Track: Algebra/Geometry/Topology
Masters students can do computational research (which involves writing code to work with some combination of computational topology, triangulations, computational algebra, geometric structures, knot invariants, finite field arithmetic, or arithmetic invariants). Students can also do an expository thesis close to the research interests of one of the faculty. Finally, well-prepared MS students can also conduct publishable independent research related to the faculty research interests.
The course pathways are below.
First Pathway (more foundational)
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Year 1:
Math 5041-42, Concepts of Analysis
Math 5067-68, Intro to Abstract Algebra
Math 5065, Topology
Math 50xx, Differential Geometry [cross-list of 4061] or
Math 5071, Mathematical Aspects of Cryptography
Year 2:
Math 8041, Real Analysis
Math 8061-62, Smooth Manifolds plus Alg Topology
Math 9xxx, Elective (see list)
Math 9xxx, Elective (see list)
Math 9996, MS Thesis
Second Pathway (more theoretical)
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Year 1:
Math 5067-68, Intro to Abstract Algebra
Math 8041-42, Real Analysis
Math 8061-62, Smooth Manifolds plus Alg Topology
Math 5071, Cryptography (or other elective)
Year 2:
Math 8011-12, Algebra
Math 9071, Hyperbolic Geometry (or other elective)
Math 9073, Geometric Group Theory (or other elective)
Math 9082, Independent Study
Math 9996, MS Thesis
List of Electives:
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MATH 5071: Mathematical Aspects of Cryptography
MATH 9001: Algebraic Number Theory
MATH 9002: Elliptic Curves
MATH 9003: Modular Forms
MATH 9011: Homological Algebra
MATH 9012: Representation Theory
MATH 9014: Commutative Algebra
MATH 9015: Algebraic Geometry
MATH 9021. Riemannian Geometry
MATH 9023. Knot Theory
MATH 9024. Low-Dimensional Topology
MATH 9061. Lie Groups
MATH 9063. Riemann Surfaces
MATH 9071. Hyperbolic geometry
MATH 9073. Geometric Group Theory
MATH 9100: Topics in Algebra
MATH 9500. Topics in Geometry and Topology