This course introduces graduate students to the foundational structures and methods of algebraic number theory through rigorous theory and illustrative examples. Offered during the fourth semester of the M.Sc. Mathematics programme at Mangalore University from 18 February to 20 June 2026, it develops algebraic numbers, number fields, and algebraic integers, including norms, traces, and integral bases. Students examine factorization phenomena, Euclidean domains, and failures of unique factorization, leading to ideals and Dedekind domains. The course further explores ramification, splitting of primes, and the ideal class group, with applications to quadratic fields and Diophantine equations. Emphasis is placed on conceptual understanding, proof techniques, and problem solving. Extensive problem sessions and standard references support independent learning and research readiness throughout the semester.
- Teacher: Sri. Bhargava K.