Welcome to the course web page for the Spring 2022 manifestation of MAT 690: Combinatorics of Genome Rearrangements at Northern Arizona University.
Don’t fear failure. Not failure, but low aim, is the crime. In great attempts it is glorious even to fail.
When comparing two genomes, the content of the DNA molecules is often similar, but the way in which it is arranged may differ substantially. The mutations that led to these differences are called genome rearrangements, and the structural differences between two genomes motivates the study of their combinatorics. In this course, we will study several combinatorial optimization problems that arise out of the evolutionary events that lead to genome rearrangements. In addition, we will study related permutation sorting problems that are independent of biology.
The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
Mathematics & Teaching
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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.