Logic and Proof: The Art of Mathematics and the Limits of Knowledge (MAT2378.01)

Andrew McIntyre

How do we know something “beyond a reasonable doubt”? What is the relationship of insight to logical argument? How can we have certain knowledge about concepts which are infinite? These questions are at the core of mathematics, but also at the core of liberal arts. In mathematics, people have found rather detailed answers to how much certainty is possible, and have found fascinating limitations to our knowledge.

This course serves two purposes. Firstly, it is for intermediate mathematics students, who are moving from introductory classes (such as Linear Algebra, Quantitative Reasoning and Mathematical Modeling, or Euclid’s Elements) to more advanced theoretical mathematics. The class is also recommended for computer science students. However, no prior mathematics knowledge is assumed. Therefore, the class is also suitable for beginning mathematics students, for students of philosophy, and for anyone interested in these questions and seeking to improve their ability to reason and form clear arguments (ideally, every student at a liberal arts college!).

The core of the course will be analyzing and developing logical mathematical arguments in various contexts. Additional topics will include symbolic logic and rules of inference; the language of sets and functions; the beginnings of abstract algebra, including Boolean algebras; and a brief introduction to the Hilbert program and Gödel’s theorems.

Learning Outcomes:
- Discover, formulate and write precise mathematical arguments ("proofs")
- Understand foundational concepts of logic
- Read mathematical texts
- Develop a working facility with the foundational concepts of modern mathematics
- Develop conceptual sophistication ("mathematical maturity")

Delivery Method: Fully in-person
Course Level: 2000-level
Credits: 4
M/Th 3:40PM - 5:30PM (Full-term)
Maximum Enrollment: 20
Course Frequency: Once a year

Categories: 2000 , All courses , Four Credit , Fully In-Person , Mathematics , Philosophy
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