Lecture: TuF 9:50–11:10am

Location: SC-214

Office Hours: Tu 11:10–1pm

Office Hours Location: TBA

## Course Description

Fundamentals of logical, probabilistic, and statistical thinking, as well as the basic principles of rational decision making. Reasoning through data (and rhetoric) encountered on a daily basis using elementary principles of deductive logic and inference.

Resolving differences of opinion isn’t always impossible. Figuring out what you should believe isn’t just a matter of checking what’s true. Deciding what you should do doesn’t have to be left up to your whim. Formal tools have been (and continue to be) developed that enable us to talk very precisely about the strength of arguments and of evidence, the rationality of beliefs we have, and the value of choices we make.

This course will introduce students to some of those formal tools and their applications to formal reasoning and decision making: Formal Logic will be used as a model for judging arguments and reasoning deductively. Probability and Statistics serve as tools for making inductive inferences, evaluating evidence, and quantifying risk and uncertainty. Decision Theory will provide a system that employs those logical and probabilistic tools in order to help guide our decision making. For all of these, we will also discuss their peculiarities, limits to their application, and their potential for expansion and sophistication.

## Course Requirements & Grading

There will be 10 short assignments, each worth 4% of the course grade, for a total of 40% of the course grade. These will range in style from regular in-class quizzes and short homework assignments, to more unusual fare, like developing a potential exam problem.

Each unit will end with an exam worth 20% of the course grade. A comprehensive final exam will be worth 20% of the course grade. The lowest exam grade will be dropped, for a total of 60% of the course grade coming from exams. This means that if you bomb an exam, you can make up for it with the final, or, if you are happy with your grade going into the final, you can skip it.

Attendance is ungraded, but highly recommended (especially since there will be regular graded in-class work).

In short:

40% — 10 Short Assignments at 4% each

60% — 3 Exams at 20% (best of 3 Unit-Specific Exams and 1 Final)

Lateness Policy: Assignments have an automatic two day grace period, but after that they lose 5 points per day (if out of a possible 100). For example, suppose an assignment is due Jan 1. If you turn it in on Jan 3 (the last day of the grace period) or earlier, all's well. An assignment turned in on Jan 4 will lose 5 points, and one turned in a week late will lose 25 points.

## Course Materials

We will be working, in part, out of the course textbook, *Choices: An Introduction to Decision Theory* by Michael Resnik. Additional notes will be posted here, and assignments will appear in the schedule below.

## Schedule

Below is the current/anticipated schedule for the course. Any known attendance issues should be brought to the instructor’s attention as soon as possible (e.g. you know now about religious holidays and away games, so if they cause a conflict you should tell me now).

### Introduction

Jan 16

read: Choices §1.1

### Formal Logic

Jan 19

Truth Tables

read: Lecture 1 - Truth Tables

Jan 23

Connectives

read: Lecture 2 - Connectives

start: Assignment 1 - Translations (due Jan 31)

Jan 26

Complex Sentences

read: Lecture 3 - Complex Sentences

Jan 30

Arguments

read: Lecture 4 - Arguments

Feb 2

Proofs

in class: Assignment 2 - Logic Quiz (on Lectures 1–4)

solutions: Assignment 2 - Logic Quiz

Feb 6 and 9

Proofs (cont.)

read: Lecture 5 - Proofs

start: Assignment 3 - Proof Problem Set (due Feb 16)

use often: Proof Rules Summary Sheet

to consult: Examples of Proofs in Logic

Feb 13

Review / Catch-up

Feb 16

Exam 1

### Probability and Statistics

Feb 20

Probability Theory

read: Resnik §3-2 (stop at 3-2a)

start: Assignment 4 - Probability Problems (due Feb 27)

Feb 23

Probability Theory (cont.)

in class: Assignment 5 - Coin Flipping for Data (due Mar 6)

Feb 27 and March 2

Statistics

read: Lecture 7 - Statistics

start: Assignment 6 - Chi^2 (Coin) Testing (due Mar 6)

Mar 6 and 9

Interpretations of Probability

read: Resnik §3-3 (stop after 3-3c)

Mar 13 and 16

SPRING BREAK

Mar 20 and 23

The Base Rate Fallacy and Priors

in class: Assignment 7 - Probability Quiz (on Mar 23)

Mar 27

Review / Catch-up

Mar 30

Exam 2

### Decision Theory

Apr 3 and 6

Decisions and Ignorance

read: Resnik §§1.2–4, 2.1–3

Apr 10 and 13

Utility and Risk

read: Resnik §§3.1, 4.1,5,6 (stop at 4.6a)

Apr 17 and 20

Games

read: Resnik §§5.1,2,4

Apr 24

Review / Catch-up

Apr 27

Exam 3

### Final exam

May TBA

Extra Office Hours / Review

May 9

8am–11am

Final Exam