Details of MA5105 (Autumn 2021)
| Level: 5 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA5105 | Algebraic Number Theory | Swarnendu Datta |
| Syllabus |
|---|
| Rings of algebraic integers, norms and traces, Dedekind domains and unique factorization of ideals, extensions of Dedekind domains, Galois extensions, decomposition and inertial groups, discriminants and norms of ideals, finiteness of class group, Dirichlet's unit theorem, units in quadratic fields with example, cyclotomic fields, Dedekind zeta function and analytic class number formula. |
| Prerequisite |
|---|
| Algebra III (MA4101) |
| References |
|---|
| Suggested Texts:
1. Ash, R.B., A Course in Algebraic Number Theory, Dover. 2. Borevich, Z.I. and Shafarevich, I.R., Number Theory, Academic Press. 3. Frohlich, A. and Taylor, M.J., Algebraic Number Theory, Cambridge University Press. 4. Marcus, D.A., Number Fields, Springer. 5. Swinnerton-Dyer, H.P.F., A Brief Guide to Algebraic Number Theory, Cambridge University Press. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Not Allowed |
| 2 | IP | 3 | Not Allowed |
| 3 | IP | 5 | Not Allowed |
| 4 | MR | 1 | Not Allowed |
| 5 | MR | 3 | Not Allowed |
| 6 | MS | 3 | Not Allowed |
| 7 | MS | 5 | Not Allowed |
| 8 | MS | 7 | Not Allowed |
| 9 | MS | 9 | Elective |
| 10 | RS | 1 | Elective |
| 11 | RS | 2 | Elective |