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The following requirements are in addition to, or further elaborate upon, those requirements outlined in the Student Services section of this Web site.
Coursework Requirements
| Courses |
Units |
| Group I: Two one-year sequences from courses listed below by end of third year |
6 |
MATH 412-1,2,3 Introduction to Modern Analysis
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| MATH 426-1 Basic Differential Equations |
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| MATH 427-1,2 Partial Differential Equations |
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| MATH 441-1 Geometry and Topology |
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| MATH 443-1,2 Introduction to the Geometry of Manifolds |
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| MATH 444-1,2 Introduction to Functional Analysis |
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| MATH 447-1,2,3 Dynamical Systems |
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| MATH 450-1,2 Probability |
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| MATH 462-1,2,3 Stochastic Processes |
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| Applied mathematics courses (approved by Graduate Committee) |
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| Group II: Two one-year sequences from courses listed below by end of third year |
6 |
MATH 441-1 Geometry and Topology
|
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| MATH 442-1,2 Algebraic Topology |
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| MATH 465-1,2,3 Algebraic Topology II |
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| MATH 470-1,2,3 Algebra |
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| MATH 477 Commutative Algebra |
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| MATH 478 Group Theory (one quarter) |
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| MATH 480 Homological Algebra (one quarter) |
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| MATH 482-1 Algebraic Number Theory |
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| MATH 483-1,2,3 Algebraic Geometry |
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| MATH 484 Lie Algebras |
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| MATH 486-1,2,3 Algebraic K-theory |
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| Total required units: |
12 |
A passed preliminary exam in a subject may be substituted for a course.
Other PhD Degree Requirements
- Examinations: three written preliminary examinations drawn from the following: algebra, algebraic topology, dynamical systems, geometry of manifolds, modern analysis (real and complex), partial differential equations and probability; oral qualifying examination
- Research/Projects: see PhD Dissertation below
- PhD Dissertation: original, independent research
- Final Evaluations: defense of dissertation
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