Course Archives    Theoretical Statistics and Mathematics Unit

Course: Algebra I     Time: Currently not offered     Level: Ph. D. First Year.

Syllabus Past Exams Syllabus 1. Group theory: Group theory, permutation groups, Cayley's theorem, Sylow theorems. 2. Ring theory: Ring theory, modules, integral domains and fraction fields, polynomial rings, matrix rings. 3. Linear algebra: Vector spaces, direct sums, tensor products; Linear transformations and Matrices; Determinants; Dioganalizability and Nilpotence; Jordan form. 4. Spectral theorem: Bilinear forms; Inner product spaces; unitary, self-adjoint, normal, and isometric transformations; Spectral theorem. 5. Fields: Field theory: Algebraic and Transcendental extensions; Finite fields, Wedderburn's theorem on finite division rings. Past Exams

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