Teaching: Duquesne emphasizes a student-centered approach to education, and many students report positive experiences with professors who are accessible and dedicated to teaching. However, the quality of teaching can vary depending on the specific professor and course. It's a medium-sized university, so class sizes are generally smaller than at massive universities, which can lead to more personalized attention.
Mathematics: Duquesne's math department is respectable but not typically ranked among the very top programs nationally. It offers undergraduate and graduate degrees in mathematics, and faculty members conduct research in various areas of mathematics. The strength of the program is likely better judged by looking at specific faculty research interests and if they align with your own. Looking at faculty publications and the specific courses offered would give a better indication of whether it meets your specific needs. You won't find the same breadth and depth of specialized research areas as you might at a larger research university.
In short: Duquesne likely has a *good* math and teaching department for many students, but whether it's *excellent* depends heavily on your individual expectations and academic goals. More research into specific faculty, research areas, and course offerings is needed for a more definitive answer.