Dr. Stange is especially interested in the relationship between geometry and number theory. She is interested in arithmetic geometry, including elliptic and modular curves, as well as the arithmetic of Kleinian groups, particularly the interplay between algebraic number theory and hyperbolic geometry. Other work focuses on the connections between arithmetic recurrence structures (such as integer sequences defined by a recurrence relation) and geometric objects (such as abelian varieties). She is also active in cryptography, including elliptic curve cryptography and latticebased postquantum cryptography. She has wideranging interests, including Apollonian circle packings, abelian sandpiles, arithmetic dynamics and game theory.
MATH 2001  Introduction to Discrete Mathematics
Primary Instructor

Spring 2018 / Spring 2020
Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Department enforced prerequisite: MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (minimum grade C).
MATH 3110  Introduction to Theory of Numbers
Primary Instructor

Spring 2019
Studies the set of integers, focusing on divisibility, congruences, arithmetic functions, sums of squares, quadratic residues and reciprocity, and elementary results on distributions of primes.
MATH 6180  Algebraic Number Theory
Primary Instructor

Spring 2019
Introduces number fields and completions, norms, discriminants and differents, finiteness of the ideal class group, Dirichlet's unit theorem, decomposition of prime ideals in extension fields, decomposition and ramification groups. Department enforced prerequisites: MATH 6110 and MATH 6140. Instructor consent required for undergraduates.
MATH 8114  Topics in Number Theory
Primary Instructor

Spring 2020
May include the theory of automorphic forms, elliptic curves, or any of a variety of advanced topics in analytic and algebraic number theory. Department enforced prerequisite: MATH 6110. Instructor consent required for undergraduates.