**UGS 303
Foundations of Logical Thought
Elaine Rich **

**Alan
Cline**

**Reasoning
Course Content**

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.

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.

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.

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.