|Course Archives Theoretical Statistics and Mathematics Unit|
Course: Algebra I |
Time: Currently not offered
Level: Ph. D. First Year.
| 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.
Top of the page
[ Semester Schedule ][ SMU ] [Indian Statistical Institute]