Skip to main content
Mathematics LibreTexts


  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    The majority of the material was written by 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.
    • Was this article helpful?