Curricula by Research SpecialtyEach student's curriculum must be approved every semester by the Department. This page provides advice about courses needed by a doctoral student depending on the student's eventual dissertation specialty. (Students seeking an MS only should click on the desired MS degree at the page Graduate Degrees.) Firstyear doctoral students normally begin with the three core1 courses: Math 7200 (Algebra), 7311 (Analysis I), and 7510 (Topology I). One hour of Communicating Mathematics is required each semester of the first year as well. In the second term, each doctoral student selects three of the six core2 courses (with a fourth required by the end of the second year for breadth): 7210 (Field Theory), 7312 (Analysis II), 7320 (Ordinary Differential Equations), 7400 (Graph Theory), 7512 (Topology II), and 7550 (Differential Geometry). Jump to Specialty:
Algebraic Number Theory and Algebraic Geometry Key Core1 Courses: 7200 (Geometric and Abstract Algebra) Key Core2 Courses: 7210 (Algebra I) Key Advanced Courses Offered Annually:
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Algebraic Topology and Knot Theory Key Core1 Courses: Math 7510 Topology I. Key Core2 Courses: Math 7512 Topology II; Math 7550 Differential Geometry. Key Advanced Courses Offered Annually:
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Applied Mathematics in Materials Science (See also the course list for Applied Analysis, Control Theory, and Partial Differential Equations. Many of those courses are applicable also to materials science.) Key Core1 Courses: Math 7311 Analysis I; Math 7510 Topology I. Key Core2 Courses: Math 7312 Analysis II; Math 7320 Differential Equations. Key Advanced Courses Offered Annually:
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Combinatorics and Graph Theory Key Core1 Courses: Math 7200 Algebra Key Core2 Courses: Math 7400 Graph Theory and Math 7210 Field Theory Key Advanced Courses Offered Annually:
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Applied Analysis, Control Theory and PDEs Key Core1 Courses:Math 7311 Real Analysis; Math 7200 Linear Algebra; Math 7510 Topology I Key Core2 Courses: Math 7320 Ordinary Differential Equations; Math 7312 Measure and Integration. Key Advanced Courses Offered Annually:
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Harmonic Analysis and Representation Theory Key Core1 Courses: Math 7311 Analysis I; Math 7510 Topology I. Key Core2 Courses: Math 7312 Analysis II; Math 7550 Differential Geometry. Key Advanced Courses Offered Annually:
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Key Advanced Courses Offered at least Every Third Year:
Key Core1 Courses: Math 7311  Analysis I Key Core2 Courses: Math 7312  Measure and Integration Key Advanced Courses Offered Annually:
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