We will not be using a traditional textbook this semester, but rather a problem sequence adopted for an inquiry-based learning (IBL) approach to real analysis. The problem sequence that we are using is an adaptation of the analysis notes by Karl-Dieter Crisman, which are a modified version of notes by W. Ted Mahavier. Both authors have been gracious enough to grant me access to the source of these notes, so that we can modify and tweak for our needs if necessary. The notes will be released incrementally. Each link below is to a PDF file.
Introduction to Real Analysis (complete set of notes)
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?
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
Unless stated otherwise, content on this site is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.
The views expressed on this site are my own and are not necessarily shared by my employer Northern Arizona University.
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 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.