2020 Demirbas

Project Title Open textbook on mathematical writing, proof and logic
Principal Investigator Seckin Demirbas
Co-Investigator Andrew Rechnitzer, Professor, Mathematics, Faculty of Science
Faculty Science
Funding Year 2019/20
Project Summary Mathematics 220, Mathematical Proof, was originally a first course in analysis for Mathematics Majors students, but has evolved over the last decade into a first course in mathematical thinking, logic and proof-writing. During that time, the enrollment has grown dramatically, roughly tripling in size to 600 students per year. Part of this growth has been driven by the growth in the number of maths major students, but also because Math 220 is now required by students in other programs including Statistics, Computer Engineering and Mathematical Sciences. It is now one of the largest 200-level courses offered by the Mathematics Department. The main aim of Mathematics 220 is to teach students how to think mathematically, prove or disprove mathematical statements, and write clear, coherent, “good”proofs. Many students struggle with the material because the objectives in the course are quite different from all other mathematics subjects they have taken. Because the material is so different for most of our students, it is very important to provide them with resources that are attuned to these difficulties.

While there is at least one free (to download) textbook that covers much of the material in the course, it emphasizes mathematical correctness rather than the intuition, process, and writing of mathematical proofs. Those are precisely the parts of the course that students find most difficult – we regularly hear this in end-of-term teaching evaluations.

The following are standard student comments: “This course is much harder than my other math classes”, “I don’t know where to start this proof”, “I have the idea, but I don’t know how to put it on paper”. There are comparable commercial texts, but these suffer from similar misalignment with the course, and have become extremely expensive. For example, one book previously used for 220 is now over $140.

This OER project will result in a textbook that emphasizes not only mathematical correctness, but emphasizes clarity of exposition and building of intuition that is so critical to constructing proofs. That is, this grant will allow us to create a text that reflects our vision for the course and the learning outcomes we desire for our students.
Grant type OER Implementation
Funded Amount $25,000