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?”
The full syllabus is available here.
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.
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.