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 lattice-based post-quantum cryptography. She has wide-ranging interests, including Apollonian circle packings, abelian sandpiles, arithmetic dynamics and game theory. She is also interested in mathematical illustration, visualization and computation.
MATH 2001 - Introduction to Discrete Mathematics
Primary Instructor
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Spring 2018 / Spring 2020 / Fall 2020 / Spring 2023
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. Credit not granted for this course and MATH 2002.
MATH 3110 - Introduction to Theory of Numbers
Primary Instructor
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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 4440 - Mathematics of Coding and Cryptography
Primary Instructor
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Fall 2020 / Fall 2022 / Fall 2023 / Fall 2024
Gives an introduction, with proofs, to the algebra and number theory used in coding and cryptography. Basic problems of coding and cryptography are discussed. Same as MATH 5440.
MATH 5440 - Mathematics of Coding and Cryptography
Primary Instructor
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Fall 2020 / Fall 2022 / Fall 2023
Gives an introduction, with proofs, to the algebra and number theory used in coding and cryptography. Basic problems of coding and cryptography are discussed; prepares students for the more advanced ECEN 5682. Same as MATH 4440.
MATH 6110 - Introduction to Number Theory
Primary Instructor
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Fall 2024
Examines divisibility properties of integers, congruences, diophantine equations, arithmetic functions, quadratic residues, distribution of primes and algebraic number fields. Department enforced prerequisite: MATH 3140. Instructor consent required for undergraduates.
MATH 6180 - Algebraic Number Theory
Primary Instructor
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Spring 2019 / Spring 2021 / Spring 2023
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
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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.
MATH 8174 - Topics in Algebra I
Primary Instructor
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Spring 2024
Department enforced prerequisites: MATH 6130 and MATH 6140. Instructor consent required for undergraduates.
