Overview

These notes are an IBL task sequence for an introduction to proof course. I would be thrilled if you used these notes and improved them. If you make any modifications, you can either make a pull request on GitHub or submit the improvements to me via email.

The majority of the material was written by me (Dana C. Ernst, but several others have contributed content. Below is a partial list of people (alphabetical by last name) that I need to thank for supplying content, advice, and feedback.

• Paul Ellis (Manhattanville College). Paul has provided lots of useful feedback and several suggestions for improvements.
• Jason Grout (Bloomberg, L.P.). I'm extremely grateful to Jason for feedback on early versions of this material, as well as helping me with a variety of technical aspects of writing these notes.
• Anders Hendrickson (St. Norbert College). Anders is the original author of the content in Appendix A: Elements of Style for Proofs. The current version in Appendix A is a result of modifications made by myself with some suggestions from Dave Richeson.
• Rebecca Jayne (Hampden-Sydney College). The current version of Section 4.3: Complete Induction is a derivative of content contributed by Rebecca.
• Matthew Jones (CSU Dominguez Hills) and Stan Yoshinobu (Cal Poly). A few of the sections were originally adaptations of notes written by Matt and Stan. Early versions of these notes relied heavily on their work. Moreover, Matt and Stan were two of the key players that contributed to shaping my approach to teaching.
• T. Kyle Petersen (DePaul University) and Bridget Tenner (DePaul University). Modifications that Kyle and Bridget made to my notes inspired me to streamline some of the exposition, especially in the early chapters.
• Dave Richeson (Dickinson College). Dave is responsible for much of the content in Appendix B: Fancy Mathematical Terms and Appendix C: Definitions in Mathematics. In addition, the current version of Chapter 5: Three Famous Theorems is heavily based on content contributed by Dave.
• Carol Schumacher (Kenyon College). When I was transitioning to an IBL approach to teaching, Carol was one of my mentors and played a significant role in my development as a teacher. Moreover, this work is undoubtably influenced my Carol's excellent book *Chapter Zero: Fundamental Notions of Advanced Mathematics*, which I used when teaching my very first IBL course.
• Josh Wiscons (CSU Sacramento). Josh contributed the content in Section 6.4: Modular Arithmetic.

License Information

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 license. You are free to:

• Share: copy, distribute, and transmit the work,
• Remix: adapt the work

Under the following conditions:

• Attribution: You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
• Share Alike: If you alter, transform, or build upon this work, you may distribute the resulting work only under the same or similar license to this one.

When attributing this work, please include the individuals listed above, as well as me.

Contributing

I would love to see people contributing to this project. In particular, I'm looking for folks to contribute to the following items:

• A section on partially order sets (see Issue 60)
• Intersperse more historical tidbits (see Issue 49)
• Add some discussion about Axiom of Choice (see Issue 50)
• Add section on Schroder-Bernstein (see Issue 51)
• Add section/discussion about continuum hypothesis (see Issue 52)

Check out the other issues for ways to contribute.