Alan Cline

Reasoning Course Content

## Goals

In this class, you’ll learn to think abstractly and to reason formally.  We’ll apply these skills to:

·       Problem solving in the real world,

·       Proving mathematical claims, and

·       Reasoning about the design of computer hardware, software and databases.

## Topics

The major topics we’ll cover are:

·       Boolean (Propositional) Logic:  This logic forms the core of almost every other logical system.  It’s also the basis for computer circuit design.

·       Boolean Logic Proofs:  Here we’ll learn the fundamental structure of reasoned arguments.

·       Predicate (Quantified) Logic: Now we’ll have the power to make useful statements about our world.  We’ll practice translating between “natural” statements and formal, logical ones.

·       Predicate Logic Proofs:  We’ll extend our proof techniques so that they work in this more powerful system.

·       Translating between English and the language of predicate logic, with a look at some reasons why this is hard.

·       A Richer Catalogue of Proof Techniques, including mathematical Induction

·       Sets: We’ll formalize our intuitive idea of what a set is and see how we can then prove useful claims.

·       Relations and functions: We’ll formalize our intuitive idea of relating objects to each other.  We’ll look at one important application of this formalism: Real world database management systems.

## Textbook

There is no paper textbook for this class.  Instead, we have created an online learning environment, FREGE, hosted on the Quest platform.  You will have to get a Quest account for this class.

You will do a lot of your learning outside of class, as you work through the online materials in FREGE.  In class we’ll discuss what you’ve learned and explore new ways to exploit your skills.

## What Will You Do?

You will learn the language of logic and the art of rational argument.  To do that:

·       You will spend time in the FREGE learning environment.  You’ll read material and watch videos.  More importantly, you will solve problems.  FREGE includes tools that will, for some of your proofs, give you immediate feedback on what you’re doing right and what you’re doing wrong.

·       You will work on additional problems (outside of FREGE) that will ask you to write clear solutions that make sense to other people.

·       You will do three small projects.

·       You will come to class and be prepared to discuss the problems that you’ve solved.