Details of MA5220 (Spring 2025)

Level: 5 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA5220 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.ProgrammeSemester NoCourse Choice
1 IP 2 Not Allowed
2 IP 4 Not Allowed
3 IP 6 Not Allowed
4 MP 2 Not Allowed
5 MP 4 Elective
6 MR 2 Not Allowed
7 MR 4 Not Allowed
8 MS 10 Elective
9 MS 4 Not Allowed
10 MS 6 Not Allowed
11 MS 8 Elective
12 RS 1 Elective
13 RS 2 Elective