**Fall 2017**

This course is an introduction to mathematical techniques used to model phenomena studied in political science, with special attention to the analysis of individual action. Mathematical topics covered include: sets, functions, and graphs; matrix algebra; differential calculus and optimization; probability, mathematical statistics, and decisions under risk; integral calculus; and sequences, series, and limits. All these topics are useful in many settings in political science, including game theory, dynamic modeling, and statistics.

This course website will be updated to reflect any changes in schedule, topics covered, or assignments, as well as to provide relevant links to materials associated with the course.

## Course Outline and Approximate Schedule

## 0. Some Preliminaries

##### Monday and Wednesday, 8/28-8/30

Sets, real numbers, and intervals (reference: Pemberton & Rao sections 3.1-3.2; 31.2)

Logic and proofs (P&R 31.1)

Sequences, convergence, and limits (P&R 5.1, 5.4; for advanced help, 31.3, 31.4)

- Exercises on sequences and convergence: prepare your answers using LaTeX and bring them to class next time.

Areas, sums, and integrals (P&R 19.1)

## 1. Probability and Statistical Inference

Text: Excerpts from Wasserman, *All of Statistics*, chapters 1-10

### 1.1 Probability

##### W 8/30; W 9/6

**For Wednesday 9/6 read: chapters 1 and 2.1-2.2**

Exercises to turn in Monday 9/11: Chapter 1, exercises 5, 12, 13, 15.

Exercises to turn in Monday 9/18:

- Chapter 1, Exercise 19; Computer Experiments 21, 22
- Chapter 2: Exercises 2, 6

Exercises to turn in Monday 9/25 (subject to adjustment):

- Chapter 2: Exercises 4, 7, 9, 18

### 1.2 Expectations and Moments

##### M 9/25-F 9/29

Read: sections 3.1-3.5

Exercises to turn in Monday 10/2 (subject to adjustment):

- Chapter 2: Exercise 17
- Chapter 3: Exercises 3, 4, 5, 11, 13

### 1.3 Convergence of Random Variables

##### F 9/29 to M 10/2

Read: sections 5.1-5.4

**First Exam 10/4 - 10/9**

- Wed. 10/4: Review session
- Wed. or Fri.: distribute exam
- Exam due at beginning of class, Mon. 10/9

### 1.4 Statistical Inference and Hypothesis Testing

##### M 10/9, W 10/11

Read: sections 6.3, 10.1, 10.2, 13.1

- 6.3 estimation, confidence sets, and hypothesis testing
- 10.1 the Wald test
- 10.2
*p*-values - 13.1 example: linear regression

**Exercises to be assigned** (subject to revision)

- Chapter 1: Exercises 5, 12, 13, 15, 19; Computer Experiments 21, 22
- Chapter 2: Exercises 2, 4, 6, 7, 9, 17, 18
- Chapter 3: Exercises 3, 4, 5, 11, 13
- Chapter 6: Exercise 2, 3
- Chapter 10: TBA

### 1.5 Subjective Probability and Expected Utility

##### W 10/18

Recommended: Peter C. Fishburn, "The Axioms of Subjective Probability." *Statistical Science*, Vol. 1, No. 3 (Aug., 1986), pp. 335-345. Click here to obtain via JSTOR.

## 2. Linear algebra

##### dates TBA

(note Fall Break 10/16)

## 3. Sets and relations, with applications to choice theory

##### dates TBA

## 4. Sequences and series; limits and continuity

##### dates TBA

**Second Exam out about W 11/1 in M 11/6**

## 5. Differential calculus and applications

##### dates TBA

(note Thanksgiving Break W 11/22)

About 1 day on each subtopic below:

### 5.1 Newton's Quotient

### 5.2 Differentiation and Optimization

### 5.3 The Exponential and Logarithmic Functions

### 5.4 Approximation

### 5.5 Multivariate calculus

## 6. Integral Calculus

##### dates TBA

**Third Exam following 12/6**

- Fri. 12/8 or M 12/11 optional review session
- within a day after review session: distribute exam
- Exam due F 12/15