Ross 2024: Perspectives on Quadratic Reciprocity (Gauss sums, Galois theory, and local-global principles)
Notes (hand-written) The first 5 pages are an exposition of part of Gauss's discussion of cyclotomic equations in the Disquisitiones Arithmeticae (notes from my Ross 2023 course); they serve as a "prequel" to the rest of the notes.
Ross 2023: Vignettes in the History of Mathematics.
Lecture Outline with References
Ross 2022: Bernoulli Numbers
Notes (hand-written, "live")
Ross 2021: Rational Points on Curves
Notes (hand-written, "live")
Utah Summer Mathematics Program for High School Students (2017-2020, an introduction to number theory, and always with a great debt to my high school participation in the Ross Mathematics Program.
Notes from class during the Zoom summer of 2020, live-texed by Matthew Bertucci: Please be aware that these are not lectures but are a condensed version of class discussion, with questions I posed and explanations contributed by the students.
That same summer of Zoom (2020) I prepared some videos that the students watched throughout the program for review and for some brief introductions to some material. Again, these do not constitute a set of "course lectures," but they may interest some students. They also have their flaws (e.g., in number 0 if you selected English (United States) closed captions you will see a couple of manually-inserted clarifications).
The heart of the summer program in all years was the problem sets, gratefully derived from those of the Ross Mathematics Program. Check it out!
Advanced problem sets on some beginning algebraic number theory and plane curves (used in summer 2018 as a supplement for students returning for their second year in the program)