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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.
本部分課程將討論基本的數學工具。你將使用STATA ®進行簡單的回歸分析，並且我們將使用在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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3
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Derivatives 導數
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4
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Maximization 極大化
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5
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Sums and Integrals 和與積分
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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.
本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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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，貝努利，泊松均勻分佈，正態分佈
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9
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Expected Value: Mean, Variance, Covariance 預期值：平均數，方差，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
隨機變數和和極限定理，大數定理，中央極限定理
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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：最大可能性估量和距量法
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13
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Inference: Confidence Interval and MSE 推測：置信區間和均方誤差
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Part 5: Statistical Models: Conditional Distributions and Causality
第五部分：統計模型：條件分佈與因果關係
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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