NUMBER THEORY
Algebraic Number Theory:Algebraic numbers and algebraic integers, Class groups, Groups of units, Quadratic fields, Quadratic reciprocity law, Class number formula. Analytic Number Theory:Fundamental theorem of arithmetic, Arithmetical functions, Some elementary theorems on the distribution of prime numbers, Congruences, Finite Abelian groups and their characters, Dirichlet theorem on primes in arithmetic progression.
Books
- Narasimham, R., Raghavan, S., Rangachari, S. S. and Sunder Lal., Algebraic Number Theory, Lecture Notes in Mathematics, TIFR, 1966.
- Niven, I. and Zuckerman, H. S., An Introduction to the Theory of numbers, Wiley Eastern Limited, 1989.
- Apostol, T. M., Introduction to Analytic Number Theory, Springer International Student Edition, 1989.
- Ireland, K. and Rosen, M., Classical Introduction to Modern Number Theory, Springer-Verlag (GTM), 1990.