Introduction to Formal Reasoning and Decision Making
Lecture: TuF 9:50–11:10am
Office Hours: Tu 11:10–1pm
Office Hours Location: TBA
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).
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.
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.
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).
read: Choices §1.1
read: Lecture 1 - Truth Tables
read: Lecture 3 - Complex Sentences
read: Lecture 4 - Arguments
in class: Assignment 2 - Logic Quiz (on Lectures 1–4)
solutions: Assignment 2 - Logic Quiz
Review / Catch-up
Probability and Statistics
read: Resnik §3-2 (stop at 3-2a)
start: Assignment 4 - Probability Problems (due Feb 27)
Probability Theory (cont.)
in class: Assignment 5 - Coin Flipping for Data (due Mar 6)
Mar 6 and 9
Interpretations of Probability
read: Resnik §3-3 (stop after 3-3c)
Mar 13 and 16
Mar 20 and 23
The Base Rate Fallacy and Priors
in class: Assignment 7 - Probability Quiz (on Mar 23)
Review / Catch-up
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
read: Resnik §§5.1,2,4
start: Assignment 9 - Decision Theory Pre-Test (due Apr 24)
Review / Catch-up
Extra Office Hours / Review