Returning Students
Students returning to PROMYS Europe are encouraged to revisit those parts of the number theory course that they didn't have time to explore fully as a first-year student. There is always more to investigate, and returning students often welcome this opportunity to deepen their understanding. Students will be able to talk to their counsellor and to the faculty to design the most suitable individual programme for them.
In addition, returning students can pursue lectures and problems specifically aimed at returning students, and can work in a small group on a research project.
In recent years, courses for returning students have covered group theory, graph theory, abstract algebra, combinatorics. The courses fit well with the number theory course and are aimed at returning students but are also accessible to students participating in PROMYS Europe for the first time.
Read more about recent advanced courses for returning students...
Returning students also have the option of working in a small group on a research project. Projects are designed by leading mathematicians, and give returning students an opportunity to explore an area of mathematics in great detail and potentially to work on open research questions. In recent years projects have included:
2024
Necklaces, permutations, and periodic critical orbits for quadratic polynomials
proposed by Matt Baker
Tiered hypertrees
proposed by Paul E. Gunnells
Summing primes better than Eratosthenes
proposed by David Lowry-Duda
2023
Counting lattice points for fun and profit
proposed by Jeremy Booher, Bryden Cais, Joe Kramer-Miller, and James Upton
The point-hyperplane incidence matrix
proposed by Alan Chang
Irreducible polynomials over a finite field
proposed by Jared Weinstein
2022
Königsberg pseudoprimes and Fermat's Little Theorem for matrices
proposed by David Lowry-Duda
Permutations, tiered trees, weights, and their generalizations
proposed by Paul Gunnells
2021
Ranks of elliptic curves
proposed by Álvaro Lozano-Robledo
2019
Lower bounds on ɑ-Numbers of Artin-Schreier curves
proposed by Jeremy Booher
Dickson's Theorem
proposed by John Bergdall
2018
Class Groups of Function Fields
proposed by Erick Knight and Ananth Shankar
Permutation Weights
proposed by Paul Gunnells
2017
2-Torsion in class groups
proposed by Erick Knight
Unimodular lattices and modular forms
proposed by Victor Rotger
Returning students working on research projects have been mentored by PhD students from the Oxford Mathematical Institute.