Video Lectures

Propositional statements are good tools but they're limited. They can only talk about one instance or one object at a time. To make the kinds of generalizations that mathematics needs, we need something stronger. Predicates are going to be our first step in that direction. (lecture slides)

Universal quantifiers or universal statements are a type of predicate that will let us talk about all of the objects in a domain rather than just an individual one. (lecture slides)

Existential quantifiers or existential statements are a type of predicate that lets us make statements about the existinence of objects with specific propoerties within a domain. (lecture slides)

There are a lot of advantages to our formal method of writing logical statements but, it's still more common to write these things in English. ith that said, it's important to be able to switch back and forth between the logical form and the more informal Englsih forms. (lecture slides)

The "universal conditional" statement is another common logical format that combines universal and conditional statements. In this lecture, we're going to talk about the connection between the two forms. (lecture slides)