This free and open-source textbook was written by me (Dana C. Ernst) and is designed to be used with an inquiry-based learning (IBL) approach to an introduction to proof course. The source files are located on GitHub.
I will not be covering every detail of the notes and the only way to achieve a sufficient understanding of the material is to be digesting the reading in a meaningful way. You should be seeking clarification about the content of the notes whenever necessary by asking questions. Here’s one of my favorite quotes about reading mathematics.
Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
The notes will be released incrementally. Each link below is to a PDF file.
An Introduction to Proof via Inquiry-Based Learning (complete set of notes, subject to change!)
If you’ve found an error or have suggestions for improvements, please let me know.
Below are links to the take-home portions of each exam. If you are interested in using LaTeX to type up your solutions, contact me and I will send you a link to the source file of the exam.
Mathematics & Teaching
Northern Arizona University
Flagstaff, AZ
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MAT 320: Foundations of Math
MAT 431: Intro to Analysis
MAT 511: Abstract Algebra I
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The source code is on GitHub.
Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.