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
| ||

Midterm
Top of the page |
||

[ Semester Schedule ][ SMU ] [Indian Statistical Institute] |