This repository contains a sequence of activities for students to work on in groups to learn how to write mathematical proofs at the undergraduate level.
These materials may be used for an undergraduate mathematics course whose goal is to help students learn the fundamental mathematical process of looking at examples, making a definition, checking more examples, making conjectures, looking for counterxamples and refining conjectures, and then writing proofs. Many of the activities are self--contained, and so could be used individually in a different course or different context.
The Git repository contains all LaTeX source code necessary for producing the materials for the course. It can be downloaded using the Download ZIP button. This makes it easy to re-order material, add your own activities, etc. From time to time, the whole course is compiled with LaTeX and is then available in the file proofcourse.pdf. Corrections, suggestions, and additions are welcome.
The activities are designed so that they can be handed out to a group of students who work on them individually and as a group while the instructor circulates among them answering questions and checking progress. The activities are intended to be self contained and to require no introduction in a lecture. The inspiration for these activities is the POGIL project, but the materials here have not been evaluated by that project.
The first (and only) time the course was taught at Bowling Green State University, the textbook Reading, Writing, and Proving: A Closer Look at Mathematics, 2011, by Ulrich Daepp and Pamela Gorkin was used, and this worked well. The students read the textbook on their own but had to present their notebook with their reading notes and solutions to a few exercises. At the end of the file proofcourse.pdf, you will find the reading assignments that I gave to students for this textbook. Some of the activities were timed to fit well with what the students had just read, while others were developed more independently.