Nature of Mathematical Reasoning (Summer 2013)

Course Description

In this course we’ll examine deductive reasoning and, more specifically, mathematical reasoning.  In order to do this, we’ll learn some formal logic and basic set theory.  Formal logic allows us to express statements precisely and ensure that our reasoning is fully rigorous.  Set theory provides a foundation for modern mathematics.  As we’ll see, these tools can be applied to some interesting examples which would be difficult to analyze otherwise.  In particular, we’ll see how to: solve logic puzzles, interpret seemingly nonsensical statements like “The present King of the United States has a mustache”, and analyze the notion of infinity.  Throughout the course we’ll be paying attention to the historical context against which mathematical reasoning developed.

Syllabus

The full syllabus is available here.

Sample Exercise

A sample in-class exercise on functions is available here.