限定理
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Additional Reading
擴展讀物
Kendall and Stuart
Kendall and Stuart的書
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Part 4: Statistical Methods
第四部分：統計方法
In this section of the course, we develop the three ideas of statistics using probability theory. These ideas are (1) data can be summarized with a probability function, (2) we can optimize that function to estimate unknown parameters of the population, and (3) our estimates are uncertain measures of the population parameters, but we can summarize that uncertainty succinctly.
課程中的此部分裏，我們將使用概率理論來發揮統計學的三個觀念：(1)數據可以用某個概率函數進行概括；(2) 我們可以通過優化函數，估計總體的未知參數；(3) 儘管我們的估計對總體參數來說是不確定的測量，但我們可以簡潔地將不確定性進行概括。
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11
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Data Model: Summary and Assumptions 資料模型：歸納與猜想
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12
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Estimation: MLE and MOM 估計：最大可能性估量與矩量法
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13
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Inference: Confidence Interval and MSE 推測：置信區間與均方誤差
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Part 5: Statistical Models
第五部分：統計模型
Conditional Distributions and Causality In this section, we apply the mathematical and statistical ideas develop to specific problems. The main idea in this section is that social scientific reasoning involves conditional statements of the form if X then Y. We focus on the tools for studying such relationships.
在此部分中，我們將應用數學與統計想法去解決具體的問題。該部分的主要想法是社會科學推理，包括如果X，則Y形式的條件陳述。我們集中關注在研究該類關係的工具。
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14
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Differences of Means 平均數差分
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15
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Analysis of Frequencies and Variance 頻數與方差分析
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16
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Regression 回歸
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17
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Regression (cont.) 回歸（續）
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