Nature of Mathematical Reasoning (Spring 2016)

Course Description

Proofs are the “lingua franca” of mathematics, and in this class we’ll be exploring them from a variety of different perspectives.  First, we’ll examine the history of proofs, considering, for example, ancient geometry and algebra.  Next, we’ll learn about the more modern formal proof systems of propositional and predicate calculus.  Finally, we’ll consider the future of proofs and discuss, for example, the role of computers.  Throughout the course, we’ll tackle philosophical questions, such as “What makes one proof better than another?” and “Can a picture ever be a proof?”

Syllabus

The full syllabus is available here.

Sample Exercises

After being introduced to Islamic mathematics, I asked students to complete this in-class exercise to help them gain a deeper understanding of Al-Khwarizmi’s work and relate it to our modern approach.

To help the students review for their final exam, I created this crossword.  Solutions are available here.

Practice Midterm (with Solutions)

To help the students prepare for their midterm exam, I made this practice exam, complete with solutions, which I went over in class.